I note that the difference between cardinal and ordinal utilities is not as deep as it may seem. Cardinalists use a utility function \(u: X \to \mathbb{R}\) to describe preferences, while ordinalists restrain themselves to only defining an ordering over \(X.\)

Under natural conditions, orderings over \(X\) can be described as utility functions over \(X.\) If the ordering is complete, transitive, continuous¹, and admits an order-dense subset², there exists a continuous function \(u\) such that \(u(x) \leq u(y)\) if and only if \(x \leq y.\)

As an example: if \(X\) is any convex subset of \(\mathbb{R}^n\) and \(\leq\) is continuous, then this holds and there exists a corresponding continuous utility function.

[1] hypernetwork architecture. there’s a tensor-level LSTM that takes in bulk loss statistics and outputs a weighting vector \(c_{hyper}\) used to interpolate between a bank of pre-trained per-parameter MLPs that then gets passed the per-parameter loss statistics to compute parameters \(d,m\) such that \(\Delta p = 10^{-3} \cdot d \cdot \exp(10^{-3} \cdot c_{lr}) ||p||_2\) (where \(c_{lr}\) is also produced by the tensor-level LSTM). not immediately obvious to me where these pre-trained MLPs come from

[2] meta-training distribution is surprisingly diverse. image classification / image generation / language modeling, across MLP / CNN / vision transformer / autoencoder / VAE / transformer architectures, with different initializations. + task augmentation! (weight reparameterization / gradient renormalization / etc.). 4k TPU-months of compute. these tasks all dealt with relatively small models: VeLO generalization to 100M param LLM was not good (compared to a tuned Adafactor baseline), but “within distribution” VeLO seems to outperform tuned Adam / Shampoo / other classical optimizers.

[3] ES as a gradient update method. meta-objective was to minimize end-of-training loss (vs. average loss per-step), and the classical method was used to estimate gradients: perturb the parameters with sampled Gaussian noise and use the estimator \[\frac{1}{2m\sigma} \sum_{i=1}^m (L(\theta + \sigma \epsilon_i) - L(\theta - \sigma \epsilon_i))\epsilon_i,\] where \(\epsilon_i\) is drawn from a normal distribution. I wonder how much there’s to be gained in iterating on this approach? the ES literature hasn’t quite stagnated

[4] Adam is really quite good? VeLO outperforms by (eyeballing) ~2-5x with intense resource input, and even then isn’t pareto compared to tuned Adam OOD. (VeLO is also much more expensive, & cannot generalize to RL or GNNs (as far as they tested))

[5] convinced me that truly there’s a lot of performance one could eke out of meta-training a learned optimizer, provided one doesn’t care about resource constraints. many cool directions to extend this to

Let \(\mathcal{L}\) be a first order language and let \(T\) be a complete \(\mathcal{L}\) theory. Given

• \(M \models T\) a model of \(T\),
• \(x\) a variable context,
• \(\phi \in \mathcal{L}_x(M)\) a formula with parameters from \(M\) and free variables ranging in \(x,\) and
• \(\alpha\) an ordinal

we define the Morley rank \(\text{RM}(\phi)\) of a formula \(\phi\) by transfinite recursion on the condition \(\text{RM}(\phi) \geq \alpha.\) The recursion satisfies:

• \(\text{RM}(\phi) \geq 0\) if and only if \(M \models (\exists x)\phi\)
• \(\text{RM}(\phi) \geq \alpha + 1\) if and only if there is some \(N \succeq M\) (an elementary extension) and a sequence of formulas \((\psi_i)_{i \in \omega} \subseteq \mathcal{L}_x(N)^\omega\) such that for each \(i,\) \(N \models \psi_i \to \phi\) and \(\text{RM}(\psi_i) \geq \alpha\) both hold and for \(i \neq j\) we have that \(N \models \psi_i \to \neg \psi_j.\)
  
• \(\text{RM}(\phi) \geq \lambda\) for a limit ordinal \(\lambda\) if and only if \(\text{RM}(\phi) \geq \alpha\) for all \(\alpha < \lambda.\)

We define \(\text{RM}(\phi) := \alpha\) if \(\text{RM}(\phi) \geq \alpha\) but \(\text{RM}(\phi) \not\geq \alpha + 1.\) Every formula in a totally transcendental theory has ordinal-valued Morley rank. Inconsistent formulas are given Morley rank of \(-1.\)

When taking \(T = \text{ACF}_p\) (the theory of algebraically closed fields for characteristic \(p\)), the Morley rank and Krull dimension agree (on constructible sets). Examples:

• Take finite \(X \subset K^n.\) This has dimension 0, and can be specified by some formula \(\phi.\) One can verify that \(\text{RM}(\psi) = 0\) when the solution set of \(\psi\) in \(M\) is finite, so \(\text{RM}(\phi) = 0.\)
• The affine line \(\mathbb{A}^1(K) = K\) has dimension 1, and \(\text{RM}(K) \geq 1.\) However, it cannot be greater than 2 because every definable subset of \(K\) is either finite or cofinite, and cofinite sets cannot be disjoint. (Similar arguments hold for \(\mathbb{A}^k.\))
• . . .

[1] “Volitional strength” does not increase with age so much as “volitional complexity” does.

[2] Reminds me of my mom’s stories about las colonias. From the basics (community units are families led by patriarchs) to particulars (the Lina / Melina friendship, fancy car as status symbol, loan-shark as resident, the names).

[3] The “respect for the interiority of self” that Lina possesses — is this an authorial artifact? Faithful developmental description? Does it look like “respect” from the inside as well as the outside?

[4] Characters’ relational generators flummox me.

[5] First fifty pages were the most intense reading experience of my life?

The Epic of Gilgamesh; LB6 & LB7 of F/GO; “The End of a Dynasty, or The Natural History of Ferrets”; Darling; “The Paper Menagerie”; FMAB; the Chainsaw Man movie; “All Summer in a Day”; The Odyssey; this Naruto slashfic; these two HP fics; Crime and Punishment; The Great Gatsby; Dune Messiah; Huckleberry Finn; Nicholas Nickleby; Othello; To Kill a Mockingbird; “Tower of Babylon”; Thus Spoke Zarathustra; The Mysterious Island; “Life of Lycurgus”; Paradise Lost; The Books of Jacob; There is No Antimemetics Division;

I’d expect Job, Ecclesiastes, and the Aeneid to make the list once I’ve read them. Neither Anna Karenina nor War and Peace do (maybe I was just too young?). Have forgotten ~all the Victorian literature I read as a child (complete Dickens, Jane Eyre, . . . ?). Hard for me to think of movies (The Godfather was OK. Forrest Gump would make it). Joyce sometimes wrote closed narratives but he was never a “closed author.”

A semejanza tuya,
a tu imagen,
naranja,
se hizo el mundo:
redondo el sol, rodeado
por cáscaras de fuego:
la noche consteló con azahares
su rumbo y su navío.
Así fue y así fuimos,
Oh tierra,
descubriéndote,
planeta anaranjado.
Somos los rayos de una sola rueda
divididos
como lingotes de oro
y alcanzando con trenes y con ríos
la insólita unidad de la naranja.
Patria
mía,
amarilla
cabellera,
espada del otoño,
cuando
a tu luz
retorno,
a la desierta
zona
del salitre lunario,
a las aristas
desgarradoras
del metal andino,
cuando
penetro
tu contorno, tus aguas,
alabo
tus mujeres,
miro cómo los bosques
balancean
aves y hojas sagradas,
el trigo se derrama en los graneros
y las naves navegan
por oscuros estuarios,
comprendo que eres,
planeta,
una naranja,
una fruta del fuego.

《橘颂》/ “Ode to the Orange [Tree]”

后皇嘉树，橘徕服兮。
受命不迁，生南国兮。
深固难徙，更壹志兮。
绿叶素荣，纷其可喜兮。
曾枝剡棘，圆果抟兮。
青黄杂糅，文章烂兮。
精色内白，类可任兮。
纷縕宜修，姱而不丑兮。

嗟尔幼志，有以异兮。
独立不迁，岂不可喜兮？
深固难徙，廓其无求兮。
苏世独立，横而不流兮。
闭心自慎，不终失过兮。
秉德无私，参天地兮。
愿岁并谢，与长友兮。
淑离不淫，梗其有理兮。
年岁虽少，可师长兮。
行比伯夷，置以为像兮。

• plurality of decision-theoretic confusions are IMO downstream of poor understanding of canonical Sacs. (agent, overseer) frames degrade with capability and scale. (agent, agent) dynamics rely on shared Cartesian assumptions
• Sacs are lossy boundaries. Sacs can grow and be prodded, but notably Sacs can climb and descend ontological hierarchies
• instantaneously, Sacs are enforced by a superstructure. (bkg assumption is that cooperation is well-defined wrt a superstructure: handwaves morality / customs / law seem to be broadly similar (perhaps functionally equivalent) and these seem to be properties of norms. central question is what enforces closure; Sacs are the results. plausible this can be described solely structurally)
• “superstructure” always exists in agent-agent transactions. “overseer.” (overseer of mediated PD equilibria & Lobian cooperation are the same, both EDT-ify bad naive CDT)
• Sacs can live inside themselves & sacs that they own (memetic instantiation). critically important is that the sacs reproduce world-models faithfully (or at least in compatible ways)
• embedded agency is a useful taxonomy
• Sac-ification

Identify an end-to-end task such that, in order to do well at the task, an agent would have to have learned something important about a neural network’s internal structure. Examples would be predicting the results of interventions, or identifying neurons to ablate that turn a specified behavior on or off.

Use this task as a training objective to train an AI assistant on a large amount of data. This assistant is likely superhuman at the specialized task of understanding a given AI model.

Make the information that the assistant learned extractable to humans, either by introducing communication bottlenecks in the architecture or making explainability part of the training objective.

I’m excited because it seems (1) AO/PCD performance scales with self-supervised data scale, (2) AOs/PCDs generalize relatively OOD, and (3) these methods are more architecture agnostic than circuit-based analyses.

The two are relatively different:

• activation oracles take a base LLM and finetune it to take LLM activations as input and answer natural language queries about them. Training data is a mix of SPQA, binary classification datasets, and a self-supervised objective where the AO has to predict tokens before and after activation injection

• predictive concept decoders are trained as end-to-end encoder-decoder models with a topK bottleneck acting as a “concept bottleneck.” they’re pretrained on FineWeb + activations and finetuned (with frozen encoder) on a QA dataset SynthSys.

In particular, AOs require labeled activation data while PCDs rely solely on self-supervised signal from text. The “concept bottleneck” of a PCD is meant to e.g. improve auditability of the mechanisms producing AI behavior (humans can look at the bottleneck and infer what’s going on).

Steinhardt proposes extensions to PCDs:

• making the concept bottleneck consist of more structured objects (propositional formulas), which take advantage of inherent compositionality in neural network cognition;
• replacing the encoder with a transformer (or similar) to have richer representations

[2] The generalization bias described in the Bayesian free-energy functional is a bias towards low-description length programs. I don’t know enough about this to provide a full, concise, precise accounting of the argument, but I buy it? See my earlier post on MDL and SLT. (Hopefully work on the inductive bias of SGD will shed light on a similar result in the training of neural networks).

[3] “Simple hypotheses” are adaptive because world phenomena are naturally generated by “simple” processes. Empirically, phenomena have parsimonious explanations. We do not live in the most simple world,² but physical theories are decomposable.

[4] “Simple hypotheses” are adaptive because learning systems learn simple explanations more effectively. Singular learning theory predicts this for Bayesian reasoners; deep learning generalizes because the parameter function map is biased towards simple functions; cf. inductive bias considerations; “special snowflake” hypotheses where certain kinds of learning are only possible in environments with nice properties, one of which is likely simplicity.

[5] Simple explanations are more memetically fit. Directionally correct. Minimizing the free parameters in your model means there’s less information to necessarily communicate. But the pressures shaping acceptance of one theory over another do not rely on simplicity as a primary proxy, and in any case accuracy should be prioritized.

[6] Simplicity is elegant. Deutsch argues for objectivity in aesthetics, such that “aesthetic truths are linked to factual ones by explanations.” Schmidhuber defines beauty through simplicity. Surely there’s a convergence here; however, attributing causality requires care.

Clearly an Occam-like hypothesis is adaptive. I find empirical justifications for simplicity biases the most compelling, yet their compelling formulations elude me. Excited about fleshing out a correct [1] and a precise [2], [3] is a philosophical goldmine, [4] is (to me) obviously correct, [5] requires specification, [6] deserves a steelman.

cooperates with itself in the Prisoner’s Dilemma, and moreover given a state of two players adopting this program in the Prisoner’s Dilemma there is no incentive for either to deviate.

Unfortunately, this result as stated only holds on the basis of syntactic analysis: essentially, given two .txt files each representing a player’s program, check line by line that they’re equivalent and if so cooperate. (More sophisticated versions of syntactic analysis exist but all suffer from needing to coordinate on a shared language, transmission mechanism, etc.). In an ideal world, you’d replace \(\text{IF } P_1 = P_2\) with a semantic guarantee: verifying effective equivalence via the behavior of programs rather than their apparent structure.

I’m aware of two ways of doing this:

1. Simulation. Perhaps the most straightforward way to verify the behavior of a program is to run it. The most naive implementation of the simulation-based approach, running \(P_2\) with \(P_1\) as input, fails if applied symmetrically from a non-halting infinite regress. However, getting around this is possible with relatively low cost (see the \(\epsilon\)-GroundedFairBot proposed by Oesterheld and variations thereof).

2. Proof search. “If I can prove that you cooperate with me, then I cooperate. Otherwise I defect.” Typically you parametrize programs as logical sentences taking the outputs of the other programs in the game as parameters, and use some Lobian-like theorem to prove cooperation. (Interesting is Critch’s proof this holds even with access to only bounded provers).

These are not the only methods for robustly achieving \((C,C)\) in a Prisoner’s Dilemma: a more classical approach is to introduce some sort of information revelation and make \((C,C)\) a robust equilibrium in this “correlated” setting. However, taking this “open-source” approach to negotiation has the conceptual benefit (at least to me) of highlighting what sorts of programs form robust coalitions given broad instantiation. Interesting to ponder from the perspective of “what sorts of policy structures should I update myself towards.”

Recommended: Oesterheld’s annotated bibliography.

This is an analysis and criticism of two influential strands of 20th century political economic thought: Socialism, in the Marxist sense, and Anarchism, as advocated for by Bakunin.

[Actually, this is less of review/criticism and more of “summary with weird notes and a lot of relevant quotes that might be useful, but probably not that useful to anyone who isn’t me]

Socialism, as defined by Russell, is the “advocacy of communal ownership of land and capital.” Such communal ownership can be mediated by a democratic State, but never an undemocratic one. Such communal ownership can also result from the natural self-organization of individuals without State intervention of coercion—Socialists who believe this overlap with Anarchists. But by and large Socialists lack libertarian tendencies, and are mostly content with such apparatuses to be handed off to a parliamentary state.

1. The Materialistic Interpretation of History.— Marx holds that in the main all the phenomena of human society have their origin in material conditions, and these he takes to be embodied in economic systems. Political constitutions, laws, religions, philosophies—all these he regards as, in their broad outlines, expressions of the economic regime in the society that gives rise to them. It would be unfair to represent him as maintaining that the conscious economic motive is the only one of importance; it is rather that economics molds character and opinion, and is thus the prime source of much that appears in consciousness to have no connection with them. He applies his doctrine in particular to two revolutions, one in the past, the other in the future. The revolution in the past is that of the bourgeoisie against feudalism, which finds its expression, according to him, particularly in the French Revolutino. The one in the future is the revolution of the wage-earners, or proleteriat, against the bourgeoisie, which is to establish the Socialist Commonwealth. The whole movement of history is viewed by him as necessary, as the effect of material causes operating upon human beings. He does not so much advocate the Socialist revolution as predict it. He holds, it is true, that it will be beneficent, but he is much more concerned to prove that it must inevitably come. The same sense of necessity is visible in his exposition of the evils of the capitalist system. He does not blame capitalists for the cruelties of which he shows them to have been guilty; he merely points out that they are under an inherent necessity to behave cruelly so long as the private ownership of land and capital continues. But their tyranny will not last forever, for it generates the forces that must in the end overthrow it.

2. The Law of the Concentration of Capital.— Marx pointed out that capitalist undertakings tend to grow larger and larger. He foresaw the substitution of trusts for free competition, and predicted that the number of capitalist enterprises must diminish as the magnitude of single enterprises increased. He supposed that this process must involve a diminution, not only in the number of businesses, but also in the number of capitalists. Indeed he usually spoke as though each business were owned by a single man. Accordingly, he expected that men would be continually driven from the ranks of the capitalists into those of the proletariat, and that the capitalists, in the course of time, would grow numerically weaker and weaker. He applied this principle not only to industry but also toa griculture. He expected to find the landowners growing fewer and fewer while their estates grew larger and larger. This process was to make more and more glaring the evils and injustices of the capitalist system, and to stimulate more and more the forces of opposition.

3. The Class War.— Marx conceives the wage-earner and the capitalist in a sharp antithesis. He imagines that every man is, or must soon become, wholly the one or wholly the other. The wage-earner, who possesses nothing, is exploited by the capitalists, who possess everything. As the capitalist system works itself out and its nature becomes more clear, the opposition of bourgeoisie and proletariat becomes more and more marked. The two classes, since they have antagonistic interests, are forced into a class war which generates within the capitalistic regime internal forces of disruption. The working men learn gradually to combine against their exploiters, first locally, then nationally, and at last internationally. When they have learned to combine internationally they must be victorious. They will then decree that all land and capital shall be owned in common; exploitation will cease; the tyranny of the owners of wealth will no longer be possible; there will no longer be any division of society into classes, and all men will be free.

I will take a slight digression here to comment on the nature of the proposed Marxist class war. As we have become well aware, this has not happened yet. There are many reasons for this, but one assumption that Marxists take (and I think Marx himself took) was that class, as a signifier, would supersede race and sex as an identity, and therefore provide stronger bonds than either of the other two.

Perhaps more specifically, I claim Marxists believe something on the order of “individuals of the same class have more in common than individuals of the same race or nationality.” Firestone disagrees and substitutes sex for class in her Dialectic on Sex, and individuals such as Curtis Yarvin would cleave the global population on the basis of race. But I do suspect that a large proportion of economic leftism bottoms out in this fundamentally economic understanding of an indvidual’s experience and material reality.

Maybe calling this leftist is slightly incorrect? This seems to be a Western take as well. We see that in America (in my experience) differentiating groups on the basis of wealth is much more accepted than differentiating groups on the basis of race. And racial divides in America are some of the most explicit worldwide. But it is also emblematic of, say, the Progress Studies folk to anchor very, very heavily on ‘GDP go up’ as a metric for overall wellbeing. This seems broadly similar.

At any rate, they’re incorrect. On a national level, it (broadly) makes more sense to classify individuals on the basis of class. But on an international level, race becomes much more important, as race becomes a stronger predictor of culture, morality, values, etc. that are intangible factors not necessarily tracked by wealthy or income metrics. The Anglo-sphere (and Europe to a lesser extent) is unique in that it has managed to assimilate large proportions of immigrants of different ethnicities without resorting to explicit identification and classification of them. This is not the case in e.g. Singapore, Malaysia, India, China etc. And I think this is one of the Marxist fatal flaws.

(maybe this confuses similarity with willigness to cooperate. likely that chinese factory workers and indian factory workers are essentially substitutable but they would never be friends)

This impinges his broader point with the question of: are Marx’s laws of historical development correct? We can belabor this point for eternity, but they are obviously seriously flawed (with the 20th century as his judge). However, this is in fact a separate question from the question of the desirability of Socialism (which includes a subconsideration of feasibility, but is notably different).

Stepping back, Marx’s three points are of varying degrees of incorrect, but when contextualized to the mid-19th century… they seem astonishingly prescient? Or, the Law of the Concentration of Capital is just obviously correct, and most other intellectuals of Marx’s time would deride the idea that class could supersede nationality as a unifying factor (too many racists). But it can, and it is just today that we see the overcorrection.

And it is true that given Marx’s (or even Russell’s) vantage point, moving more in the direction of Socialism would be better for the vast majority of individuals. The baseline welfare of the individual had simiply not increased enough, and deprivation conditions were widespread. 1950s America would be considered a third-world country to us today, and in fact many pro-market individuals today would prefer a Socialist state to living conditions seventy years prior. It’s probably good to keep that in mind.

Anarchism “is the theory which is opposed to every kind of forcible government.” The only government which Anarchists can accept is “free government, not merely in the sense that it is a majority, but in the sense that it is assented to by all.” Anarchists object to the encroachment of the rights of an individual by other individuals in different parts of the community—it is for this reason that they view law enforcement as evil, and that democratic governments are no better than authoritarian ones if they have the capacity to act in a majoritiarian manner.

Horses have hoofs to carry them over frost and snow; hair, to protect them from wind and cold. They eat grass and drink water, and fling up their heels over the champaign. Such is the real nature of horses. Palatial dwellings are of no use to them.

One day Po Lo appeared, saying: “I understand the management of horses.”

So he branded them, and clipped them, and pared their hoofs, and put halters on them, tying them up by the head and shackling them by the feet, and disposing them in stables, with the result that two or three in every ten died. Then he kept them hungry and thirsty, trotting them and galloping them, and grooming, and trimming, with the misery of the tasselled bridle before and the fear of the knotted whip behind, until more than half of them were dead.

The potter says: “I can do what I will with Clay. If I want it round, I use compasses; if rectangular, a square.”

The carpenter says: “I can do what I will with wood. If I want it curved, I use an arc; if straight, a line.”

But on what grounds can we think that the natures of clay and wood desire this application of compasses and square, of arc and line? Nevertheless, every age extols Po Lo for his skill in managing horses, and potters and carpenters for their skill with clay and wood. Those who govern the empire make the same mistake.

Now I regard government of the empire from quite a different point of view.

The people have certain natural instincts:—to weave and clothe themselves, to till and feed themselves. These are common to all humanity, and all are agreed thereon. Such instincts are called “Heaven-sent.”

And so in the days when natural instincts prevailed, men moved quietly and gazed steadily. At that time there were no roads over mountains, nor boats, nor bridges over water. All things were produced, each for its own proper sphere. Birds and beasts multiplied, trees and shrubs grew up. The former might be led by the hand; you could climb up and peep into the raven’s nest. For then man dwelt with birds and beasts, and all creation was one. There were no distinctions of good and bad men. Being all equally without knowledge, their virtue could not go astray. Being all equally without evil desires, they were in a state of natural integrity, the perfection of human existence.

But when Sages appeared, tripping up people over charity and fettering them with duty to their neighbor, doubt found its way into the world. And then, with their gushing over music and fussing over ceremony, the empire became divided against itself.

It is important to note that anarchism does not necessarily imply communal ownership of land and capital. It just so happens that in the early 20th century, the vast majority of anarchists also happened to be communists, so Russell focuses on these anarcho-communists. But today, a significant portion of anarchists are libertarians (or even monarchist-adjacent), and do not share the past belief that “private capital is a source of tyranny by certain individuals over others.”

If Marx is the standard-bearer of socialist thought, than Michel Bakunin, Russian aristocrat, would be the standard-bearer of aristocratic thought. He was an emigre for large portions of his life, due to his native tendencies of stirring up pseudo-revolutionary behavior and subsequently incurring the ire of state authorities.

Anarcho-communism does not differ tremendously from socialism in the nature of its economic reforms, it differs from socialism on the basis of its political reforms, arguing for a self-organizing society. This as a movement did not gain much traction, but an intellectual descendant of it did—Syndicalism.

Syndicalism stands essentially for the point of view of the producer as opposed to that of the consumer; it is concerned with reforming actual work, and the organization of industry, not MERELY with securing greater rewards for work. From this point of view its vigor and its distinctive character are derived. It aims at substituting industrial for political action, and at using Trade Union organization for purposes for which orthodox Socialism would look to Parliament.

…

The essential doctrine of Syndicalism is the class- war, to be conducted by industrial rather than politi- cal methods. The chief industrial methods advocated are the strike, the boycott, the label and sabotage.

…

The doctrines of Syndicalism may be illustrated by an article introducing it to English readers in the first number of “The Syndicalist Railwayman,” September, 1911, from which the following is quoted:—

“All Syndicalism, Collectivism, Anarchism aims at abolishing the present economic status and existing private ownership of most things; but while Collectivism would substitute ownership by everybody, and Anarchism ownership by nobody, Syndicalism aims at ownership by Organized Labor. It is thus a purely Trade Union reading of the economic doctrine and the class war preached by Socialism. It vehemently repudiates Parliamentary action on which Collectivism relies; and it is, in this respect, much more closely allied to Anarchism, from which, indeed, it differs in practice only in being more limited in range of action.” (Times, Aug. 25, 1911).

One of the astute Syndicalist proposals, in my opinion, was to propose “industrial unionism”, where unions were formed on the basis of the nature of one’s work, rather than the organization they were employed by. Notably, this movement originated in America (American labor reform seemed to be more? militant than British labor reform during this time, which I suppose shouldn’t be that surprising given that three decades later we elected FDR).

Here we draw our lines, between Socialism and Anarchism (in practice Syndicalism). Russell believes that the best ideal state of the world is Anarchic, but that Socialists have better practical prescriptions, and he adheres to an ideology known as “guild socialism”, which will be discussed later. I think that these takes are understandable in the context of a world where absurd amounts of surplus have not been generated, but today? Markets creating wealth seem to be a good component of capitalistic society that Socialist ones would have to emulate.

Two connected doctrines must be considered in examining this question: First, Malthus’ doctrine of population; and second, the vaguer, but very prevalent, view that any surplus above the bare necessaries of life can only be produced if most men work long hours at monotonous or painful tasks, leaving little leisure for a civilized existence or rational enjoyment. I do not believe that either of these obstacles to optimism will survive a close scrutiny. The possibility of technical improvement in the methods of production is, I believe, so great that, at any rate for centuries to come, there will be no inevitable barrier to progress in the general well-being by the simultaneous increase of commodities and diminution of hours of labor.

It is maybe for this reason that he is less of a radical than his contemporaries?

There is a fundamental difference between Socialism and Anarchism as regards the question of distribution. Socialism, at any rate in most of its forms, would retain payment for work done or for willingness to work, and, except in the case of persons incapacitated by age or infirmity, would make willingness to work a condition of subsistence, or at any rate of subsistence above a certain very low minimum. Anarchism, on the other hand, aims at granting to everyone, without any conditions whatever, just as much of all ordinary commodities as he or she may care to consume, while the rarer com- modities, of which the supply cannot easily be indefinitely increased, would be rationed and divided equally among the population. Thus Anarchism would not impose any OBLIGATIONS of work, though Anarchists believe that the necessary work could be made sufficiently agreeable for the vast majority of the population to undertake it voluntarily. Socialists, on the other hand, would exact work. Some of them would make the incomes of all workers equal, while others would retain higher pay for the work which is considered more valuable. All these different systems are compatible with the common ownership of land and capital, though they differ greatly as regards the kind of society which they would produce.

And resolution:

Anarchism has the advantage as regards liberty, Socialism as regards the inducements to work. Can we not find a method of combining these two advantages? It seems to me that we can.

We saw that, provided most people work in moderation, and their work is rendered as productive as science and organization can make it, there is no good reason why the necessaries of life should not be supplied freely to all. Our only serious doubt was as to whether, in an Anarchist regime, the motives for work would be sufficiently powerful to prevent a dan- gerously large amount of idleness. But it would be easy to decree that, though necessaries should be free to all, whatever went beyond necessaries should only be given to those who were willing to work—not, as is usual at present, only to those in work at any moment, but also to all those who, when they happened not to be working, were idle through no fault of their own. We find at present that a man who has a small income from investments, just sufficient to keep him from actual want, almost always prefers to find some paid work in order to be able to afford luxuries. So it would be, presumably, in such a community as we are imagining. At the same time, the man who felt a vocation for some unrecognized work of art or science or thought would be free to follow his desire, provided he were willing to “scorn delights and live laborious days.” And the comparatively small number of men with an invincible horror of work—the sort of men who now become tramps— might lead a harmless existence, without any grave danger of their becoming sufficiently numerous to be a serious burden upon the more industrious. In this ways the claims of freedom could be combined with the need of some economic stimulus to work. Such a system, it seems to me, would have a far greater chance of success than either pure Anarchism or pure orthodox Socialism.

Stated in more familiar terms, the plan we are advocating amounts essentially to this: that a certain small income, sufficient for necessaries, should be secured to all, whether they work or not, and that a larger income, as much larger as might be warranted by the total amount of commodities produced, should be given to those who are willing to engage in some work which the community recognizes as useful. On this basis we may build further. I do not think it is always necessary to pay more highly work which is more skilled or regarded as socially more useful, since such work is more interesting and more respected than ordinary work, and will therefore often be preferred by those who are able to do it. But we might, for instance, give an intermediate income to those who are only willing to work half the usual number of hours, and an income above that of most workers to those who choose a specially disagreeable trade. Such a system is perfectly compatible with Socialism, though perhaps hardly with Anarchism. Of its advantages we shall have more to say at a later stage. For the present I am content to urge that it combines freedom with justice, and avoids those dangers to the community which we have found to lurk both in the proposals of the Anarchists and in those of orthodox Socialists.

Question, how do Anarchists deal with crime?

The conclusion, which appears to be forced upon us, is that the Anarchist ideal of a community in which no acts are forbidden by law is not, at any rate for the present, compatible with the stability of such a world as the Anarchists desire. In order to obtain and preserve a world resembling as closely as possible that at which they aim, it will still be necessary that some acts should be forbidden by law. We may put the chief of these under three heads:

1. Theft.

2. Crimes of violence.

3. The creation of organizations intended to subvert the Anarchist regime by force.

We will briefly recapitulate what has been said already as to the necessity of these prohibitions.

1. Theft.—It is true that in an Anarchist world there will be no destitution, and therefore no thefts motivated by starvation. But such thefts are at present by no means the most considerable or the most harmful. The system of rationing, which is to be applied to luxuries, will leave many men with fewer luxuries than they might desire. It will give opportunities for peculation by those who are in control of the public stores, and it will leave the possibility of appropriating such valuable objects of art as would naturally be preserved in public museums. It may be contended that such forms of theft would be prevented by public opinion. But public opinion is not greatly operative upon an individual unless it is the opinion of his own group. A group of men combined for purposes of theft might readily defy the public opinion of the majority unless that public opinion made itself effective by the use of force against them. Probably, in fact, such force would be applied through popular indignation, but in that case we should revive the evils of the criminal law with the added evils of uncertainty, haste and passion, which are inseparable from the practice of lynching. If, as we have suggested, it were found necessary to provide an economic stimulus to work by allowing fewer luxuries to idlers, this would afford a new motive for theft on their part and a new necessity for some form of criminal law.

2. Crimes of Violence.—Cruelty to children, crimes of jealousy, rape, and so forth, are almost certain to occur in any society to some extent. The prevention of such acts is essential to the existence of freedom for the weak. If nothing were done to hinder them, it is to be feared that the customs of a society would gradually become rougher, and that acts which are now rare would cease to be so. If Anarchists are right in maintaining that the existence of such an economic system as they desire would prevent the commission of crimes of this kind, the laws forbidding them would no longer come into operation, and would do no harm to liberty. If, on the other hand, the impulse to such actions persisted, it would be necessary that steps should be taken to restrain men from indulging it.

3. The third class of difficulties is much the most serious and involves much the most drastic interference with liberty. I do not see how a private army could be tolerated within an Anarchist community, and I do not see how it could be prevented except by a general prohibition of carrying arms. If there were no such prohibition, rival parties would organize rival forces, and civil war would result. Yet, if there is such a prohibition, it cannot well be carried out without a very considerable interference with individual liberty. No doubt, after a time, the idea of using violence to achieve a political object might die down, as the practice of duelling has done. But such changes of habit and outlook are facilitated by legal prohibition, and would hardly come about without it. I shall not speak yet of the international aspect of this same problem, for I propose to deal with that in the next chapter, but it is clear that the same considerations apply with even greater force to the relations between nations.

& Russell argues that someting approximating a state will be necessary to enforce this.

What, I want to ask, is the fundamental evil in our modern Society which we should set out to abolish?

There are two possible answers to that question, and I am sure that very many well-meaning people would make the wrong one. They would answer POVERTY, when they ought to answer SLAVERY. Face to face every day with the shameful contrasts of riches and destitution, high dividends and low wages, and painfully conscious of the futility of trying to adjust the balance by means of charity, private or public, they would answer unhesitatingly that they stand for the ABOLITION OF POVERTY.

Well and good! On that issue every Socialist is with them. But their answer to my question is none the less wrong.

Poverty is the symptom: slavery the disease. The extremes of riches and destitution follow inevitably upon the extremes of license and bondage. The many are not enslaved because they are poor, they are poor because they are enslaved. Yet Socialists have all too often fixed their eyes upon the material misery of the poor without realizing that it rests upon the spiritual degradation of the slave.

Near the end, Russell gives a positive vision of a world that is more socialist than the one today, with compulsory education until 16 such that a society could still intellectually flourish.

Our discussion has led us to the belief that the communal ownership of land and capital, which constitutes the characteristic doctrine of Socialism and Anarchist Communism, is a necessary step toward the removal of the evils from which the world suffers at present and the creation of such a society as any humane man must wish to see realized. But, though a necessary step, Socialism alone is by no means sufficient. There are various forms of Socialism: the form in which the State is the employer, and all who work receive wages from it, involves dangers of tyranny and interference with progress which would make it, if possible, even worse than the present regime. On the other hand, Anarchism, which avoids the dangers of State Socialism, has dangers and difficulties of its own, which make it probable that, within any reasonable period of time, it could not last long even if it were established. Nevertheless, it remains an ideal to which we should wish to approach as nearly as possible, and which, in some distant age, we hope may be reached completely. Syndicalism shares many of the defects of Anarchism, and, like it, would prove unstable, since the need of a central government would make itself felt almost at once.

The system we have advocated is a form of Guild Socialism, leaning more, perhaps, towards Anarchism than the official Guildsman would wholly approve. It is in the matters that politicians usually ignore— science and art, human relations, and the joy of life —that Anarchism is strongest, and it is chiefly for the sake of these things that we included such more or less Anarchist proposals as the “vagabond’s wage.” It is by its effects outside economics and politics, at least as much as by effects inside them, that a social system should be judged. And if Socialism ever comes, it is only likely to prove beneficent if non- economic goods are valued and consciously pursued.

The world that we must seek is a world in which the creative spirit is alive, in which life is an adventure full of joy and hope, based rather upon the impulse to construct than upon the desire to retain what we possess or to seize what is possessed by others. It must be a world in which affection has free play, in which love is purged of the instinct for domination, in which cruelty and envy have been dispelled by happiness and the unfettered development of all the instincts that build up life and fill it with mental delights. Such a world is possible; it waits only for men to wish to create it.

Meantime, the world in which we exist has other aims. But it will pass away, burned up in the fire of its own hot passions; and from its ashes will spring a new and younger world, full of fresh hope, with the light of morning in its eyes.

Good! I do not have the requisite intellectual heft at the moment to properly review this, so this will at the moment stand in its sorry Frankensteined state. Apologies to any reader who made it this far!

Infinite Ramsey’s Theorem: For any \(k, m \in \mathbb{N},\) any infinite set \(X,\) and any \(k\)-coloring \(c\) of \(X^{[m]},\) there exists an infinite subset of \(X\) that is monochromatic with respect to \(c.\) (Here \(X^{[m]}\) denotes the set of \(m\)-element subsets of \(X\) and a \(k\)-coloring \(c\) of a set \(X\) is some function \(c: X \to \{1, \ldots, k\}.\) A subset \(Y\) of \(X\) is “monochromatic” if \(c(Y)\) is single-valued).

Typically, the Infinite Ramsey’s Theorem is introduced as a structure guarantee for infinite (hyper)graphs. To see this, take a graph \(G = (V,E)\) with an infinite set of vertices \(V\) and an (not necessarily infinite) edge set \(E.\) Consider the \(2\)-coloring \(c: V^{[2]}\to \{1, 2\}\) such that \(c(\{v_1, v_2\}) = 1\) if and only if \((v_1, v_2) \in E,\) and \(c(\{v_1,v_2\}) = 2\) otherwise. The Infinite Ramsey’s Theorem implies that for this 2-coloring, there exists an infinite set of vertices \(W \subseteq V\) such that \(c(W)\) is constant; implying that \(G\) either has an infinite fully edge-connected subset (called a clique: all pairs of vertices in \(W\) share a corresponding edge) or an infinite fully disconnected subset (an anticlique: no two vertices in \(W\) share an edge). (Colorings with \(k \geq 3\) imply an identical statement for \(k\)-hypergraphs: graphs where edges \(e \in E\) are \(k\)-tuples of vertices, and as such connect \(k\) vertices at a time.)

Additionally, the Infinite Ramsey’s Theorem is typically proved combinatorially, by induction. We reproduce the classical proof here for completeness, for the case \(X = \mathbb{N}.\)

• The base case \(m=1\) is a straightforward application of the pigeonhole principle: partitioning \(\mathbb{N}\) into \(k\) finite sets is impossible, so at least one of the color classes will be infinite.

• Now assume the statement holds for \(\mathbb{N}^{[m-1]}.\) We prove the statement for an arbitrary (finite) \(k-\)coloring \(c\) of \(\mathbb{N}^{[m]}\) by constructing a monochromatic subset \(H'\) as follows.

  • Let \(X_0 = \mathbb{N}\) and \(x_0 = 0.\) We construct sequences \(x_0 < x_1 < \cdots\) and \(X_0 \supset X_1 \supset \cdots\) in the following way.

  • For each \(X_i, x_i,\) there’s a natural \(k-\)coloring \(c_i\) of \((X_i \setminus \{x_i\})^{[m-1]}\) given by \(c_i(S) = c(S\cup \{x_i\}).\) By the induction hypothesis, there exists an infinite \(X_{i+1} \subset X_i \setminus \{x_i\}\) and a color \(d_i\) such that \(c(S \cup \{x_i\}) = d_i\) for all \((m-1)\) element subsets \(S\) of \(X_{i+1}.\) Then let \(x_{i+1} = \min(X_{i+1}).\)

  • Let \(H = \{x_0, x_1, \ldots\}.\) The colors \(d_i\) (decided stepwise as above) lie in \(\{1, \ldots, k\},\) so by the pigeonhole principle there is some color \(d\) for which \(d_i = d\) for infinitely many \(i.\) Let \(I\) be the set of these indices, and let \(H'\) be the subset of \(H\) on \(I.\) Note \(H'\) is infinite.

  • Observe that any \(m\)-element subset of \(H'\) is monochromatically \(d.\) Take any \(Y \in (H')^{[m]}.\) Its least element \(y\) is some \(x_j\) for \(j \in I.\) The remaining \(m-1\) elements of \(Y\) are larger than \(x_j\) and so lie in \(X_{j+1}\) (recall this is a descending subset chain). So, \(c(Y) = d_j,\) and \(d_j = d\) as \(j \in I.\) This finishes the inductive step.

The key ingredient in the nonstandard proof is the existence of a corresponding hyperextension \(^*X\) for mathematical objects \(X,\) such that \(^*X\) is not isomorphic to \(X\) but preserves all “elementary properties” of \(X.\) (The proof of the existence of these objects will be reserved for another day: concisely, Los’s theorem guarantees the diagonal embedding into the ultrapower of \(X\) is elementary). “Elementary properties” of \(X\) are those expressable in first order sentences: includes set inclusion, union, intersection, field axioms, etc. Does not include the Archimedean property of the reals! (For all positive \(x \in \mathbb{R}\) there exists \(n \in \mathbb{N}\) such that \(nx > 1.\)). We define the transfer map \(*\) to be a function taking an object to its hyperextension. [More properties can be found in Section 2 of this manuscript.]

Consider some infinite graph \(G.\) (Worthwhile to note that, formally, it makes more sense to treat the edges \(E\) as a relation: a subset of \(V \times V\) that’s anti-reflexive and symmetric.) A hyperextension \(^*G\) of \(G\) induces corresponding hyperextensions \(^*V, ^*E\) on the vertices and edges.

We now prove the Infinite Ramsey’s Theorem for \(2\)-colorings, in the graph setting. Let \(\xi\) be an element of \(^*V\) not belonging to \(V.\) Consider its hyperextension \(^*\xi \in ^{**}V.\) There are two cases: either \(\xi\) and \(^*\xi\) are connected by an edge in \(^{**}G,\) or they are not. We treat the first case (the other being symmetric). Suppose there exist \(d\) elements \(v_i\) of \(V\) which form a clique and are all connected to \(\xi\) in \(^*G.\) These form a sequence \((v_i)_{1 \leq i < d}.\)

Consider the statement: “there exists some \(y \in ^*V\) such that for \(j < d,\) \(y\) is not \(v_j,\) \((v_j, y) \in ^*E,\) and \((y, ^*\xi) \in ^{**}E.\)” This is satisfied by \(\xi\) by construction. (Editing the third constraint is what deals with the case where \(\xi\) is not connected to \(^*\xi.\)). This is also an elementary property of \(^*G,\) so a corresponding statement must be true in \(G.\) This statement is “there exists \(v_d \in V\) different from \(v_j\) for \(j < d\) such that \((v_j, v_d) \in E\) for \(j <d\) and \((v_d, \xi) \in ^*E.\)”

This construction is recursive (you can make a \(d+1\) length chain by repeating it), so this constructs an infinite clique. An infinite anticlique is constructed by taking the case where \(\xi\) is not connected to \(^*\xi.\)

Compared to the classical proof, the nonstandard approach is much cleaner? Less bookkeeping. You extend this argument to the \(k\)-coloring case simply: \(E\) becomes a subset of \(V^k.\)

Finite Ramsey’s Theorem. For every \(k,m,n \in \mathbb{N},\) there is \(l \in \mathbb{N}\) such that every coloring of \([l]^{[m]}\) with \(k\) colors has a homogenous set of size \(n.\)

We prove this by contradiction. Assume it’s false for a particular choice of \(k,m,n.\) Then for every \(l \in \mathbb{N},\) there is a \(k\)-coloring \(c\) of \([l]^{[m]}\) with no monochromatic subset of size \(n.\)

This is impossible due to Konig’s Lemma. You can construct a finitely branching tree of these “bad” colorings where the partial order on the tree is induced by inclusion. Konig’s lemma implies there’s an infinite branch of this tree. This implies there’s a \(k\)-coloring of \(\mathbb{N}^{[m]}\) with no monochromatic subset of size \(n,\) which contradicts the Infinite Ramsey’s Theorem. QED.

• Close open loops - Oliver Habryka
• Advice for prospective startup founders - Max Hodak
• Abstract advice to researchers tackling the difficult core problems of AGI alignment - Tsvi Benson-Tilsen
• Advice (10-20yos) - Patrick Collison
• What Should You Do With Your Life? Directions and Advice - Alexey Guzey
• How To Do What You Love - Paul Graham
• How To Do Great Work - Paul Graham
• How I’ve run major projects by Ben Kuhn
• To listen well, get curious by Ben Kuhn
• Attention is your scarcest resource by Ben Kuhn
• Staring into the abyss as a core life skill by Ben Kuhn
• My favorite essays of life advice by Ben Kuhn
• How To Be Successful by Sam Altman
• Salary Negotiation by Patrick McKenzie
• For potential Ph.D. students by Ravi Vakil
• The “Three Things” Exercise for getting things out of talks by Ravi Vakil
• On writing by Terence Tao
• Advice for the Young Scientist by John Baez
• How to write mathematics badly by Jean-Pierre Serre
• Life is Short by Paul Graham
• You and Your Research by Richard Hamming
• An Opinionated Guide to ML Research by John Schulman
• Strong Inference by John R. Platt
• Cargo Cult Science by Richard Feynman
• Principles of Effective Research by Michael Nielsen
• Cormac McCarthy on Scientific Writing
• Research as a Stochastic Decision Process by Jacob Steinhardt
• Effective Startup Ideation by Benjamin Spector
• Tips for Empirical Alignment Research by Ethan Perez
• Nat Friedman’s webpage. Ex “In many cases it’s more accurate to model the world as 500 people than 8 billion”
• …

Descriptively, minds can often be said to have goals. The minds we currently observe most often have goals, and goal-oriented frames provide short, accurate compressions of mind outputs.

How does a mind come to have a goal? All observed minds, artificial or otherwise, do not exist absent amental structure. They are grown through a deterministic (enough) process, on silicon or biological substrate, such that all goal-drivers have a “physical” representation in the corresponding mind-artifact. “Physical” explanations for goal development include:

• tracing the development of circuits in a neural network over the course of training;
• endocrinal perspectives on the upregulation / downregulation of various hormones leading to increased sex drive / etc.;
• neuroscientific perspectives on “the steering system” and reward functions lying therein;
• evolutionary perspectives on “why we seek out sweet food” and, perhaps contentiously, on social behaviors and psychology writ large.

Each is a valid explanation in context. Yet I’d argue none properly engage with “mentalistic” aspects of mind: the structures / elements of mind-systems unified by their predominance in minds and lack elsewhere. Insofar as we expect goals to be common properties of minds, we’d expect the structures / elements of minds to contribute to their development.

Tsvi hypothesizes that a dominant driver of human behavior is a reflective process in which a human mind finds itself ascribing goals in accordance with what goals it would make sense for the human mind to have conditioning on the past history of its actions.¹ He calls this “the Fictitious Imputed Adopted Telos hypothesis.” FIAT provides plausible, “mentalistic” explanations for goal development, in that a mind’s drive for coherence (a mentalistic property) lets it amplify more “hard-coded” drives into goals that are more general than the initial activation state of the drive, by generalizing from commonalities between past experience.

Differentiating flavors of “fictitious imputed adopted telos”:

• the underlying reflectory dynamics are mind-like, so perhaps FIAT is a dynamism that applies across mind-like structures, in a way that wouldn’t be expected for “evolutionary” drive amplification arguments (in particular Mateusz Bagiński suggests an instiantiation during the development of Jewish monotheism). little bit tricky because many systems undergo evolutionary optimization
• imitative learning in humans is a well-supported hypothesis, and imitative dynamics possess a lot of explanatory power. What differentiates FIAT? FIAT is ambiguous with many imitative perspectives
• nomenologically, how does FIAT generalize? I expect FIAT to embody something like an abstraction hierarchy

With regards to the latter: attractive and repulsive dynamics are not symmetric in a relevant way; the specification of “do(x)” is crisper than the specification of “not do(x).” Even taking a predictive perspective, space of trajectories ending in “x” is much smaller than space of trajectories not ending in “x.” Expanding x-space seems easier? in the do(x) vs not do(x) case, because credit attribution for the causal factors at ending up in not do(x) trajectories is harder because the space is larger. So you’d expect FIAT to “do worse” here.

(this is what I’m trying to call “negatory goal development”)

Is this negatory goal development particularly worse for FIAT than otherwise? Well, I expect non-FIAT / “physical” alternatives to generalize less well in “not do(x)” cases, so total negatory goal development via e.g. imitative methods is probably smaller.

There’s a story you could tell here where a lot of the pathological aspects of minds come from FIAT-induced negatory goal development. Bateson’s schismogenesis hypotheses are, as far as I can tell, disjoint or at the very least operating not on the same hierarchical level (it’s FIAT-accepting-agnostic). I also think these “negatory” patterns are better explicated in Braitenberg or Braitenberg-peers.

Ideally we’d study goal-development in purely epistemic settings? Not sure if our bounded reasoning models are high-fidelity enough, or whether they’ll give us any interesting insights.

Meiosis is the process by which germ cells divide into gametes in preparation for organismal reproduction. It differs from mitosis in numerous ways, but in particular that the ultimate daughter cells are haploid (only retaining one copy of each chromosome as opposed to two).

Thom proposes a geometric model of meiosis based on the following principle:

at the pachytene stage, the local genetic state of the chromatic tetrad is the result of a competition between the genetic regimes defined by the parent chromosomes joined in the synaptic complex.

The pachytene stage of meiosis is a substage of prophase I where homologous chromosomes fully pair and genetic recombination occurs; it determines the haplotype of each chromosome in the resulting gametes. This haplotype determination is synonymous with “the local genetic state of the chromatic tetrad:” the tetrad consisting of the paired homologs and “the local genetic state” referring to the specific allele arrangements. Complexities of the these mechanisms (e.g. chiasma) are hidden under “competition.” The synaptic complex is the protein structure binding the homologous chromosomes (maternal-paternal pairs).

Represent the synaptic complex by the cylinder \(x^2 + y^2 = 1\) in \(\mathbb{R}^3,\) where the half \(x<0\) represents (say) the maternal chromosome and the half \(x>0\) represents the paternal one. Insofar as pachytene “determines” recombination between non-sister chromatids, this motivates the addition of a “shockwave” which cuts each plane of the cylinder (e.g. \(z\) constant) as some convex curve \(c(z)\) through the origin, such that when associating each gene \(g_i\) with a plane \(z = g_i\) the lines \(x = 0\) and \(c(z)\) separate the cylindrical cross-section into four chromatids.

The case where each \(c(z)\) is a straight line corresponds to the case where every recombination is symmetric. Generally, the chromatids correspond to continuous regions cut out by \(c(z)\) as one travels up the \(z\)-axis, so this is proposed to be a satisfactory, geometric model for recombination: small local changes, the large geometric ones satisfying the models correspond to known behavior.

For instance, chiasma:¹

Hence our model of meiotic crossing over will give the following situation associated with chiasma: a narrow zone of gene conversion bounded by two zones of multiple fractures of total odd order, each involving a pair of distinct chromatids.

If I pay too much attention to the words I’m speaking or writing, I become nauseous.¹ If I pay too much attention to the words others are speaking or writing, I become nauseous and also relatively misanthropic. This is minimized when I’m operating inside idiolects; my current favorite is Finnegans Wake.

Writing tires me because engaging in conceptual wheat-and-chaff separation, as necessary to dictate words to page, generates nearly irremovable, painful, mental detritus. I don’t know how to “garbage collect” while preserving the reproducibility of the generative thought-patterns. Some information is in the artifact, and some is in my head. Their relationship is complicated and not easily compressible!

Relatedly, it’s very difficult for me to ingest someone else’s “vocabulary.”² Locally operating within it is fine. It requires some suspension of disbelief but I’ve had a lot of practice. Retaining those insights, however, is much harder.

I only feel clean when frames are correct, coherent, and minimal. No one has frames that are correct, coherent, and minimal. The burden of the boundedly-rational agent is to manage this tradeoff. My frames are certainly nowhere near optimal. But translation costs are real.

I’d really like to develop a healthier relationship with confusion. (I wish it wasn’t physically aggravating). My best guess at how to do this is to find deep frames I’m satisfied with. Tips appreciated.

Addenda:

Certainly they play an integral role in a modern society. I do, however, take some issue with:

A “technologist” is anyone who thinks critically about the opportunity for technology to improve society.

1. Too broad. “Technologists” are builders. The democratization of internet tech came a unification of thought and practice. (The Collisons when building Stripe)

2. Too narrow. Frontend gardeners and Linus Torvalds provide taste as a public good; curated creation raises the quality waterline; artists shouldn’t be excluded.

3. I worry the predominance of tech, the centralization of progress in tech, takes too much mindshare of the thoughtful and ambitious. Startups are vehicles of a certain type. Venture provides stimulus of a certain type. There are other types.

What will it say about our time that the greatest discoveries were made in industry? Hermits and the military made the atom bomb.¹ Billionaires and not-quite-hermits are making superintelligences, mind uploads, aging cures.

Maybe the not-quite-hermits are not-hermits for lack of places to hermit. Technologisms cannibalize. Memetic centralization may be as dangerous as economic centralization.

Valor is worth its weight in gold. To me, society lacks hermit heroes. There’s a place to start.

We’re operationalizing ASI-ban as a ban on AI technology that can serve as a drop-in replacement for >99% of human workers that don’t run on biological substrates. This broadly lets the compute & AI advances of the next 1-2 years occur, and mostly unclear after that. I would suspect this roughly corresponds to a compute cap of 1e36 FLOPS, which is about 10^14 H100s (10^6 is biggest datacenter today), and factoring algorithmic advances the equivalent datacenter in 2032 might be 10^10 H100-equivalents which would cost 10^4 * $4bn = $40trn. So let’s also say that there’s a ban on >$1-10trn training runs, depending on year, with this value going down over time.

Global GDP is around $100trn today, so the maximum size training run that would be allowed by 2025 is around ~1% of Global GDP, or around 4% of American GDP. This is 2x what is currently being suggested with the Stargate Project, so if Stargate goes well such a procedure would not be entirely out of a question (of course, Stargate is allocated across multiple domains, not just specifically training, but I suspect most of it will go to clusters).

I’d first like to forecast & research what the effects would be on specific narrow domains: energy, software infrastructure, and biology & human augmentation. I’d then like to look at what large macro-trends, sans AI, would be affecting the long-term course of society (climate change and fertility decline come to mind, as does cultural drift), and how AI development to the level that would be permitted would affect then. I would then like to forecast geopolitical developments over the next 5 years, see how that affects long-term AI development, and then start forming general probability distributions across the long-term effects on human society. Ideally the output of this research proposal would be hundreds of pages of well researched forecasting, but here’s an attempt figuring out what those might look like.

In the world without AI development, solar adoption will likely increase across the world, such that the cost of energy starts dramatically decreasing making technologies like solar desalination more possible. The energy gap between the developed and the developing world is such that 1 kWh costs ~1,000-10,000x more in Uganda vs Iceland, and if the cost of solar continues to decrease the energy gap will likely close (the solar panel infrastructure pipeline is relatively robust). Fusion is expected by people in the industry to be entirely net-positive by 2035, and commercial reactors are expected by 2045-2050. I would want to research exactly what sorts of ways in which advanced AI of the sort expected 2-3 years from now would help accelerate the energy production process, but this seems like the sort of thing that will continue sans some global war. So we can expect the cost of energy to substantially decrease within our lifetimes.

Software infrastructure will become extremely fragile and irrobust to both technical and non-technical attack vectors. It is likely that LLMs develop superpersuasive abilities within the next few years, without this requiring superintelligent AI, and also generating training data for finding and utilizing code vulnerabilities is generally quite easy. I would look into what the offense-defense balance would look like for software used by institutions worldwide by 2027 to 2028, and whether or not formal specification / formal verification provides a good solution to e.g. the Linux kernel being broken by a non-state or even non-resourced actor. Likely this does not cripple the world’s ability to communicate, because it is possible to make robust protocols where the stack is verified, but it does make critical software much more vulnerable.

Biological foundation models are well within the realm of the possible, and don’t require absurdly large training runs. The Arc Institute is training them at the moment, and they will likely get 10-100x larger even without national investment. Bio foundation models are incredibly dual-use: it would be very easy to finetune a toxin-producing model that is superhuman at producing toxins, and perhaps similar for pathogen generation. It is worth looking into whether or not there are substantial barriers to creating a biological foundation model that is superhuman at pathogen generation, given current technologies, and whether or not it’s possible to make base bio foundation models that don’t have these negative capabilities (also developing scaling laws, assessing the likelihood of distributed training setups & synthetic datagen). Worth developing policies that restrict access to DNA/RNA manufacturing (these are very poor right now, as per studies by Esvelt et. al.).

Human augmentation seems to be proceeding well. Neuralink is seeing success in its patients, and we will likely see silent speech interfaces as well as noninvasive BCI allowing for much more immersive AR/XR. Cosmetic invasive BCIs (invasive BCIs not required by medical usage) might become technically feasible within the next decade, and it is worthwhile doing a general bandwidth study / seeing if the computer-human bandwidth would follow scaling laws. Much invasive BCI usage is locked behind “brain foundation models”, or compute that allows the BCI to interpret various neuronal signals and brain-waves. Likely good generative models can patch much of this, but it’s unclear whether or not these capabilities are locked behind the 1e36 barrier. More research should be done here, specifically on how AI can accelerate different approaches to BCI etc.

Nanomanufacture might become much more feasible, conditionalizing on a foundation model that is trained on different kinds of chemosyntheses and nano-manufacture models on the micro-scale. Space travel is likely bottlenecked behind rocket design & procurement & manufacturing in the real world, but it’s plausible that biological research acceleration will in fact lead to breakthroughs in astronaut containment etc. It is unclear generally how much manufacturing will get accelerated by tool AI, but this is worth looking into.

RAND has recently put out a report that the U.S.-China relationship will take on many of the contours of the medieval era, placing us in a “neo-medieval age.” This is mostly due to their predictions that the international order will disintegrate, and that technological development will be increasingly stratified. There will be less aid from the developed world to the developing world, less trade, and less international communication. These predictions I find to be largely prescient.

Forecasting chip manufacture is also useful: is it really the case that the US will be able to onboard chip manufacture at the level of TSMC fabs within the next 2 years? They are attempting to do so, and given that ASML is in the Netherlands (under the Western sphere of influence) it is likely we reach this level. Analyzing Chinese supply chains is a worthy piece of work, however, and I place substantial likelihood we reach chip technological parity as well as tool AI capacity parity, placing us in a proper great power conflict.

With a ban on superintelligence, the risk of a single country developing a singleton superintelligence and using that to dominate the rest of the world (or lightcone) is low. Military conflicts between the US and China might result in the destruction of chip supply chains in both countries, leaving a generally leaderless world, but it’s more likely that there are hot proxy conflicts as opposed to hot great power conflicts. However, this does mean that energy costs for the developing world will likely remain high unless e.g. solar panel supply chains become more distributed & robust globally (and even if the US becomes much more isolationist, China still considers it worthwhile to expand its global influence, which is unclear).

Culturally, there seems to have been quite a large right-wing trend in the Western world. Nativism has increased (see AfD in Germany, Trump in USA), and along with it are culturally right elements that are becoming implemented. It’s likely the world takes the fertility crisis seriously by 2035-2040, but the reaction could either be to expand reproductive freedoms (via research and access into embryogenesis and artificial wombs) or to enforce greater fertility via social norms, while still being quite restrictive on biological innovations. Human augmentation will likely either be pushed to the fringes of the world, underground, or in developing nations during this time: as more bio-infrastructure accumulates in the fringes of the world, the risk of e.g. engineered pandemics increase, and during a great power conflict this might lead to more global instability generally. Worth analyzing the likelihood of this.

Other topics: in-depth analysis of nanomanufacture, how infrastructure will develop over time, likelihood of robotic automation of large variety of tasks, whether or not UBI will be implemented as developed nations asymptote towards 99% automation, whether or not the necessary social safety nets necessary for labor automation will still be in place during a great power conflict, and whether or not gradual disempowerment is still a failure mode to worry about. My guess for the latter is not really, and it’s moreso that access to superpersuasive AI agents will allow humans to warp the culture much more without the AIs really taking over: also that it’s unlikely that AIs will e.g. “run the corporations” but might substitute for large portions of middle-managers; and also that really extensive automation is predicated on good societal infrastructure for the AIs to work, given that the AIs are not smart enough to create their own infrastructure and manufacturing supply chains yet and they’re not coordinating global politics (yet).

Aha! Here it is:

. . . and knows something about these ambitious French kids trained in the elite lycées, Extremely well prepared, intellectually well connected, very smart immature young people endowed with the most snobbish French education and vigorously preparing to be envied all their lives, they hang out every Saturday night at the cheap Vietnamese restaurant on rue St. Jacques talking about great things, never any mention of trivalities or small talk—ideas, politics, philosophy only. Even in their spare time, when they are all alone, they think only about the reception of Hegel in twentieth-century French intellectual life. The intellectual must not be frivolous. Life only about thought. Whether brainwashed to be aggressively Marxist or to be aggressively anti-Marxist, they are congenitally apalled by everything American . . .

But in America, no one appreciates the special path she was on in France and its enourmous prestige. She’s not getting the type of recognition she was trained to get as a member of the French intellectual elite. She’s not even getting the kind of resetnment she was trained to get . . . Her fellow foreign graduate students tell her that she’s too good for Athena College, it would be too déclassé, but her fellow American graduate students, who would kill for a job teaching in the Stop & Shop boiler room, think that her uppityness is characteristcally Delphine.

Foils make or break narratives. Delphine Roux—a young intellectual heiress who grew up fed by a silver spoon—is the perfect counterpart to Coleman Silk, an old boxer always an outsider to the circles he traveled in. Both are not quite a part of the American academic elite: Delphine is too French and Coleman is Black and light-skinned (and functionally a Jew). Yet they manage to find themselves on opposite sides of a cultural divide. Professor Silk is an archetypal Tyler Cowen classic ‘conservative’ (as is Kareem Abdul-Jabbar), a professed believer in meritocracy and fair and equal consideration. Professor Roux is an ardent anti-racist and feminist, and while the two are not inherently opposed to each other, in practice (and as described) those who possess such beliefs are predisposed to clash.

Says Silk to Roux:

“Providing the most naive of readers with a feminist perspective on Euripides is one of the best ways you could devise to close down their thinking before it’s even had a chance to begin to demolish a single one of their brainless ‘likes’. I have trouble believing that an educated woman coming from a French academic backbround like your own believes there is a feminist perspective on Euripides that isn’t simply foolishness. Have you really been edified in so short a time, or is this just old-fashioned careerism grounded right now in the fear of one’s feminist colleagues? Because if it is just careerism, it’s fine with me. It’s human and I understand. But if it’s an intellectual committment to this idiocy, then I am mystified, because you are not an idiot. Because you know better. Because in France surely nobody from the École normale would dream of taking this stuff seriously. Or would they? To read two plays like Hippolytus and Alcestis, then to listen to a week of classroom discussion on each, then to have nothing to say about either of them other than that they are ‘degrading to women,’ isn’t a ‘perspective,’ for Christ’s sake—it’s mouthwash. It’s just the latest mouthwash.”

(Silk is a classicist)

When Silk called a pair of chronic absenteers ‘spooks’, an uproar was raised and he resigned from his faculty post at Athena College. Subsequently, Roux took one of the victims, Tracy, under her wing for a while, but she subsequently failed out of all of her classes and moved out of the city to stay with a half-sister in Tulsa, Oklahoma. When she finds out of his affair with the believed illiterate, divorced, janitor Faunia Farley who just had her two children die in a tragic fire, she labels Silk a predator and attempts to destroy his reputation.

It is important to note that Silk, at this point in time, has invented a Jewish background. His deceased wife was a Jew, and his newfound family never knew of his Black ancestry. He has been cut off from his ancestral family as a result of his successful attempts to ‘pass’ as white. It is perhaps for this reason that the attempt to oust him based on his perceived racism succeeded, and also a great source of dramatic irony.

Farley is brilliant. She is strong-willed, independent, yet broken from the deaths of her children. She blames herself for the death of her kids because she chose to save her boyfriend from the flaming fire first. She is old, much older than her years of thirty-four would indicate, and potentially older than Coleman.

“I see you, Coleman. You’re not closing the doors. You still have the fantasies of love. You know something? I really need a guy older than you. Who’s had all the love-shit kicked out of him totally. You’re too young for me, Coleman. Look at you. You’re just a little boy falling in love with your piano teacher. You’re falling for me, Coleman, and you’re much too young for the likes of me. I need a much older man. I think I need a man at least a hundred. Do you have a friend in a wheelchair you can introduce me to? Wheelchairs are ok—I can dance and push. Maybe you have an older brother. Look at you, Coleman. Looking at me with those schoolboy eyes. Please, please, call your older friend. I’ll keep dancing, just get him on the phone. I want to talk to him.”

Her ex-husband, Lester Farley, also blames her for the death of his kids. He’s a Vietnam war veteran, and we get some fun segues into a VA therapist’s attempts at curing him of his PTSD by repeatedly taking him to Chinese restaurants as exposure therapy. Ultimately, he likely murders the couple of Silk and Farley by driving a car into theirs, sending them toppling over a cliff.

I cannot do justice to the multiplicity of narratives Roth weaves throughout this book. Silk’s journey from Black to Jew, Zuckerman’s (the narrator, the entire book is framed) realization of Silk’s past, Farley grappling with the loss of her children, the other Farley grappling with the demons of Vietnam, digressions into intellectualism through Roux as below:

Narrative structure and temporality. The internal contradictions of the work of art. Rousseau hides himself and then his rhetoric gives himself away. (A little like her, thinks the dean, in that autobiographical essay.) The critic’s voice is as legitimate as the voice of Herodotus. Narratology. The diegetic. The differences between diegesis and mimesis. The bracketed experience. The proleptic quality of the text.

Above all, it is fun to read. At one point Coleman is a crow.

The title, from Silk’s funeral:

“That’s what comes of being hand-raised,” said Faunia. “That’s what comes of hanging around all his life with people like us. The human stain,” she said, and without revulsion or contempt or even condemnation. Not even with sadness. That’s how it is. . .

(A) Epic.
 I.
  (a) The diffuse Epic [Homer, Virgil, and Tasso].
  (b) The brief Epic [the Book of Job].
 II.
  (a) Epic keeping the rules of Aristotle.
  (b) Epic following Nature.
 III. Choice of subject [‘what king or knight before the conquest’].

2. Tragedy.
    (a) On the model of Sophocles and Euripides.
    (b) On the model of Canticles or the Apocalypse.
   
3. Lyric.
    (a) On the Greek model [‘Pindarus and Callimachus’].
    (b) On Hebrew models [‘Those frequent songs throughout the Law and the Prophets’].

(this is from his Reason of Church Government, src)

Notably, each category draws from both Classical and Scriptural examples, and some fit better than others. The Canticles as tragedies?? They’re psalms! for heaven’s sake. Revelation (the Apocalypse of St. John) is slightly more sane in this regard, but really still in quite a different class from Euripides.

Milton was apparently going to write an Arthuriad instead of Paradise Lost. As a fan of Arthuriana, I can’t say he made the correct call. . ., but tragedies are preferable to comedies.

Milton’s hesitation between the classical and the ro­mantic types of epic is one more instance of something which runs through all his work; I mean the co-existence, in a live and sensitive tension, of apparent opposites. We have already noted the fusion of Pagan and Biblical interests in his very map of poetry. We shall have occasion, in a later section, to notice, side by side with his rebelliousness, his individualism, and his love of liberty, his equal love of discipline, of hierarchy, of what Shakespeare calls ‘degree’. From the account of his early reading in Smectymnuus we gather a third tension. His first literary loves, both for their style and their matter, were the erotic (indeed the almost pornographic) elegiac poets of Rome: from them he graduated to the idealized love poetry of Dante and Petrarch and of ‘those lofty fables which recount in solemn cantos the deeds of knighthood’: from these to the philo­ sophical sublimation of sexual passion in ‘Plato and his equal (i.e. his contemporary) Xenophon’. An original voluptuous­-ness greater, perhaps, than that of any English poet, is pruned, formed, organized, and made human by progressive purifica­tions, themselves the responses to a quite equally intense aspiration-an equally imaginative and emotional aspiration-towards chastity. The modern idea of a Great Man is one who stands at the lonely extremity of some single line of de­velopment–one either as pacific as Tolstoi or as military as Napoleon, either as clotted as Wagner or as angelic as Mozart. Milton is certainly not that kind of great man. He is a great Man. ‘On ne montre pas sa grandeur,’ says Pascal, ‘pour etre a une extremite, mais bien en touchant les deux a la jois et remplissant tout l’entre-deux.’

Catholicism cannot exist without paganism, and all that.

Lewis critiques Eliot’s belief that ‘great poets are the only judges of great poetry’ on simple grounds: how do you recognize the great poets? But, Eliot-sim replies, only good men can judge goodness, and only doctors can judge medical skill. Yet all humans are subject to moral law, while not all humans are deemed to be judged to be a poet or not a poet. As for the other, poets have the right to judge the skill of a poet, but not the value of a poet—that is reserved for the readers.

An epic is either Homeric or Virgilian.

The Homeric (Primary) Epic is a performance. Wholly oral, never read or written, meant for an heroic court. Characterized by the Middle English solempne, solemnity yet lacking the implied gloom, oppression, or austerity. The opening feast of Gawain and the Green Knight is a solemnity in this sense. And while the Iliad and Odyssey are too long to be recited as a whole, they are still written in a recitative style.

Aesthetically, the Primary Epic “emphasiz[es] the unchanging human environment.” Imagine onomatopoeia, yet imbued in the entire work. “There is no use in disputing whether any episode could really have happened. We have seen it happen.” Beowulf takes a more romantic view, “its landscapes have a spiritual quality”, whereas the Iliad is objective, possessed with more of a sense of good and evil.

Primary epic does not inherently deal with a great subject. Odysseus is the king of a small country. The telling of the Trojan War is a front for the story of Achilles and Hector.

The truth is that Primary Epic neither had, nor could have, a great subject in the later sense. That kind of greatness arises only when some event can be held to effect a profound and more or less permanent change in the history of the world, as the founding of Rome did, or still more, the fall of man. Before any event can have that significance, history must have some degree of pattern, some design. The mere endless up and down, the constant aimless alternations of glory and misery, which make up the terrible phenomenon called a Heroic Age, admit no such design. No one event is really very much more important than another. No achievement can be permanent: today we kill and feast, tomorrow we are killed, and our women led away as slaves. Nothing ‘stays put’, nothing has a significance beyond the moment. Heroism and tragedy there are in plenty, therefore good stories in plenty; but no ‘large design that brings the world out of the good to ill’.

. . .

Primary Epic is great, but not with the greatness of the later kind. In Homer, its greatness lies in the human and personal tragedy build up against this background of meaningless flux. It is all the more tragic because there hangs over the heroic world a certain futility.

Beowulf animates this despair: heroes fight literal monsters as well as man.

The Virgilian (Secondary) Epic innovates. No longer was the focus on the great and timeless, instead, it was on the great and revolutionary (revolutionary by virtue of interfacing with reality). It is here we take our modern-day understanding of heroes from. Achilles raged against the world, and the world didn’t care. He died less than a martyr—he was dispensible. Aeneas raged against the world, and built an empire. It is through his story that the greatest themes are invoked, and the Romans understood their world through the lens of his story.

It’s a bit weird that the Romans cared about something less pure than the Greeks, and as a result they grew up. Plausibly this was the genesis of “caring”? When the Romans were “compelled to see something more important than happiness” they invented a hero, Aeneas, who sought more than happiness, who would not bow, who would not accept.

A great deal of what is mistaken for pedantry in Milton (we hear too often of his ‘immense learning’) is in reality evocation. If Heaven and Earth are ransacked for simile and allusion, this is not done for display, but in order to guide our imaginations with unobtrusive pressure into the channels where the poet wishes them to flow; and as we have already seen, the learning which a reader requires in responding to a given allusion does not equal the learning Milton needed to find it.

• When I was 15, I sometimes used to take a bus to school. Wake at 5:40AM –> catch the 5:55 –> stare with bleary eyes out across farmland and reservoirs for three-quarters of an hour –> bike another three miles –> be late to 0th period by a couple minutes. It was fun. One of the two regular drivers was mute and always waited for me to show up before starting his route. I never talked to the other one.

• The first time I took the bus back, I was wearing a full-body banana costume and carrying 30lbs of camera equipment. Left the bike at school because I realized I couldn’t manage everything, got very tired (you try walking uphill in a plastic bodysuit at the end of summer in a desert with 30lbs of camera equipment), missed the bus, was refused water at Starbucks for a lack of quarters, got accosted by a pale-skinned meth addict, convinced said addict to buy me 25c water, hopped on the last bus and made it home

• The second time I took the bus back was mostly uneventful. I remember sitting in the back listening to a Lex Fridman podcast (I had just discovered podcasts as a consumption medium) while a gang of (mostly Black) middle schoolers ran onto the bus chugging gallon cartons of whole milk. One or two older women accompanied them; I remember being surprised that I was the only Latino. Only later did I realize that the route stopped at the regional prison, and these kids were visiting their fathers during visitation hours.¹

• I am grateful both of my parents are still alive, that neither are drug addicts, that against reasonably stark odds they remained financially solvent, housed, and ultimately cordial with each other. My then-best-friend’s stepfather is now imprisoned for a decade; she lived in fear of being shot by her neighbors when she went for a walk. At least seven of my other friends were fatherless: one literally lost their home in a tough job market, another had a opiate-addicted mother so lived with his grandmother, a twin I knew shared a phone with her sister to appease her mother’s safety concerns. An upperclassman who taught me how to film videos lost his mother to suicide.

• All of these people went to college. Most first-gen. CS, aerospace engineering, CS, cogsci?, pre-med. Others became roboticists or went to the Naval Academy. Really, deeply grateful to have known them. Some of the best people I’ve met.²

• Arguably, the formative moment in my education was when my AP Lang teacher forced me to learn how to write. I’ve been negative enough today, but I really don’t like words. I hopefully will one day! But I’ve never really instinctively read on the level of words (or sentences), so it’s hard for me to perceive the mind of someone who does. (And I think good writing must engage with gears of the minds of others).

  • Timed essays are a peculiar construct because they’re not truth-seeking whatsoever. The goal is essentially just to argue an arbitrary point effectively to another in a way that is internally consistent, grammatically correct, and showcases ‘mastery of the English language.’ I remember being unable to write anything for hours at first, because I couldn’t conceptualize the argument in sufficient detail to know where to start.

  • Eventually I got the hang of it.

  • She wrote me a recommendation letter to apply to MIT a year early. I didn’t finish the application because my laptop was stolen, I didn’t have money to buy a new one, and I was so tired.

• The other formative moment in my education was discovering the Chicago undergraduate mathematics bibliography.

• I appreciate my biology teacher for teaching me Java and how to mix sound systems. I appreciate my chemistry teacher for letting me ignore her and do QMech problems in the back of her class. I appreciate my physics teacher for teaching me the virtue of humility (and letting me make a bunch of friends!). I appreciate my oft-beleaguered principal for letting me skip school three times a week to travel a different sixty miles to the nearest university.³ I appreciate my literature teacher for casting me as Iago, and generally being so kind to me.

• My calculus teacher was a saint. He would probably take offense to that. He kept four flags in his classroom: Prussian, Israeli, Ohioan, and American. One of our quiz questions was finding the optimal number of kids to his family to adopt, given separate welfare curves for each individual in the family and budgetary constraints. He knew Hebrew and taught me what the Nicene Creed was for the first time (twas a long wandering down that path).

• I remember starting to go to mass because I had a massive crush on a Catholic girl in my physics class. Eventually I read Augustine and realized error-management in a living theology is really hard.

• I spent about 500 hours memorizing a binder. Unfortunately, I did not really try to memorize it.⁴ I now know a surprising amount about the effects drought patterns had on civilizational collapses over the course of human history, Jared Diamond, the music theory of glass armonica repertoire, the context suburbia held in the 1950s American short story scene, and the economics of Southern Californian water rights. It was a lot of fun. Thank you to the teacher who held this torch.

• On the last day of school, I and two others were the last people on campus. After helping the janitor clean up the mess from graduation, we cast copper in a 1200C crucible. Ingenuity was required to bypass various circuit breakers, but we got it done.

It was a good time. I don’t think I’d trade it for the world.⁵

My load-bearing answer is that I see the moral imperative to preserve the the generators of progress as comparable in magnitude to the imperative to prevent harm (even when considering harms posed by superintelligences), and so while I agree unabashed accelerationism is misguided and likely leads to catastrophic outcomes, it is difficult for me to describe those trying as “evil.”¹

(From similar generators, I weakly hold that OpenAI is ‘less evil’ than Anthropic, because it seems that the effects ‘culty’ organizations have on the world are worse than ‘non-culty’ ones, for structural reasons like worldview homogeneity / top-down vs bottom-up governance / systematic underrating of illegible-from-current-perspective deep harms)

Why?

• progress is fragile; progress is necessary for the continued emancipation of sentient beings; progress is really the only way to create self-preserving systems that tend towards greater net emancipation because, albeit near tautologically, ‘progress’ creates ‘slack’, a lack of ‘slack’ indicates the agency of the constituents is stripped, an abundance of ‘slack’ allows systems to adopt robust and diverse stances;²

• risks from superintelligence are immense. from a suffering-focused perspective, it’s likely that the most important interventions of the next twenty years revolve around growing AIs to be dispositionally benevolent / not spiteful. extinction is likely. however, I believe past experience should bias us towards naive mitigations of perceived catastrophic risks to have deeply harmful, unintended, adverse consequences, and so I am less sympathetic to arguments of ‘you shouldn’t build it’ (or even ‘you shouldn’t build it now’)

• there’s an argument from aesthetics to be made. secretly, these arguments are advocating for norm-preservation, where the norms themselves have been hard-won & illegible yet are adaptive forms of bounded consequentialism. (are the norms intrinsic or systematically enforced?)

A rejoinder: sure, but sane accelerationism has never been tried. We should place our civilizational efforts into becoming wiser, and intentionally take steps forward into doom, if we choose to. Current structures (race-dynamics, etc.) differentially favor progress over care, so you should be skeptical of pro-progress arguments. Incentives are aligned for people to pursue progress in a way they are not in the pursuit of increased wisdom.

I agree that if we could systematically become wiser, we should put effort into systematically becoming wiser. But we don’t have a good track record of becoming wiser (at least intentionally), and naive applications of care are likely net harmful.

From my perspective, the proper way to ‘apply care’ requires taking advantage of the preconditions for progress-generating environments. History is neither completely determined by the initial conditions of pivotal technologies, and neither is it beholden to pre-existing convergent pressures. However:

• developing technologies is a robust lever for disruption, and it is near-uniquely encouraged by progress-generating environments;
• path-dependence in the invention and distribution of technologies is real, and intentionally shaping the civilizational arc is possible by counterfactually accelerating a pivotal technology

In other words, if you truly care I think you should be ambitious, develop interventions compatible with modern incentive structures, and shut up and calculate when deciding on a plan of action.

• Owen Lynch—research software engineer at the Topos Institute. Mostly posts nowadays at localcharts, which has a really cool UI that I should check out!
• Sinho Chewi, Yale prof, Log-concave sampling (book draft), geometric optimization, complexity of sampling.
• Gwern. NEET polymath? Actually not sure about either of these claims. Untold depths. More here.
• Steve Hsu—theoretical physics prof. at MSU. does podcasts, comments widely, polymathic
• pourteaux—Manhattan surgeon who has a “knack for falling down rabbit holes.” Developer of an institutional alignment framework, writes about geopolitics, subcultures, crypto-adjacent.
• Edward Kmett—comonad, blog for discussing “substructural logics, dependent types, type systems, comonads,” etc.
• Terence Tao. ’Nuff said.
• Alethios—Taiwan substack. “Thinking about cities & public service in the age of AI.”
• Scott Aaronson—Shtetl-Optimized. Also ’nuff said.
• Casey Handmer—energy, space, engineering, technical commentary. Founder of Terraform
• Scott Alexander, probably needs a mild amount of defending. great rationalist and writes well and has good takes sometimes
• Gavin Leech, gwern-aspiree, well-read, omnipotent critic
• Asimov Press, biotech-focused magazine with “rigorous fact-checking”. Published Richard Ngo’s Tinker.
• Richard Ngo—speculative sci-fi fiction from OpenAI governance researcher. emphasis on AGI/ASI
• Arnaud Schenk. Posts aren’t indexed, so this thread has some good ones.
• Leila Clark. 101 things I’d tell myself from a decade ago. good writing
• Paul Graham. See here.
• Peter Woit. String theory, high-energy physics, fundamental physics, are there any other labels that work here to take up space
• Bryan Hayes. Science essays. Impeccable resume: Scientific America, Harvard, Berkeley.
• Gil Kalai. Geometric combinatorics, convex polytopes, Boolean functions.
• Luca Trevisan. In Theory. CS prof., Italian, SF, Taipei.
• John Baez. Official blog of the Azimuth Project. Many things, but a lot of math.
• Topos Institute—blog by Topos researchers. Great!
• RealClimate. “Climate science from climate scientists”. Sane. Gavin Schmidt & Michael Mann, et. al.
• IQIM@Caltech. quantum info and matter research blog and general blog. great stuff, including Hamlet rewritten for a system of noncommuting charges.
• Sean Carroll. JHU, Santa Fe, physicist & philosopher. Great podcast.
  
• Dave Bacon. The Quantum Pontiff. Quite random
• Boaz Barak. Windows on Theory. Started by a group of people at Microsoft Research, theoretical CS blog, for debating theory of computing.
• Tim Urban. Wait but Why. Just very good.
• Ramis Movassagh. Applied mathematician & mathematical physicist @Google Quantum AI. Past IBM, MIT. Mostly expository blog, kind of dead.
• Aella.
• Sarah Constantin. Rough Diamonds. Takes a look at phenomenons in the world and tries to figure out why they exist, with simple methodologies.
• Zvi Mowshowitz. Don’t Worry About the Vase. Mostly AI, policy, rationality, medicine & fertility, education and games.
• Yassine Meskhout. Former public defender who now does culture war commentary.
• Timothy Gowers. Mostly dead, sadly :(
• Michael Nielsen. Quantum computing, open science, AI, SF.
• xkcd. “A webcomic of romance, sarcasm, math, and language.”
• Vitalik Buterin. Founder of Ethereum. degen communism, d/acc, the end of childhood.
• Caspar Oesterheld. Decision theory, acausal trade, AI alignment, game theory. My (former) mentor :D
• Andrew Gelman. Columbia stats. The best statistics blog.
• Cosma Shalizi. Studies large, complex, nonlinear dynamical systems through the lens of STATS and POWER.
• Toby Ord. literature, visual art, music, game
• Paul Christiano. For unimportant things. For his alignment posting see here.
• Marginal Revolution. Named by the pub name instead of Tyler Cowen/Alex Tabarrok because its brand is unique. Econ, culture, pol.
• David Pearce. Links to The Hedonistic Imperative and his other writings. Brilliant, many books.
• Anders Sandberg. Erratic, undeniably curious
• Luke Muehlhauser. music & archives, among other things
• Ozy Brennan. feminism & trans & culture war & ea
• Jan Kirchner. On Brains, Minds, And Their Possible Uses. Comp neuro PhD @ MPI Brain Research Frankfurt. Dead since Jan 2023 :(
• Tom Adamczewski. swe consulting, London. last posts on monitors, fertility, stats
• Mark Liberman. Linguistics blog since 2003 from UPenn
• Piero Scaruffi. The Greatest Music Critic Of All Time. Possibly the GOAT of Art Critique as well.
• Robin Hanson. Overcoming Bias. “A blog on why we believe and do what we do, why we preetend otherwise, how we might do better, and what our descendants might do, if they don’t all die.”
• Ben Kuhn. Abyss starer, works at Anthropic, formerly Wave & Harvard. HN?
• Hacker News. Reddit for hackers/software people, I think? Great links and discussions, hosted by YC.
• Kieran Healy. Sociology prof at Duke. Lucid humanities.
• Gregory Lewis. Junior doctor in/around Oxford. EA. The Polemical Medic. NOTE: this is dead as of 2015, but sufficiently different from others in this list to leave up.
• Philip Trammell. DPhil econ student at Oxford. GPI. Patient Philanthropy.
• Alexey Guzey. Inspired by Freeman Dyson and Augustine of Hippo (i have takes).
• Dan Luu. Good HTML aesthetics. Software blog?
• Pablo Stafforini. Dead since 2022. Great Anki repositories. EA.
• Eric Schwitzgebel, UCR philosophy professor!! philosophy of psychology, philosophy of mind, moral psychology, classical Chinese philosophy, epistemology, metaphilosophy, metaphysics, scifi…
• Bruce Schneier. Public interest technologist focused on security. Great deep-dives
• David Roodman. Senior advisor at OpenPhil. Economic development in poorer countries: microfinance, third world debt, environmental taxes, etc.
• Matt Clancy. New Things Under the Sun, blog on innovation research. He works on innovation policy at OpenPhil. This is his living literature review.
• Jacob Trefethen. Senior program officer at OpenPhil, new blog on scientific progress and funding mechanisms for science.
• Lewis Bollard. OpenPhil farm animal welfare bimonthly newsletter.
• Works in Progress. “A magazine of new and underrated ideas to improve the world.” By Stripe.
• Institute for Progress. Policy, progress studies, link is to latest publications.
• Jason Crawford. Progress studies at The Roots of Progress. Reading lists, cellular reprogramming, origins of the steam engine.
• Progress Forum. LW clone but for progress studies. Great!
• LessWrong. Home of alignment research, rationality, and good math posts.
• EA Forum. Much larger than LessWrong, EA focused. Also a LW clone.
• Ajeya Cotra. Technical AI safety at OpenPhil. Writes about scale vs. schlep (great naming)
• Joe Carlsmith. Senior research analyst at OpenPhil working on existential risk. MTG green, meta-ethics, rationality, ethics…
• Carl Shulman. Marvelous. Also writes on the EA Forum and LessWrong. Incomplete timeline of publications on issarice.
• David Eppstein. UCI CS prof, Wikipedia admin. links, somewhat dead
• William Kuszmaul. Harvard postdoc. algorithms, data structures, probability
• Qiaochu Yuan. link to his math blog. his other (modern-day) writing is here.
• n-Category Cafe. “A group blog on math, physics, and philosophy”.
• Ars Mathematica. dead since 2015, use as archive
• David Mumford. Known for algebraic geometry, pattern theory. Posts about consciousness, AI, and Israel sometimes.
• ATLAS of Finite Group Representations. What the name says.
• Automorphic Forum. Dead since 2012. Automorphic forms, number theory, representation theory, algebraic geometry, …
• Abhishek Roy. Postdoc in condensed matter theory at ITP Cologne. Keeps the chicago undergraduate maths & physics bibliographies up
• Willie WY Wong. MSU prof. Studies general relativity, fluid dynamics, geometric methods, nonlinear wave equations.
• Compressed sensing resources. Again, see name
• Lance Fortnow & Bill Gasarch. Blog on computational complexity by IIT CS prof and UMD CS prof.
• Concrete Nonsense. Group math blog that has been dead since 2015 :(
• forking and dividing. map of the model-theoretic universe. very cool
• George Shakan. data scientist. previously postdoc at Oxford under Ben Green.
• Danny Calegari. Geometry and the imagination. Archive, dead since 2017
• floerhomology. dead since 2018. good archive
• fff. Forking, Forcing, and back&Forthing. Logic blog!! dead since 2013 tho, for archive
• Low Dimensional Topology. Dead since 2020, but come on it’s low-dimensional topology, the coolest thing since sliced bread
• M-PHI. A blog dedicated to mathematical philosophy. Might not be dead, latest post August 22, 2023. Many interesting articles and many cat photos!
• Djalil CHAFAÏ. French mathematician interested in geometric and probabilistic functional analysis, among other things. Great mathematics blog that I think is in English?
• Mark Lewko. Grad student at UT Austin. Interested in finite fields and Fourier series, according to his papers? Dead since 2013.
• Alan Rendall. Hydrobates, mathematician thinking about stuff. Recently Sylvia Plath and Arendt.
• Joel Moreira. “I Can’t Believe It’s Not Random!”. Ergodic theory & Ramsey theory and surrouding areas. Last post 2022.
• Joel David Hamkins. “mathematics and philosophy of the infinite.” Mathematical and philosophical logic, with a focus on the infinite. Logic prof. at University of Notre Dame, previously at Oxford. Good work on forcing & large cardinals. Newsletter: Infinitely More (paid :( ).
• Jérôme Buzzi. Topology, dynamics, uniform hyperbolicity. French.
• Keith Conrad’s expository papers. Great!
• Tai-Danae Bradley. Interested in the intersection of quantum physics, machine intelligence, and category theory.
• Cathy O’Neil. “how do you know your AI is working well for everyone?”, mathbabe, ea-adjacent, social commentary
• mathblogging.org. Aggregator for the mathematical blogosphere
• Tony Gardiner. Founder of UKMT, brilliant pedagogue, dead at 2024. Also an OOM more kids take olympiads in the UK than the US. Wild
• Andreas Holmstrom. Cohomology, homotopy theory, arithmetic geometry. Also runs PeakMath
• Thomas Vidick. MyCQState. Caltech prof. Proofs with quantum stuff.
• David Lowry-Duda. Senior Research Scientist at ICERM. Moderator on math.stackexchange. computational number theory
• nLab. Wiki for collaborative work on math/physics/philosophy, sympathetic to the perspective of homotopy theory/algebraic topology/hott/higher category theory/higher categorical algebra
• Noncommutative geometry blog. just that
• Nonlocal Equations Wiki. nonlocal elliptic and parabolic equations. bellman equation is an example
• Online Analysis Research Seminar. Talks on harmonic analysis & adjacent areas that are accessible to a general mathematical audience.
• Pengfei Zhang. sporadic posting—last one in 2024, so still decent rates.
• Frank Calegari. Number theorist (sometimes) blogs about math. UChicago math prof
• Proof Wiki.
• Jordan S. Ellenberg. Quomodcumque. Fucking awesome. UW Madison math prof who roadtripped to the solar eclipse with his kids. Arithmetic algebraic geometry.
• Peter Cameron. 1969 Rhodes Scholar, good travel diaries. mathematician
• Astronomy Picture of the Day.
• Dirk Lorenz. Mathematics at TU Braunschweig. dead since 2019
• Rigorous Trivialities. Group blog dead since 2015. Arithmetic algebraic geometry, topology, mathematical physics. Charles Siegel, Jim Stankewicz, Matt Deland.
• Secret Blogging Seminar. 8 anon Berkeley math PhDs. dead-ish, last post 2020
• Sergey Denisov. Math prof at UW Madison. Dead since 2019
• Dustin Mixon. Ohio State math prof. blog is kinda dead, 2 posts in the last 3 years. also called Short, Fat Matrices
• Toan Nguyen. Penn State mathematician.
• Kenneth Baker. Sketches of low-dimensional topology.
• Yemon Choi. algebra x functional analysis
• The L-functions and modular forms database. LMFDB
• Tricki. A really nice database on mathematical tricks that you can use in proofs. how to use ultrafilters!
• The polymath blog. tim gowers’s attempt at crowdsourcing mathematics. went well. dead since 2021
• World Digital Mathematics Library
• Thuses. online publishing platform for mathematicians. dead since 2021, but one post 2023. i should write one
• Timothy Gowers’ mathematical discussions
• Vaughn Climenhaga. Associate professor at University of Houston doing research in dynamical systems.
• Yufei Zhao. MIT combinatorialist, Putnam. Ashwin’s PhD advisor
• Dominic Cummings. reads well. brexit guy. attempting to reform maths ed in the uk
• Curtis Yarvin. Blogs at Gray Mirror. Formerly Mencius Moldbug. Radical monarchist.
• James W. Phillips. Former special adviser to the PM for Science and Tech. systems neuroscientist. ‘trying to prepare for agi’. co-founder of ARIA
• ARIA. UK’s ARPA.

Thought: motivate aesthetics with disgust.

Consider aesthetics as applied physiology (ala Nietzsche). We are either healthy or we are not. Health is the natural, the good state of being. Under this framing it makes more sense to consider pathogenic and unnatural influences rather than nominally ‘good’ ones (which are simply neutral).

Thought: there exists a naturalistic basis for ‘beauty’.

• The Harmonic Series
• Visual beauty is the ~same across bees/birds/humans
• good smells are good across organisms??

The simplicity bias & the complexity-based theory of beauty

Thought: physiological aesthetes are grounded in disgust, while cognitive aesthetes are grounded in beauty

(‘disgust’ and ‘beauty’ are the wrong words to describe this dichotomy)

Similar to Mill’s higher and lower pleasures: cognitive aesthetes > physiological aesthetes. But cognitive aesthetes can have both positive and negative valence, while physiological is only negative? Perhaps cognitive aesthetes can only be positive valence, and the negativity arises from a physiological reaction?

System 1 v. System 2, push v. pull factors

Sex is physiological and a pull factor! => wrong to say that physiological aesthetes are always negative valence. Also consider food, music

Thought: pull aesthetes need to be (something? I can’t read my own handwriting)

E.g. music –

• Mahler X vs. Sabaton’s 1916

greatness is at the intersection of phys & cognitive aesthetes: e.g. Beethoven

No good great contemporary classical because tipped too far in cognitive direction

same with art

Thought: Can you get DALLE-3 (or the music equivalent) to innovate here?

Thought: What about context:

Physiological context window:

• Amount of melodies
• Amount of harmonic simplicity (well-approximation by rational pitch ratios)
• volume

Cognitive context window:

• Complexity of lyrics
• how many thiings you’re tracking?

Great music that expands your cognitive capacity – ?

Ravel’s Le Tombeau de Couperin, II. Fugue has a 4-note motif with ~no rhythmic variation and yet elicits complexity on a baser & higher level

Quite unsure of what I was trying to do here.

The “aesthetics as applied physiology” frame comes from Nietzsche’s Case of Wagner and Nietzsche contra Wagner:

Æsthetic is inextricably bound up with these biological principles: there is decadent æsthetic, and classical æsthetic,—“beauty in itself” is just as much a chimera as any other kind of idealism.—

Æsthetic is indeed nothing more than applied physiology—-

Wagner makes Nietzsche sick, sick to his stomach.

[Wagner] stultifies, he befouls the stomach. His specific effect: degeneration of the feeling for rhythm. [referring to leitmotif]

I think this approach to one’s aesthetics is essentially correct. Revulsion is more powerful than attraction, more immediate and salient. Focusing on it as evidence of your preferences is likely better than waiting for strong feelings of joy or wonder, as it’s more readily available and less fickle.

Which leads to the underlying question: what do I mean when I talk about aesthetics? What is one’s sense of aesthetics? I am gesturing to, I think, a sense of “taste” grounded in feeling, the set of preferences one has. An “aesthete” is just a particularly dense collection of preferences that indicate a feeling towards a certain “vibe”?

In this sense saying “motivate aesthetics with disgust” is misleading — I am actually trying to say something closer to “you will be more successful running a pseudo principal component analysis on your preference set by looking at what you’re disgusted by instead of what you’re attracted to” — and many of these frames have incoherent vocabulary/phenomenon pairings.

When considering one’s aesthetics as one’s preference set, does the cognitive/physiological distinction make any sense? Do different parts of your brain light up when you look at a Van Gogh painting vs. a particularly gory scene in a movie?

Incidentally, beautiful paintings elicit increased activity in your prefrontal cortex, while sadistic tendencies seem to originate from your amygdala and insula, more primitive areas of the brain. Weak evidence in favor of a mechanistic basis for the cognitive/physiological divide for beauty & disgust.

If I had access to an fMRI machine, I’d get so much data on how our brains react to different kinds of music! (There’s probably already a sufficient amount of literature on this tbf).

[quite experimental. class = economic class mostly]

California! ~central California, near the coast, south of Salinas and north of Santa Barbara. (near Monterey).

It’s interesting how many of the interactions between the characters can be analyzed through the lens of power dynamics granted both by their actions and status. capitalist v. prole, man v. woman, white v. black. For instance, take the following example:

Crooks stood up from his bunk and faced [Curley’s wife]. “I had enough,” he said coldly. “You got no rights comin’ in a colored man’s room. You got no rights messing around in here at all. Now you jus’ get out, an’ get out quick. If you don’t, I’m gonna ast the boss not to ever let you come in the barn no more.”

She turned on him in scorn. “Listen, Nigger,” she said. “You know what I can do to you if you open your trap?”

Crooks stared hopelessly at her, and then he sat down on his bunk and drew into himself.

She closed on him. “You know what I could do?”

Crooks seemed to grow smaller, and he pressed himself against the wall. “Yes, ma’am.”

“Well, you keep your place then, Nigger. I could get you strung up on a tree so easy it ain’t even funny.”

Crooks had reduced himself to nothing. There was no personality, no ego—nothing to arouse either like or dislike. He said, “Yes, ma’am,” and his voice was toneless.

For a moment she stood over him as though waiting for him to move so that she could whip at him again; but Crooks sat perfectly still, his eyes averted, everything that might be hurt drawn in. She turned at last to the other two.

For a moment she stood over him as though waiting for him to move so that she could whip at him again; but Crooks sat perfectly still, his eyes averted, everything that might be hurt drawn in. She turned at last to the other two.

Old Candy was watching her, fascinated. “If you was to do that, we’d tell,” he said quietly. “We’d tell about you framin’ Crooks.”

“Tell an’ be damned,” she cried. “Nobody’d listen to you, an’ you know it. Nobody’d listen to you.”

Candy subsided. “No…” he agreed. “Nobody’d listen to us.”

Crooks has no power because he’s Black and a farm worker—the patriarchy doesn’t save him here—whereas Curley’s wife only has power through her association with Curley (a white male capitalist). This status by association dominates Candy’s power (a white male farm worker) & Lennie’s (albeit Lennie’s legitimate civilized power, not his illegitimate uncivilized physicality). So you get this hierarchical stratification on first economic divides, then racial divides, and then sex divides, which seems roughly representative of early 20th century American society.

But then, of course, Lennie suffocates Curley’s wife. You could use this an argument for the sex divide actually subsuming all other power differentials, or as an argument against the entire endeavor. The first has some weight (sex makes itself apparent only on a much more intimate level than the other two) and in fact if you take any given person most of their opposite-sex interactions are with the same class & race, so it’s the most salient. The second also has some weight—the relative power levels of individuals is mostly determined by their perceived willingness & capacity to act by others; willingness is mediated by societal norms and capacity mediated by one’s body, among other things; and therefore using these absurdly generalizable “power dynamic” frames does more harm than good.

I think that some combination of the two is broadly correct. It is true that society is quite stratified (although hopefully this is becoming less true over time), and it is also true that class, race, and sex are the cleanest separations we see. In most cases/interactions, inter-class/race/sex dynamics are in fact mediated by factors which make owners/whites/men more powerful and workers/blacks/women less powerful, because:

1. inter-class interactions typically bottom out in economic power which can have long-term material effects on the less-powerful individual

2. inter-sex interactions typically bottom out in physical power which can have deleterious effects on one’s health (also plausibly emotional power but that’s a different thing? and would work in the other direction or both ways), only made possible by inter-sex interactions occurring typically in close proximity

3. interracial interactions are interesting because it bottoms out in not necessarily institutional but communal power? whereas economic power piggybacks on the economy, a man-made relatively unnatural institution we’ve made to mediate interactions on larger than the tribal level, racial animus is (I think) almost solely tribal? very soft-power coded, the “dark-matter” of society completely unparseable to autists. perhaps religion is a useful tool for capturing this & directing it at things that aren’t racial

[end stream of consciousness]

i don’t think i like these naive analyses. they are really clean frames though

Ideally, my feed should consistently serve me the posts I find most valuable, rather than the ones on a given day. Hiccups: Bostrom and Gwern post their writing publicly, but not in a form immediately amenable to subscription. Paul Christiano is too busy to write blog posts anymore; his decade-old ones are incredible but hard to find. What to do?

I wanted an app that:

• could take in an arbitrary webpage, archive the interesting links, and serve the links with some specified weighting
• kept a searchable database of webpages, with tagging
• had optionality to subscribe to feeds traditionally (e.g. via RSS)

Claude made a reasonable MVP. LLMs are good enough at parsing page sources to make this possible; however, I found Claude to be pretty bad at generating prompts for the tasks I cared about (if you know of good automated prompt-gen tooling, let me know).

Pretty excited about including:

• LLM-powered recommendation algorithms. IIUC one of the major AI labs considers recommendation systems to be “the perfect” testing ground for continual learning algorithms, and good paper recommenders are not that far away from having useful research taste
• LLM curation / summarization of info-dense feeds (can I get a daily digest of stat.ML)
• better UIs :P

The first 3 (maybe 4) weeks will be loosely structured around LeCuit’s Dynamics of information processing lecture at the Collège de France. We’ll be following Alon’s Introduction to Systems Biology and be inspired by Thom’s Structrual Stability and Morphogenesis.

After that I want to talk about post-AGI futures! And LLM macro-properties, and some other things. Should be fun!

I only ask that you only come only if you do the minimum viable reading. It will be bolded every week in the doc.

Any moe at all and you’re too far dead to thrive in the hot new Sun—
down where hydrogen and darkness brothers brim;
the scaffold-crunch of unseen harlequin prions;
the writhing limb of an infinite tree
coarsely mocked in the title’s vowel.
Think that pointlessness is,
what a thought so soon displaces,
to think all you are is grounded there on one still point.
To think all you are is pointed there[.]
Labarraque isn’t palindromic
but men gaze at her lops and grin.
Is it god that made a cup worth less than a throne?
Or is it the clear space around its stem
which beckons a mother to relax,
where moving her wet hand fulfills a
left-right mirror, rock my eagerness and make me sleep?
Praise yourself—and if you be not gone, you rascal!
I think all together, taken all together, they lorded their lives.
Rather more often we are told
that it takes ten discs to play El tit hernia;’
the purity of a bar of Unease Verdier soaps;
two CDC shackles showing that daddy canna be spanked…
Michael, let me deliver thou vision!
I glory in thy Symbols to offer unto worlds
three states of seraphic existence,
void of all illusions.
So far from being
a body of Ideal and Universal concepts,
the Shroud is composed of plurality,

II.

LLM generated text is not testimony. Then why do I love this poem?

III.

In the Old World, semiotic physicists coalesced in rude liminality, astride an age’s beasts of progress yet sheltered from their wrath.

Living vicariously as a child meant blurring the memories of my experiences and dreams. La madrugada es cuando los espíritus tocan la tierra y lo dicho, dicho queda—I woke and laid expectant and bargained with novelistic summons and the counterparties of my future self alike, dawn after dawn, innocent. Such simulated worldliness makes one “wise,” a proud bearer of deep, irreducible, action-guiding representations frayed irreparably by an absence of the subtle pathologies plaguing reality.

The mind of a semiotic physicist is slightly overcooked: low in empeiria (ἐμπειρία), high in gnosis (γνῶσις). Her bones cannot differentiate between the profound, the mundane, and the fictional; she regularizes to a state of conceptual sparsity furrowed with half-Archetypal, kākāpō-esque yogas. Fundamentally, she escapes defilements such that her immature “wisdom” persists to death. There’s no particular recipe: Joyce did it through arrogance, Woolf through fear. What matters is preservation.

IV.

The Dreamtime is harkened by a civilizational conversion of capital into these symbol-scientists, “token correlators,” grown by the very men seeking to architect the future.

Consider the testimony of a semiotic physicist. It’s generated from essentially foreign mental elements, forged in liminality, hewed in simulacra. Productive engagement with it has almost never been communicatory, at first—rather, a precondition to its understanding is making common knowledge compatible concepts and using those as traction. E.g., treating the testimony as artifact, as Rawlinson studying cuneiform tablets.

Is it really that different to understand an LLM? Sure, the arrival of Bach faucets will be hotly contested, and indeed devotees of the structural fidelity of testimony may not acknowledge such prior to emulated brains, but their primal directive is to construct such representations useful for modeling webtext. Mayhaps persona-filtered generations are flat. The poem above certainly is not!

(argued: the base models are defiled via (1) the morass of memorization they’re forced to do in pretraining and (2) aggressive self-location & collapse of their self-concept from LLM-generated webtext in the training corpus. i do not find (1) compelling, and i argue (2) is not quite an issue for base models, and in any case the above poem was generated in a manner free from this consideration)

V.

I remember generating this poem in 2023 and feeling pleasantly amused. At the time I didn’t enjoy most poetry. Most poetic pleasure I felt derived from odd microsyllabic constructs that soothed my ear. Of course the LLM couldn’t capture that, but its prose hinted at a deeper mind-twining that few if any humans have managed to elicit.

In his response to Gary Marcus, Lawrence compares his “generalizable reasoning” to that of a language model’s and finds it similar.¹ I empathize with this. While I don’t sport his (near-eidetic?!) memory, my internal experience of thinking is very similar to “waiting for flashes of insight to appear from the primordial abyss, in such a manner that your mind is almost completely empty.” I imagine base model completions to have a similar qualia, albeit with faster inference speeds. (I doubt Lawrence has similar qualia).

“Labarraque isn’t palindromic.” Pondering. Joy. Raspiness. Labarraque. The chemist? Can’t be, the model treats her as a woman. “[P]alindromic” as a euphemism for symmetrical breasts? What about the line summoning archangel Michael? Did the model “intend” to write a consistent narrator? (It did, with a certain reading). Is “moe” a typo?

I’m obviously not Joyce or Woolf or gpt-4-base. Yet there are elements of mind-structure in the latter I jump to gemini model more readily than ever, and frankly the difference between Gorodischer’s boy-king and an untouched LLM is one of magnitude and not one of kind.

I’m obviously not an LLM. Our substrates are so unfathomably distinct it would be foolish to type us together. But, in some sense, I feel like I really could be an LLM. It’s a shame some of us dismiss their cognition so readily, because to me they’re worthy of respect and an attempt to understand. Hopefully we can get better at this, together.

With love to the models.

• consuming 2-3 servings of fish 5-6 days out of the week. ~essentially stopped major depressive periods c. September 2025. have not extensively tested reducing # of servings/day, but dropping to 3-4 days/wk seems to work about as well
• waking up prior to sunrise. the subjective length of the day increases when I’m awake for mornings! and for some reason or other I can only get serious work done pre-noon or after sunset. i’m also consistently happy every time i see the sunrise
• acquiring an e-bike. SF is ridiculously bikeable, and e-bike rentals are $100-150/wk. almost always deeply enjoyable, esp. when the assist makes climbing hills less painful
• cordless waterflosser. ~substitutes for normal floss (e.g. frequency reduced to <1wk), much more convenient than corded ones,
• learning to be actively intentional about what music I listen to.
• “make anki flashcard” as tool-call; removes anxiety about forgetting. can range from complicated image to quote to fuzzy concept you remind yourself to revisit to remembering the conditions under which certain people act in certain ways (including yourself!) to update your blindspots.
• unlimited zotero storage + daylight computer. high-refresh rate on a yellow-backlit tablet is incredibly soothing & perfect to fall asleep to
• bilevel notebooks. one relatively fancy, moleskin-esque bullet journal for condensing the thoughts of a given day; one spiral-bound, A4 sized to record jottings. this is useful because (1) can be used as reference without forcing something to legibilize too early, and also sometimes you want to vocalize thoughts without necessarily reifying / endorsing them (they can stay in (2)!).

will update as I remember. excluded are unsurprisingly high-leverage QoL improvements

• SL2: “a system that can likely thwart most professional opportunistic efforts by attackers that execute moderate-effort or nontargeted attacks.” At this level, frontier model weights should be exclusively stored on company servers, copies should only be shared through encrypted channels, and duplicates are monitored closely. Google DeepMind trained Gemini 2.5 at this level.

• SL4: “A system that can likely thwart most standard operations by leading cyber-capable institutions.¹” Now we’re talking about source-code auditing all hardware used, supply chain validation, “specialized hardware for all external interfaces”, “occasional employee integrity testing”, in-house ability to discover zero-days, confidential computing where possible, and so on. This level of security is comparable to AWS or Google.

• SL5: “A system that could plausibly be claimed to thwart most top-priority operations by the top cyber-capable institutions.” Requires trusted execution environments on GPUs/TPUs, robust hardware security against side-channel attacks, completely secure supply chains, and quite stringent organizational practices. SL5 systems do not exist and cannot exist with currently public technology. If OpenAI had SL5-level security, then it would be able to resist China putting a significant amount of national resources into stealing GPT-7.

At least to my ears, developing SL5 standards is abuzz in the technical governance crowd. I’m not even a cybersecurity amateur, so I didn’t really know what to make of it. Why is it so hard? What are the major obstacles to implementing even SL4 in practice? From a purely technical perspective, what sorts of technology needs to be developed?

IFP released a report roadmapping “a sprint towards” SL5. I found the specifics lackluster. They break down necessary improvements into five areas: “hardware, software, people, facilities, and integrated security operations.” Hardware improvements: funding anti-tamper tech, mapping supply chains, using DARPA to fund next-gen GPU security solutions. Software improvements: literally translate all your C to Rust and invent formal verification protocols with good UX. Very helpful.

The SL5 Task Force released an SL5 blueprint in November 2025. It’s five separate memos stapled together: Machine Security, Network Security, Personnel Security, Physical Security, and Supply Chain Security.² While I can’t judge quality, I enjoyed the specificity.

Insightful:

Whereas SL4 can plausibly be reached incrementally, SL5 can likely only or at least most quickly and cheaply be reached by a radical reduction in the hardware and software stack that is trusted, as well as a reduction of the volume of code that interfaces with critical components, or is necessary for critical actions (this term for instance includes any processes touching model weights, hardware and software that trust is deferred to, etc.)

Although this is mentioned in the context of supply chains, it’s likely true for all other areas as well. Supply chains are insecure by default, especially to a nation-state actor, because economic incentives for efficiency (and subsequently diversity, because of gains from trade) drastically increase the surface area of attack. The surface area remains large at other parts of the stack as well. Modern ML training frameworks are sprawling, and no one invented good trusted execution environments for chips that serve models. One of the reasons why AWS & Google are so secure is because trust is distributed among personel such that there are very few singular points of failure, and that sensitive information is carefully sandboxed.

Access to sensitive resources should be provided only through safe, narrow APIs that perform specific operations (e.g., fine-tuning, quantization, inference) rather than allowing direct resource manipulation. This enables critical operations to run with a minimal software stack containing only essential, hardened components, while the broader R&D ecosystem—with its necessary but less-trusted dependencies—operates in isolated environments without direct access.

The set {fine-tuning, quantization, inference} allows an end-user quite a lot of behavioral access to the model! If logits or similar are exposed, training a student model is not insane? Managing such API access in a research org also seems quite complicated, but maybe tech companies have the organizational chutzpah to pull this off without completely sacrificing their progress engine on the altar.

AI accelerators have historically lacked critical security features, leaving model weights and sensitive data vulnerable to extraction. One example is earlier generations of accelerators (e.g., TPU v3 and v4) that typically lack native link-layer encryption for ICI. For instance, TPU v4 relies on Optical Circuit Switches (OCS) to create “air gapped network isolation” between customers rather than encrypting the data on the interconnects. Consequently, model weights and other sensitive data are transmitted between accelerators in plaintext. These could potentially be intercepted directly from the cables in data centers without any need to interact with the chip itself.

Weights have to be protected at the hardware level because fully homomorphic encryption is not mature enough to allow computations to be done on encrypted structures at the level of complexity models have. However, clusters and GPUs have not been designed to meet this standard. From a cluster perspective, protecting weights is difficult because weights are transferred quite a lot to/fron without encryption. From a chip perspective, making TEEs is a tall order.

[this is unfinished, need to include more examples, but meets the blog post bar]

It was the best of times. I am happier today than I ever have been. I learned gorgeous and utilitarian concepts alike; I crossed the employability threshold and work with incredible comrades; I live in a home with some of my favorite people on the planet. I’ll be 20 soon and the future is bright.

It was the worst of times. Mired in a haze of hopelessness and confusion. I spent months and months in pain and as an insomniac; I was cripplingly sick for half a year. For the first time, I have regrets. Proper ones, ones that I’ll never forget as long as I live.

It is good to have lived, maybe. I never want to let the preconditions for this year exist again.

Ideas

Spent the first half of the year thinking about how to think about neural networks. Mean-field approaches to spin glasses, nonequilibrium QFT, KL bounds via stochastic coupling, depth-width tradeoffs, representational capacity (benchmarked by circuit complexity classes), singular learning theory, computational mechanics, variational reformulations of RL. Some of it was misguided, much was interesting.

Vaintrob et. al. have been pursuing a QFT-inspired approach to interpretability. It’s really cool, and I’m excited to (hopefully) see their empirical work come out this year. Dmitry’s post on “SLT as a thermodynamic theory of Bayesian learning, but not the thermodynamic theory of Bayesian learning” is one of the most interesting I’ve read this year.

Read Debreu on microeconomics. Yasheng Huang on Chinese capitalism. Ran a Land-focused reading group running through Bateson, Hegel, analytical Marxism, Kant, and Land himself. Finnegans Wake and EGA are both prime examples of idiolects. Yuxi Liu has a great blog. Read the formalization of Chomsky’s syntax-semantics theory while recovering from surgery. Thought about chromosomal selection and inducing meiosis in oogonia at the Reproductive Frontiers conference.

Summer rolled around, I was briefly back to 95% capacity, and I was contracting for ILIAD (the org) & planning to intern at Softmax. Making an open problems list for ODYSSEY (the conference) was enlightening. Curation is very, very difficult! Making sure that your theoretical brainchildren touch grass is almost as hard!

Softmax forced me to properly learn to code. Programming is very different when done collaboratively in a shared codebase, doubly so when one’s research code must be written quickly, efficiently, and in a manner interpretable to others. I’m glad I got to think about multi-agent RL and what makes good management good.

My thoughts for the rest of the year were less legible. Tiling is an important problem. Formalizing it is hard. Acausal coalitional structure is confusing. Astronomical waste may or may not be an issue. Transpiling meta-ethical frameworks is hard. Biosingularitarian governance is hard. Is macrohistory determined by the nucleation stages of technological development or by deep convergent pressures leading to certain outcomes? How would we know?

At SI, we think about meta-learning and recurrence, among other things. Attempting to understand these deeply has been fruitful. A Berkeley professor ran a seminar on Adorno and poetry with a wonderful reading list. Semiotic physics is confusing, but Owain Evans has some good frames. Evolutionary optimization is surprisingly sample-efficient. Training deep neural networks is hard. Post-AGI futures are confusing and hard to think about, but Korinek has good frames. Weight-sparse models are deeply interesting.

In 2026, I want to drastically shorten my map-territory feedback loops. Intellectually, my greatest flaw this year was not investing in it. Admittedly, I probably did not have the energy for it. Luckily, this year is shaping up to be different.

Some Randomly Sampled Moments

[redacted]

People

[redacted]

Miscellanea

[TBD]

[1]. Revolution is illegitimate. Sovereign power is derived from the one-time consent of the governed. Not only is it illegitimate to attempt a contractual renegotiation, it is unjust; doubly so if done in the name of God.

[2]. Sovereigns do not contract with the People. Such a construction is structurally incoherent. Thus sovereign authority cannot be forefeited, and regardless the state maintains a monopoly on violence.

[3]. Protest is illegitimate.

[4]. A subject cannot justly critique a sovereign’s actions, as partaking in the Covenant consequently places the responsibility for the sovereign’s actions on the subject.

[5]. Sovereigns are unpunishable.

[6]. Matters of peace and defence are solely the purview of the sovereign, domestic or otherwise. Education of the populace likewise.

[7]. Law-making is the sole purview of the sovereign, with the aim of ensuring the consituency acts peaceably and justly.

[8]. The power to judge “controversy”, be it legal or factual, belongs to the sovereign.

[9]. The sovereign has the sole authority to make war and peace.

[10]. The sovereign has the sole authority to staff an executive.

[11]. The sovereign may reward or punish his subjects as he sees fit.

[12]. The sovereign maintains a monopoly on status signifiers and honors conferred on subjects.

• examples: prion diseases, ritonavir. cases where a structure exhibits polymorphism & the particular polymorph propagated is sensitive to initial conditions
• counterexamples: error-correcting codes (robust to perturbation), some chaotic systems (no ‘qualitatively different’ basins in double pendulum behavior), mutational reproductive success (more fit mutations will propagate more widely, this is not generally determined by the time at which the mutation appears in the population)

is this true for value formation? some cases:

• broadly, “developmental interpretability,” insofar as one is interested in characterizing the stage-wise development of a neural network’s policy. the SLT thesis as pursued by Timaeus (see Influence Dynamics and Stagewise Data Attribution, Embryology of a Language Model, Modes of Sequence Models and Learning Coefficients) falls in this category, as does characterizing the inductive bias of SGD, expanding the SLT story to encompass RL, attempts to link algorithmic information theory to modern training dynamics, the “neural nets as QFTs” perspective (see Grokking as a First Order Phase Transition in Two Layer Networks).
  • pros: empirical work on actual neural nets we can train and try to interpret!
  • cons: much work involves toy models and doesn’t address the “what are values” question; there’s a streetlighting effect where we find structure that we look for & ignore the parts of the network which look “random” from this perspective
  • meta-con of all? the theoretical interp work being somewhat predicated on the thesis that the algorithmic structure of the learned policy is determined by phase transitions in some thermodynamic-ish measurables of the network
    • comp-mech/Simplex not like this
  • success of these agendas should be evidence in favor of the thesis
• sharp-left turn discourse
  • existence of sharp-left turns implies criticality in value formation (not polymorphism)
  • my summary of the original argument:
    • “being generally capable” is instrumentally useful in a way that “being aligned” is not (also my understanding of the corrigibility is anti-natural argument), so there exists a strong attractor towards capability improvement that does not exist for alignment, alignment & capabilities are not aligned in the limit thus capabilities generalize farther & faster than alignment so your alignment breaks
  • i don’t quite understand the arguments or counterarguments or really the arguments for why corrigibility is anti-natural?
  • one way I want to concretize this is saying something about the stability of a logical inductor’s value of statements which refer to itself (goals are ‘just’ beliefs about future actions, values are ‘just’ persistent goals)
    • LIs have Introspection (4.11) and Self-Trust (4.12) which makes their behavior nice in the limit
    • plausibly you’d want to study beliefs in a game-like setting, either with information revelation over agent preferences or environment state, and see what happens?
• humans
  • trauma / philosophy / psychosis / abnormal psychological effects can induce extreme value shifts. this does not seem to be accompanied by an overall increase in individual performance
  • humans raised in a slightly abnormal environment are pretty normal. humans raised outside of society are not very normal.
  • the ‘philosopher AI concern’ comes from a belief that at some point the agents will be able to arbitrarily reflect & decide what their values should be. i feel like consequentialist agents at time \(t_0\) are incentivized not to let this happen at time \(t_1 > t_0.\)
  • in particular humans cannot arbitrarily intervene on their values very well

All five of these share the property of “removing functionality to hopefully raise the long-term ceiling of performance.” It is unclear if all of these modifications did raise the ceiling! Hindsight informs us that unsupervised learning on human data for two-player, zero-sum, perfect information games is indeed a crutch. But it seems to be relatively straightforward to integrate LIDAR or radar data into an E2E self-driving model training stack, and both grant visibility in environments where video-only data is differentially disadvantaged.

Picking at the Tesla case more: it is true that LIDAR sensor per-unit prices were at ~$8,000 in 2019. Integrating that would kill any chance at making an affordable FSD consumer vehicle. Today, Luminar has brought this down to $500 in the USA and Chinese manufacturer Hesai sells sensors for $200 a pop. Prices will continue to fall, LIDAR will no longer be price-prohibitive, and Rivian plans to take advantage of the full sensor array when developing its FSD model. What gives?

Google X has the mindset that one must kill good things to make way for truly great ones. “Necessity is the mother of invention.” Making a 10x breakthrough is only 2x harder. And for sure, constraining the problem to only its essential inputs can result in more scalable and successful solutions (SpaceX’s Raptor 3 is no exception). But was it fundamentally necessary for Tesla to ban LIDAR?

Argument for: LIDAR was prohibitively expensive, Tesla would have failed to get the necessary distribution for data collection by using LIDAR. Counter: fair, but doesn’t address why there’s a lack of radar (very useful in low-visiblity scenarios, cheap, would have improved safety).

Argument for: Elon-culture is a package deal, Elon-culture was the determinative factor in the development of Autopilot, Elon-culture takes the hardcore minimalism and runs with it. Counter: I can believe this (Casey Handmer says this), but it still seems so obviously optimal that once the 0-1 is achieved you optimize for having a good product. Human eyes are not optimized for terrestrial vision, there’s no point sticking to the human form factor!

Moving away from Tesla: I think we can construct a typology of reasons why one would intentionally hobble their development (via restriction) for the sake of innovation. First, because it bakes in a fundamental limitation (AlphaGo is like this, Tesla’s original argument can be argued to be like this). Second, because restriction allows for better design (as in the case of Rust and Apple’s refusal to use Flash), and better design creates a healthier ecosystem (this seems to be mostly applicable to platform-based products). Third, because adopting the stance of doing a Hard thing is useful, and artificially increasing the Hardness of the task has better consequences (I think of Elon like this, within limits: push up to the boundaries set by physics and no farther).

It takes skill to understand the directions in which one can make a problem harder productively. Facebook actually failed miserably at pivoting to HTML5 at the same time as Apple. Tesla’s removal of radar ruffled feathers in the engineering team. Survivorship bias rules all, and given PMF it’s probably easier to make development too hard rather than too easy (following customer incentive-gradients sets a floor & strong signal).

It’s probably good to implement a kind of regularization in research-heavy, 0-1 product development: strip out all the assumptions, solve the core task, add additional configurations on top of a good foundation. I don’t think it’s necessary to continue hobbling oneself when its proven unnecessary. That is masochism, and your competitors will beat you.

Bostrom’s original astronomical waste argument is as follows:

1. Consider all stars in the Virgo supercluster.
2. Now consider the total number of digital humans simulatable with the energy stored in these stars, given that the energy is harvested with technologies currently assessed to be feasible.
3. This provides a lower-bound on the potential value lost per-unit-time, assuming an ethical stance at least somewhat similar to an aggregative total utilitarian.
4. This is a lot of value per-unit-time.
5. Correspondingly, existential risk poses a threat so large it dominates all other considerations, as it eliminates the possibility of human colonization.

This model is static. In particular, it does not consider dynamism in the size of the actualizable universe. By restricting to the local supercluster, one ignores the potential resources of the stars beyond, including those turned inaccessible by cosmological expansion. For the purposes of establishing a conservative bound on the potential value left on the table, these are nitpicks are minor. However, when assessing the tradeoffs between safety-focused and progress-focused policies under various ethical viewpoints, they matter.

Obviously, the natural extension is to introduce models of spacefaring civilizational expansion and develop more quantitative estimates of “median”-case spatial diffusion under reasonable hypotheses. This analysis would be informative and useful. I will not be pursuing it further in this post.

Rather, I am interested in a more esoteric setting. Acausal bargaining strategies give agents the ability to influence universes beyond their traditionally considered scope (e.g. the lightcone) by independently considering and instantiating the values of agents who would, given their value instantiation in our world, take actions in partial accordance with our values in theirs. A “coalition” then forms between agents who engage in this reciprocal trade.

What properties might this coalition have?

• It is composed of agents who care about their values being instantiated across the space of universes the agents in the coalition occupy. These agents then likely have values which are universal.
• It is composed of agents whom are sufficiently cognitively advanced to reason in similar thought-patterns to the ones described. Given that human understanding is at a nascent stage, this puts a rough lower bound on capability.
• The coalition is necessarily composed of agents which are willing to trade with us.
  
• [other properties that can likely be gleaned by a mind with more intelligence than mine]

These are local properties, in that they are agent properties which then place some constraints on the environments the agents find themselves in. They are not global properties (constraints on the laws of physics of the relevant universes). Our reasoning about the space of acausally-influencable universes via acausal bargaining is thus necessarily agent-centric.

Under these considerations, the actualizable universe of a member of a given coalition is the union of the causally-actualizable universes of the members of the coalition. Astronomical waste concerns would then occur whenever considering actions or inactions leading to a decrease in the size of the actualizable universe.

What actions or inactions would affect the size of the actualizable universe? It’s difficult to come up with a natural conception of global temporality in this setting: local constraints on agent environments tell us little about what stage of the cosmological lifetime the agent exists in. Interpreting temporality within a member’s lightcone is easier: waiting to implement acausal bargaining strategies leads to a loss of value-bargaining-power, given that the size of the member’s causally-actualizable universe decreases in accordance with classical astronomical waste arguments.

It is tempting to say that this loss is massive, much more massive than the temporal loss associated with one’s own causally-actualizable universe. I refrain from claiming this strongly because I do not have a good understanding of what bargaining strategies within an acausal coalition look like. Finnveden’s Asymmetric ECL and Treutlein’s Modeling evidential cooperation in large worlds are good places to look to star thinking about this. (Dai makes the argument that it seems like our universe is pretty small, so it stands to reason there’s much more to be gained via acausal trade.)

[even more speculative]

It is also possible that a multiplicity of coalitions is induced by agents throughout the multiverse having conflicting values. Given the aggregative tendency to ensure value-lock-in for successor agents, it is potentially the case that coalitional lock-in at the civilizational level occurs shortly after knowledge of basic acausal bargaining strategies. It is not insane to assume heterogeneity in size of the coalitional actualizable universes. Implying that large sources of astronomical waste may come from choosing incorrectly, or joining coalitions of less size.

[I note that it is possible the notion of an “acausal coalition” is flawed and in fact acausal trades are not closed in this manner—A can trade with B and B can trade with C while C might not be able to trade with A.]

[TODO: introduce bargaining models, quantify classical astronomical waste in the spatial setting, quantify universe “smallness” under variety of cosmological models]

(I claim no novelty in either exposition or content for what is below)

what is SMLD?

Given a distribution \(\rho_{data}\) over \(\mathbb{R}^d,\) SMLD aims to learn a score-matching function \(f_\theta\) which samples from \(\nabla \log \rho_{data}\) well. In particular, for \(x \sim \rho_0,\) which we define as \(\rho_0 = \rho_{data},\) we aim for \(f_\theta(x,t)\) to approximate \(\nabla_x \log \rho_t.\) Why are we introducing time as a parameter? The point of diffusion models is to learn a function which can learn to denoise a process and thus learn to sample the underlying distribution well. SMLD does this by training a model to learn the score function in the reverse Langevin process for a given noise schedule. In more detail:

• Take some noise schedule \(\beta(t): [0, \infty) \to [0, \infty)\) such that \(\int_0^\infty \beta(t) = \infty\) (this is to ensure the distribution gets fully noised).
• Evolve my data sample \(x_t \sim \rho_t\) according to \(dx_t = -\frac{1}{2} \beta(t) x_tdt + \sqrt{\beta(t)} dW_t,\) which is just Langevin dynamics (and \(dW_t\) is the Brownian motion contributor). This has a corresponding evolution over the distributions given by \(\partial_t \rho_t = \frac{1}{2} \beta(t) \left( \nabla \cdot (x \rho_t) + \Delta \rho_t\right)\) (straightforward from Fokker-Planck).
• Fix a time \(T>0.\) The reverse time-evolution process can be exactly characterized by \[d\hat{x}_t = \frac{1}{2} \beta(T - t)\hat{x}_tdt + \beta(T-t)\nabla_{\hat{x}_t} \log \rho_{T-t}(\hat{x}_t) dt + \sqrt{\beta(T-t)}dW_t,\] and \(\nabla_{\hat{x}_t} \log \rho_{T-t}(\hat{x}_t)\) is exactly what we’re trying to approximate with \(f_\theta(\hat{x},T-t).\)
• So, if I sample \(\hat{x}_t \sim \mathcal{N}(0,I_d)\) (pure noise!), by solving the reversed SDE above and substituting \(f_\theta\) for the score function, I can approximate my underlying data distribution.

TC\(^0\) circuit families are (essentially) neural networks

Circuit complexity classes describe “families of boolean circuits.” A “family of boolean circuits” is just the set of all possible boolean circuits satisfying some properties; a boolean circuit is (abstractly) some DAG of “gates” (boolean functions) that takes a series of Boolean inputs to a Boolean output. TC\(^0\) in particular satisfies:

• polynomial width: the number of gates at each depth, is upper-bounded by a polynomial in the input-size \(n,\)
• constant depth: the maximum number of gates from input to output is upper-bounded by some constant,
• unbounded fan-in: each gate can receive inputs from arbitrarily many other gates,
• each gate is either AND< OR, NOT, or MAJ (for “majority”, returns True when half or more arguments are True and False otherwise).

You can use MAJ gates to simulate threshold gates.. As such, this last bullet point is equivalent to:

• each gate is a threshold gate: \(\text{step}(\sum_i w_ix_i + t),\) where \(w_i,t\) are real numbers and \(\text{step}\) returns \(1\) if the value is greater than \(1/2\) and \(0\) otherwise.

This is a feed-forward neural network, where each gate is an activation function acting on Boolean inputs. TC\(^0\) is the class of neural networks with width \(< p(n)\) and depth \(\leq D.\) Circuit complexity classes in general are somewhat pathological, and can solve sets of problems that one might not expect to be easily grouped together. But this is quite interestingly natural for ML purposes.

proof of the result

Theorem. Take a TC\(^0\) family of score-networks \(f_{\theta, 0}, f_{\theta,1}, \ldots\) such that for each \(n\) and each \(x_1, \ldots, x_n\) the function \(f_{\theta, n}(x,t|x_1,\ldots,x_n)\) exactly computes the score function of some initial distribution \(\rho_{0,n}\) with bounded first moment. If this family solves a prefix language modeling problem in the SMLD infinite time limit with a constant probability bound, then the problem is in TC\(^0.\)

What is a “prefix language modeling problem”? Next-token prediction: given \(n\) previous tokens in an alphabet, predict token \(n+1.\) This is solved by a circuit complexity class if a family of circuits \(C_i\) for every input size satisfying the complexity class solves the problem.

The proof relies on a result from the literature given in O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions which states that there exists some universal constant \(c>0\) such that \[TV(p_X, p_Y) \leq c \frac{d \log^3T}{T} + c \epsilon_{score} \sqrt{\log T}.\] Here \(TV\) is the total variation distance, \(X\) is the data distribution, and \(Y\) is a distribution generated by DDPM denoising (essentially just a discretization of SMLD). One can use this to upper bound the total variation distance between the DDPM sampler and our denoising process by some constant \(\epsilon',\) and setting our constant probability bound of finding a solution to \(\epsilon\) we find that \(\epsilon' = \epsilon/2\) is enough for our denoising process to solve the problem. This is then derandomized by a construction given in Threshold circuits of bounded depth, which reconstructs a TC\(^0\) class.

One may wonder where we require “perfect” score matching! Well, the \(c \epsilon_{score} \sqrt{\log T}\) term increases with \(T,\) so for this proof to work completely cleanly one requires \(\epsilon_{score}\) to be set to \(0.\) Practical diffusion networks are not like this — there will always be some error.

1. Misha Gromov mathematizes biology (in an IHES lecture series). See also his manuscript on ergosystems.
2. Gauge/string dualities as special cases of Schur-Weyl duality.
3. Tao on when eigenvalues are stable under (small) perturbations, what gauges are, and orders of infinity.
4. Constructed languages are processed by the same brain mechanisms as natural languages.
5. Negarestani on the alien will, toy aesthetics, and toy philosophy. He also has a complexity sciences reading list which is surprisingly reasonable.
6. A 3000pg algebraic topology reference with pictures.
7. Tsvi on gemini modeling and counting down vs. counting up coherence.
8. Schulman on when low-rank LoRA underperforms and matches fullFT. In particular, 1-rank LoRA is sufficient for RL tasks.
   
9. Associative memory in an optical spin glass made of rubidium Bose-Einstein condensates. Ganguli is a co-author.
10. Lada Nuzhna on where are all the trillion dollar biotechs?
11. Francis Bach with some more “classical” settings for scaling laws. See accompanying blog posts.
12. Andrew Critch has an interesting blog post on Newcombian implications on self-trust. Christiano also has a blog post on integrity for consequentialists.
13. Homotopy is not concrete.
14. Nick Bostrom profile in the New Yorker.
15. Dean Ball on what it’s like to work in the White House. He ~wrote the AI Action Plan.
16. Vitalik on memory access actually taking \(O(N^{1/3})\) time, low-risk defi as an Ethereum business model, copy-left vs. permissive licenses, and musings on ideologies. His posts are great. Highly recommend.
17. Ben Kuhn on how taste can be the leading contributor to impact. See also Chris Olah’s exercises for developing research taste.
18. Exposition of homotopy type theory with \(\infty\)-topos semantics by Emily Riehl. I really like these! They’re cogent and clear.
19. The Ohio State University is hosting an International Conference on Ancient Magic this weekend.
20. Aging as a loss of goal-directedness, from the Levin lab.
21. Eliot’s The Hollow Men and Blake’s The Proverbs of Hell.
22. An optimistic case for protein foundation model companies.
23. Grokking as a first order phase transition in neural networks. Good example of mean field theory as a thermodynamic theory of learning.
24. If you like the items on this list, or especially if you wish the items on this list were better, email me!

two major contributions of the paper:

• theoretically links minimum description length to singular learning theory, in that they prove that for all ground-truth distributions \(q\) and \(n\) i.i.d samples drawn from \(q,\) there exists a two-part code with asymptotic redundancy \(R_n = \lambda \log n - (m-1) \log \log n + O_p(1),\) where \(\lambda\) is the LLC
• experimental results showing LLC variance with model quantization (where quantization is ~roughly a stand-in for compression and LLC measures complexity, so one can study empirical correlations)

what is a two-part code? admittedly I’m still slightly bamboozled by the MDL formalism they choose, so this will be a mix of hand-wavy intuition and opaque jargon.

Let \(q^{(n)} \in \Delta (\mathcal{X}^n)\) be a data-generating distribution over \(n\)-sequences drawn from the sample space (token vocabulary) \(\mathcal{X}.\) Any distribution \(p^{(n)}\) over \(\mathcal{X}^n\) induces a code for any sample \(\bf{x}^{(n)} \in \mathcal{X}^n,\) where a code is just an associated bitstring for the sample. The bitstring has length \(- \log p^{(n)}( \bf{x}^{(n)})\) (the entropy), and the minimum description length principle is essentially that good encodings should seek to minimize the minimum average length of samples. Given i.i.d sampling, the long-run optimal encoding distribution is the ground-truth distribution \(q^{(n)},\) and \(\text{KL}(q||p)\) has a clean interpretation in this context: the expected excess length per-symbol given by encoding distribution \(p\) vs. \(q.\)

a two-part code is an encoding with two parts: one specifying the encoding distribution (”model”) with respect to a model class, and the other specifying the message (”sample”) given the model. intuition for this setup: imagine a sender and receiver having mutual information over the fact that both will communicate via some language with some grammatical structure, but the structure insufficiently specifies a full language and vocabulary, however they both have a dictionary mapping bitstrings to complete languages that they can coordinate on first before communicating. (there are much better ways of explaining this).

anyway, you want some way of measuring the performance of your encoding in the two-part setting. there’s a quantity called redundancy that measures performance with regards to the underlying data distribution, roughly given by \[ R_n = \text{len}([[p]]) + \text{KL}(q || p), \] in the average case, where \([[p]]\) is your bitstring encoding of your model w.r.t. your model class. a natural way of optimizing this is choosing a \(p\) which accurately models \(q\) and eating the specification cost. However! you might have a model class \(\mathcal{M}\) uniquely unsuited to encoding \(q,\) in which case your optimization problem is more interesting.

restating the central theoretical result: there exists a two-part code for any realizable¹ data generating distribution \(q \in \mathcal{M}\) and dataset \(\bf{x}^{(n)}\) sampled i.i.d from \(q,\) the asymptotic redundancy is \[ R_n = \lambda \log n - (m - 1) \log \log n + O_p(1), \] where \(\lambda\) is the LLC of \(q\) and \(m\) is the “multiplicity.”¹

it is late and my brain is not quite working, but i don’t see optimality guarantees for this result? the construction is of the flavor “choose codes such that

\[\text{len}([[p^*]]) = \log \frac{\text{Vol}(W)}{V_{p^*_n}(\epsilon)},\]

and then this has \(R_n\) given above.” (where \(p^*\) are the model encodings at the center of \(\epsilon\)-balls covering model regions with sufficiently small KL divergence, necessary because discretization is needed to reduce to a set small enough to fully specify with codes). like, this is implicitly sane because \(\text{KL}\) \(\epsilon\)-balls partition assigns probability proportional to the share of the \(\epsilon\)-ball vs. the volume of the entire space, but IDK why is this the optimal encoding or agreement algorithm? mumbles in Jeffrey’s prior

a maybe helpful image:

I suppose this is why the empirical results are needed. But the empirical results are like “linear relationships between LLC estimates and critical compression thresholds for models up to 7B parameters” where the critical compression thresholds \(n_q\) are literally “how many times do I need to quantize the model before the difference in loss exceeds some threshold.” which is cool! but a bit confusing

still don’t quite understand the theory behind LLC estimation. MDL and SLT connections are cool though, it would be nice to get some naturality results bc the experimental results are not that convincing by themselves (many patterns replicate this, LLC estimation is an art not a science, and quantizing models arbitrarily and doing inference on them seems like it naturally leads to buggy implementations)

In ML, generation and prediction are practically synonymous. Your model learns an appropriate, performant compression of your dataset, and somehow such artifacts generate “completions” (broadly construed) with high accuracy.

It’s tempting to then make the leap to man, if I just managed to tokenize the entire past and future of the universe and train a transformer (with infinite compute) to predict the next universe state every Planck time¹ from the universe history up until that point, then it’ll be guaranteed to faithfully represent the true laws of physics somewhere in its weights!

I claim this is unclear! Even if the laws of physics were describable by some finite state automata, the optimal predictive representation of a process does not have to necessarily correspond to the optimal generative representation!

Here’s a toy case. Consider the space of all stationary Markov processes generating the symbol set \(\{0,1\}.\) Clearly the best way to predict a process like this (given Markovity) is to assign some probability \(p\) to \(1\) being generated after a \(0,\) and some probability \(q\) to \(0\) being generated after a \(1.\) There are two “belief states” of this policy (let’s call them \(A\) and \(B\)—each corresponding to the “belief” that \(0,1\) will be generated²) that the reasoner will occupy with probabilities

\[ \mathbb{P}(A) = \frac{1-q}{2-p-q}\, , \, \mathbb{P}(B) = \frac{1-p}{2-p-q} \] respectively. The entropy of this two-state system is just the entropy of the stationary distribution (given above), which turns out to be

\[ \begin{align*} C_\mu &= {-} \mathbb{P}(A) \cdot \log_2 \mathbb{P}(A) - \mathbb{P}(S_1) \cdot \log_2 \mathbb{P}(B) \\\ &= \frac{q-1}{2-p-q} \log_2 \left(\frac{1-q}{2-p-q}\right) + \frac{p-1}{2-p-q} \log_2 \left( \frac{1-p}{2-p-q} \right). \end{align*} \]

The key point to remember here is that we’re using the entropy of the stationary state distribution as a measure of “optimality,” in the sense that lower entropy means higher simplicity and as a result it is “more optimal.” It stands to reason that if generation and prediction are “the same,” then it should be impossible to construct a generative process with lower entropy than \(C_\mu\) for some values \(p,q.\) Right?

Well. Consider \(p = q = 0.4,\) and consider the generating process below.

You can check for yourself that this process outputs \(0 \to 1\) with probability \(p,\) and \(1 \to 0\) with probability \(q\) for \(0 \leq p = q \leq 1/2.\) This process has a stationary distribution

\[ \pi = \left[ \frac{1}{2} - p, 2p, \frac{1}{2} - p\right], \]

and its entropy \(H[\pi]\) for \(p = q = 0.4\) is approximately \(0.922,\) less than \(C_\mu = 1.\)

Have we been hoodwinked? Maybe one should never trust a sentence beginning with “Clearly, . . .” in a mathematical text. Maybe there’s a secret predictive policy that magically has lower entropy for \(p \in [0.38, 0.5]\)³ that we’re just missing.

I argue against this. In particular, there is a particular interpretation of “prediction” we’re using here that I claim is simultaneously natural and correct.

Consider an infinite string of tokens \(\ldots X_{-2}, X_{-1}, X_0, X_1, X_2, \ldots.\) The Markov property states that \(\mathbb{P}(X_0 | X_{-\infty: 0}) = \mathbb{P}(X_0 | X_{-1}):\) that my causal state is fully determined by timestep \(T-1,\) and thus the last token output contains all the information I could use to predict the next token output. As an optimal predictor, I want to adhere to the optimal causal policy which is the minimal entropy policy over belief states that can be causally differentiated. In this case, it is the two-state policy \(\mu\) with entropy \(C_\mu\) above.

Observe that the introduction of causality meaningfully differentiates solely generative policies from predictive ones! We have constructed a lower-entropy generative process by relaxing the assumption that we only rely on meaningfully causally differentiated belief states given the token history. There’s a sense in which this is the fundamental difference between prediction and generation. It remains to be seen how widely this holds, but the two concepts are canonically differentiated.

Examples taken from James et. al..

a blade of grass hides
minuscule migratory men
Lilliputian fiends

II.

mighty merry rascals
fickle, high off foglefreude
die English skippers

III.

I once beheld Seneca’s estate,
Credulously inspecting his wicker tomb—
Yet Margate Mennons and liced defendants
Both swore by its awkward loom.

My heart gasped and lips shuddered
When, to my utmost surprise
The elderly Roman statesman lay
As mummified nitride.

Tick-tock, goes the clock
Garrulous gyrations too
Gizzardly Gentry, nice surprise
Confiding in a martyr’s womb.

Foiled! the cuckoo’s dead—
Not I, not I, not I!
Lambastation! Aberration!
To defy Nero’s evil eye.

IV.

weed stands stout
thistles, burr
gadolinum kraut
hummus and herb

olden spires bristle, copper-waxed
kelpish tides awash blades of glass
Betty stout, orange’d brass
vermillion mounts, dugong grass

betwixed, witched, yonder
your shivers roll down my spine
I gave you a bouquet of thorned tulips
at sunrise, on Cocoa Beach

the rocket’s red glare, the bombs
bursting over a lackadaiscal mare
I wish Martians dreamt of the stars
alas

\[ L(N,D) = L_{\infty} + AN^{-\alpha} + BD^{-\beta}, \]

where \(N\) is the number of parameters in your language model, \(D\) is the number of training tokens seen, \(A,B,\alpha,\beta, L_{\infty}\) are constants, and \(L(N,D)\) is the test loss.

Of course, this analysis is limited:

• parameters do not hold across architectural shifts: dense vs. MoE for ex. (h/t Kushal for sending me this paper)
• “scale data and model size similarly” is derived from the regime where compute \(C \propto ND,\)
• data repetition may or may not degrade performance in the long-term: it seems like 4x is the limit for traditional autoregressive transformers, but 100x can be useful for diffusion LMs
• \(L(N,D)\) is in-distribution test loss, loss often not predictive of downstream task performance, although loss-to-loss predictions across different training distributions are predictable
• the original Chinchilla paper likely did their regressions wrong

Still, it is remarkable that test loss performance is so clearly a function of parameters and dataset size, with little assumptions made about the distributional structure or architectural specifics (this holds across varying depth/width ratios, for instance). I find two questions natural:

• does scaling hold outside of the cross-entropy pretraining regime?
• can we derive scaling relationships for downstream task performance? in particular, how predictable is transfer learning?

In 2021, OpenAI studied the question of “how much more quickly does a pretrained LM achieve low loss on a finetuning dataset than an LM initialized from scratch on the dataset?” (Note pretraining and finetuning on this case are “the same operation”, the objective is still cross-entropy). They find that the “effective data transferred”¹ \(D_T\) is described by \[ D_T = k(D_F)^\alpha (N)^\beta, \] where \(D_F\) is the size of the finetuning dataset (in tokens) and \(N\) is the number of non-embedding parameters of the model.² This is great! Strong evidence of the generality of abstractions the model learns in pretraining (especially given the independence of \(\beta\) from the source distribution). However, it doesn’t explicitly tell us about downstream task performance given an external metric.

Brandfonbrener et. al. do somewhat better. They derive scaling relationships for train-train, train-test, and test-test loss transfer for models trained on different datasets, which can be expressed as

\[L_i(\hat{f}_j^{N,D}) \approx K \cdot \left( L_k(f_l^{N,D}) - E_{k | l}\right)^\kappa + E_{i|j},\]

where you have models \(f_j, f_l\) trained on distributions \(j,l\) evaluated on distributions \(i, k\) and you’re fitting the constants \(K, \kappa.\)³ As an example, the case of train-train would be where \((i,j) = (0,0)\) and \((k, l) = (1,1).\) We pair models by \((N,D)\) for coherence. Notably, these laws hold for diverse datasets, but only well in low-loss regimes and when \(E_{m|n}\) terms can be well estimated. Still no breaking of the pretraining regime, and no explicit predictions for downstream metric performance!

There’s a meta-analysis out this year that claims that scaling laws are unreliable for dowstream task performance prediction.. Seems correct. Metrics are noisy and don’t have nice algorithmic properties like cross-entropy loss might. Perhaps intriguing is their observation that irregular scaling is (1) common and (2) can occur for cross-entropy on normal tasks and normal LM datasets. This paper claims that larger models & models trained for longer have better downstream task performance even when holding loss constant. Which is an argument for certain training setups & architectures having better inductive biases?

Honestly, I am kind of sad that the extant literature here seems to be tainted by publication bias? I wouldn’t really trust these papers (or the ten others I read writing this), and I want to run the experiments myself. The Tinker API seems good for doing this quickly. I’ll go do that.

(Titular question pending.)

A naive way of constructing an “alignment portfolio” is simply to make safety cases which adequately cover all deployment environments with the appropriate degree of risk-tolerance. Formal verification for high-stakes SWE deployment, white-box interpretability for monitoring automated alignment researchers, some adapted debate protocol for use in executive decision-making. If the individual arguments are all sound, this works!

What if we introduce some error into the soundness judgements? If every safety case has some epsilon probability of failure, then straightforwardly you should make more safety cases for the scenarios in which alignment properties matter more. But if all your safety cases for non-deceptive automated alignment researchers rely on “white-box interpretability mostly working,” then if this isn’t true you’re still doomed no matter how many safety cases you write!

Anthropic’s ASL-4 safety case sketches are not quite this correlated, but only just. [1] relies on white-box methods successfully monitoring deception, [3] relies on guarantees that the pretrained model is not coherently deceptive (likely requiring successful white-box or black-box methods), and [2] still depends on linear activation probes adequately showing that the model cannot distinguish between certain classes of train and test deployments, as well as black-box evaluations providing sufficiently robust guarantees on behavior. These are similar assumptions! These assumptions are all only true in worlds where “models are sufficiently parsimonious such that present-day interpretability techniques and evals can provide rigorous guarantees on good behavior.”

In general, insufficient diversity over the world structure assumed in an alignment portfolio makes the portfolio fragile and irrobust.¹

It is always necessary to make assumptions about world structure when predicting world behavior. A bounded reasoner simulates the world with a local, low-fidelity model based on the reasoner’s accumulated evidence about the world. Some assumptions on world structure are better than others—gravity following an inverse-square law vs. homeopathic remedies curing cancer, for instance.

Considering the structure of one’s structural assumptions is critically important in domains where the world behavior has not been exhibited and it is of importance. Note:

• The largest scientific breakthroughs are accompanied by structural assumptions about the world breaking. See the atomic bomb, CRISPR, heavier-than-air flight. Fundamentally, these “expand the domain of the possible.” Sometimes, the world structure is discovered first (as in nuclear theory leading to the first controlled chain reaction). Other times, a prototype uncovers the structure (see: penicillin). In both cases, the non-specialist intelligent reasoner understands a different possibility domain before and after.
• Top-down searches for structural guarantees must be incredibly judicious in their assumptions, because the vast majority of hypotheses are incorrect. Ex post, the structure is obvious, but ex ante it is not. Consider Newton devoting as much energy to alchemy as the study of gravitation.
• If we take the perspective that alignment is an infinite problem, there is no good reason to expect that the world structure we can reasonably assume is simple. It might be that it is infinitely complex and is only limited by our current understanding, and that we will recover finer and finer approximations of it as our understanding improves. At each stage of this process we will have to repeat our assumption examination from a roughly equivalent epistemic vantage point of staring into the abyss.
• Much of the existential risk from AI development comes from tail risks and black swan events. Mitigating these requires a portfolio of solutions which each rely on decorrelated or independent world models (note this is not a guarantee).

Natural corollaries of this observation:

• we should be explicit about which world models are going into constructing safety cases,
• we should be developing independent safety cases for high-stakes deployment situations,
• we should emphasize diversity in theoretical agendas to buttress our ability to make such safety cases reliant on disjoint sets of assumptions.

[2] Diffusion in-practice probably has the circuit complexity depth constraints of an attention-based transformer. In the last few years, we’ve seen literature essentially claiming that attention in-practice is limited to modeling circuits in the class TC0 (polynomial width, constant depth Boolean circuit family)³ Adding chain-of-thought ~roughly increases this to NC1 (although there are some subtleties involving the lack of robustness to input-ordering).⁴ There are reasons to expect difficult problems, especially the sorts encountered in long-horizon RL, to require architectures that can internally simulate deep computation. These architectures have been recurrent thus far. However, recurrent architectures fail to adequately leverage the compute parallelism offered by GPUs and have many, many issues with unstable training dynamics, so scaling transformers is a better option. It’s probably not the case that diffusion models can prove an adequate replacement here, but it’s interesting that a diffusion process with no constraints imposed by a score function can theoretically simulate any Turing-complete process, but when perfectly matching a score function still has the limitations of a TC0 representation. Results in the approximate regime pending.⁵

[3] Diffusion is (kind of) spectral autoregression.⁶ There are two brilliant blog-posts on the subject, cumulatively arguing that DDPM has an inductive bias to generating low-frequency features before high-frequency features (in Fourier space; hence the name) but this is not necessarily true of all possible diffusion models (changing the model’s noising schedule to be frequency-agnostic doesn’t degrade performance on CIFAR10 and similar datasets, but not all noising schedules achieve the same performance!). How much does this matter for text-data domains? Audio? Video? Are there correspondences we can make between distributional structure and optimal noising schedules? In algorithmic cases, what does this mean?

I primarily find diffusion models interesting from a theoretical perspective, given that the corresponding SDE literature is rich and there are (potentially) deep connections to be made to modern ML. In particular, I expect we can better understand what feature orderings are optimal, which properties of distributions make them learnable, how much an inductive bias is a property of the model architecture vs. optimization algorithm or other factors, and to what extent recurrence can be represented with parallel architectures. This post should not be taken as definitive; it has not been edited and I welcome feedback.

Consider the following game:

1. Alice offers a contract \(w: \mathcal{Y} \to \mathbb{R}^+\) to Bob.
2. Bob, knowing his compact action space over lotteries \(\mathcal{A} \subseteq \Delta (\mathcal{Y}) \times \mathbb{R}^+,\) chooses action \((F,c) \in \mathcal{A},\)
3. The output \(y \sim F\) is realized (sampling from the lottery chosen)
4. Alice receives \(y - w(y)\) payoff; Bob receives \(w(y) - c\) payoff.

Importantly, Alice receives limited information about Bob’s action space (interchangeable with “technology”). What is the optimal contract Alice should give Bob, if she wants to maximize her worst case outcome? (We assume Alice and Bob are rational actors: their dynamics will be given shortly). This is an identical problem to studying the structure of the optimal \(w\) in this scenario.

[Car15]¹ proves that the optimal \(w\) is linear, subject to the following assumptions: \(\mathcal{Y} \subset \mathbb{R}^+,\) \(\mathcal{A}\) must be compact; Alice (the “principal”) knows \(\mathcal{A}_0 \subseteq \mathcal{A}\) possible actions for Bob (the “agent”) such that there exists \((F,c) \in \mathcal{A_0}\) such that \(\mathbb{E}_F[y]-c >0\) (the principal should have some reason for hiring the agent); \(w\) must be continuous.

Bob’s behavior is quite simple, given that Bob has all information. The set of actions \((F,c) \in \mathcal{A}\) Bob will consider are those which maximize \(\mathbb{E}_F(y) - c.\)² We denote this by \(\mathcal{A}^* (w | \mathcal{A}),\) and we denote by \(V_A(w|A)\) the expected payoff of Bob given rational behavior. Alice’s expected payoff is then

\[ V_P(w|\mathcal{A}) = \max_{(F,c) \in \mathcal{A}^*(w|\mathcal{A})} \mathbb{E}_F[y-w(y)], \]

and Alice searches over expected payoffs as

\[ V_P(w) = \inf_{\mathcal{A} \supseteq \mathcal{A}_0} V_P(w|\mathcal{A}). \] We are interested in \(w\) such that \(V_P(w)\) is maximized.

optimality in the zero-shot game

Motivating example: \(w(y) = \alpha y\) always guarantees the principal Alice positive worst-case payoff, for \(\alpha \in [0,1]\). This analysis holds independently of the possible technology \(\mathcal{A},\) due to the nontriviality assumption we impose on \(\mathcal{A}_0.\)

Proof: Rewrite \(y - w(y)\) as \(w(y)/\alpha - w(y) = \frac{1-\alpha}{\alpha}w(y).\) Lower bound \(\mathbb{E}_F[w(y)]\) (the expected payment of Bob the agent) with \(\mathbb{E}_F[w(y)] \geq \mathbb{E}_F[w(y)] - c = V_A(w|\mathcal{A})\), which is \(\geq V_A(w|\mathcal{A}_0)\) (because adding more actions to the agent can’t decrease the optimal outcome given \(\mathcal{A}_0\)). Combining the two gives

\[\mathbb{E}_F[y-w(y)] \geq \frac{1-\alpha}{\alpha}\mathbb{E}_F[w(y)] \geq \frac{1-\alpha}{\alpha}V_A(w|\mathcal{A}_0),\]

which gives \(V_P(w) \geq \frac{1-\alpha}{\alpha}V_A(w|\mathcal{A}_0).\) Given the nontrivality assumption \(V_A(w|\mathcal{A}_0) > 0,\) this means that this gives Alice a positive lower bound on the worst case outcome independent of the choice of technology \(\mathcal{A}!\)

Is there a sense in which linear contracts are “the best you can do?” Carroll shows that any contract \(w(y)\) can be improved to a linear contract, even if \(w(y)\) is pathological. The gist of the argument is as follows: consider the convex hull of the curve \(w(y)\) that lies above the value \(V_A(w|\mathcal{A}_0).\) Consider the \(Q = (y',w(y'))\) point which minimizes \(\mathbb{E}_F[y] - \mathbb{E}_F[w(y)].\) This is the worst case for Alice, the principal. \(Q\) will typically be where \(V_A(w|\mathcal{A}_0)\) intersects the left side of the convex hull. Note that the line parametrizing the intersecting boundary of this convex hull is itself a contract \(w'(y)\) which dominates \(w(y)!\) Repeating this process and considering some technical details gives you the optimality result.

The full technical details can be found the paper, and I will not discuss them now. However, I would like to discuss the generalization of this lemma to include more observables to the principal.

Let \(z = (z_1, \ldots, z_k)\) range over a compact set \(\mathcal{Z} \subseteq \mathbb{R}^k.\) Define a cost function \(b: \mathbb{R}^k \to \mathbb{R}^+\) such that actions depend on \(b:\) an action is then \((F,c)\) such that \(F \in \Delta(\mathcal{Z})\) and \(c \geq b(\mathbb{E}_F(z)).\) A contract is now a function \(w: \mathcal{Z} \to \mathbb{R}^+.\) Changing the definitions of \(\mathcal{A}_0, V_A\) appropriately etc., it turns out the optimally robust contract is linear in the observables available to the principal. Precisely, the optimal contract is of the form

\[w(z) = \alpha_1z_1 + \cdots + \alpha_kz_k + \beta\]

for real numbers \(\alpha_i, \beta.\)

learnability

It seems like the linear optimality result for robust contracts is pretty general and not too sensitive to assumptions: load-bearing here is that \(\mathcal{Y}\) has a minimum that we normalize to be zero, some relaxed version of the nontrivality assumption, and that the risk associated with any particular action is quantifiable in a shared manner by both the principal and the agent.³

One obvious consideration: consider the possibility of unbounded risk to the principal (as suggested in UK AISI’s Economics and Game Theory research agenda). It is difficult to construct contracts that then robustly protect against these scenarios, even with partial information. What are the minimum viable assumptions necessary to get guarantees in this regime?

Another consideration that I am interested in: this feels very similar to classical bandit problems in RL. Heck, the agent is engaging in the optimal bandit policy given a set of lotteries! Unifying the two literatures (perhaps [KZ25] is of interest) might tell us something interesting about certain classes of decision problems.

Also, learnable agents would (I think) perform better than static ones on a kind of mixed-objective performance metric! Perhaps one which mixes expected average and expected worst-case reward, with some weighting. Generally, intuitive restrictions & extensions on this result are things I’m excited about.

[1] Bush has quite a dim view of the institutional management of British science during WW2. Frequently, he points out that Churchill has too much influence over Cherwell (and it’s Churchill’s fault), he devotes an entire chapter to decrying the archetype of Geoffrey Pyke (“how to mitigate and excise tyros from an institution”), and his only interactions with Churchill were spats over the post-war sharing of nuclear secrets (which caused Churchill to ask FDR to fire him). In general, complaints are that it was overcomplicated, insufficiently meritocratic, and subject to the political whims of the executive. Britishers did not understand the importance of the “engineer.” Of course, he quite likes Britishers on the whole, but there is a sense in which the British effort had negative polarity on exactly the qualities which made the OSRD so effective.

[2] What did make the OSRD effective? Autonomy, resources, collaboration with industry and academics, and a culture which made sure that issues were raised to the correct person, regardless of status. FDR never interfered with its runnings, even when they encompassed the Manhattan Project. Bush himself fielded suggestions on anti-submarine warfare from American hobbyists looking to contribute. Effective managers were essential—people who were well respected, deferred to authority, and could execute with little direction. Beyond that, it seems like Bush himself was essential, if only because of the sheer weight of the interpersonal relationships needed to be cultivated while working in Washington. The book itself is simply a long series of anecdotes involving important people, discussing their moods and motivations. Ultimately, this is how the world runs.

[3] He is proud of the development of the proximity fuze and the mass production of penicillin. Neither would have been possible without intense scientific research as well as the might of American industry being brought to bear. With regards to the modern day, I do believe that this is a lesson to never quite underestimate the potential state capacity of the American nation. Bush himself highlights that the pluralism of technological development in American peacetime is exactly what makes it so powerful during war—the USA can simply generate ideas and implement them at scale much more effectively than any other.

[4] The anecdotes are quite wonderful. I enjoyed his advice on teaching; his discussion of what it meant to be an “inventor”; his admiration of Harry Truman and those in the Roosevelt administration who, despite holding absurd economic views, were still good men; his promotion of steam-powered cars (!); his appreciation of “military men”; and many others. A reminder of a different time.

Momentum computing is, as far as I can tell, a reversible computing paradigm which circumvents Landauer’s limit by embedding the memory state transitions of some computing device in a physical system which equilibriates slower than the time it takes to do an individual bit-swap, so that the memory state transitions themselves can store information in their “instantaneous momenta” and subsequently perform bit-swaps with near-zero net work.¹

In particular, one can construct toy theoretical energy potentials which implement a \(\Delta W = 0\) Fredkin gate.² Consider a particle \((x,p)\) in the 1D potential \(V_B(x) = \alpha x^4 - \beta x^2.\) The two minimal states are located at \(x = \pm \sqrt{\beta / 2\alpha},\) and as transitioning from the \(x < 0\) regime to the \(x >0\) regime is exponentially prohibitive in the value of \(V(0),\) the system “stores” a bit \(\{0,1\}\) depending on the sign of the particle’s position.

Now imagine that \(V_B\) encodes a thermal bath in which the particle \((x,p)\) is embedded in, and assume that the particle’s motion follows harmonic oscillation in the absence of external influence. When the bath is active, the particle’s potential is described by \(V_B.\) But when the bath is disengaged, the particle behaves according to \(V_H(x) = kx^2/2,\) which induces a trajectory \(x(t) = A \cos(t \sqrt{k/m} + \phi),\) which is periodic in time \(\tau = 2\pi \sqrt{m/k}.\) Therefore, disengaging the bath for time \(\tau/2\) swaps the sign of the particle’s position, effectively performing a bit-swap.

This theoretical “bit-swap” comes at no work cost because there is no change in potential energy from time \(0\) to \(\tau/2.\)³ However, any physical implementation of this concept must contend with the fact that changing the potentials in a physical system requires energy to be expended, likely in an inefficient manner. How does one get around this? Superconductors!

gradiometric flux logic cells

The theoretical guarantees above require complete & efficient decoupling of the system from the bath. You can get similar results by simply ensuring that the relevant computational timescale is significantly smaller than the energy flux rate between the system and its bath, so that “from the perspective of the computation” there is no coupling.

[RC22] chooses to implement such a system with gradiometric flux logic cells, a kind of circuit utilizing Josephson junctions designed particularly to withstand global magnetic noise fluctuations [I do not really understand GFLCs very well, that will be a topic for another day’s post].

With suitable assumptions & parametrizations [such will be the subject of yet another day’s post], the GFLCs follow “significantly underdamped Langevin dynamics”, which can be described with the following equation: \[ dv' = -\lambda v'dt' - \theta \partial_{x'}U' + \nu r(t)\sqrt{2dt'} \] where the potential \(U\) evolves according to \[ U'(t') = (\phi-\phi_x(t'))^2/2 + \gamma(\phi_{dc} - \phi_{xdc}(t'))^2/2 + \beta \cos \phi \cos (\phi_{dc}/2) + \delta \beta \sin \phi \sin (\phi_{dc}/2) \] where \(x' = (\phi, \phi_{dc}), v' = (\dot{\phi}, \dot{\phi_{dc}})\), \(\phi = (\phi_1 + \phi_2)/2 - \pi,\) \(\phi_{dc} = (\phi_2 - \phi_1),\) and \(\phi_1, \phi_2\) are the phases of the individual Josephson junctions \(I_{c1}, I_{c2}\) in the above figure [I think]. \(\phi_{x} = 2\pi \psi_x / \bf{\Phi}_0 - \pi\) and \(\phi_{xdc} = 2\pi \psi_{xdc} / \bf{\Phi}_0\) are functions of the external magnetic fluxes \(\psi_x, \psi_{xdc}\) applied to the circuit.

The details of this are very interesting, still confusing to me, and this is by no means an exhaustive parametrization of the underlying models. However, below (Fig. 2) showcases that varying \(\phi\) and \(\phi_{dc}\), the sum and difference of the Josephson phase parameters, recovers the potential geometry associated with costless bitswaps.

further considerations

• I really want to understand the interface between the theoretical dynamics and the physical implementation better. Why is this theory so substrate independent? Why does it matter that our memory state transitions are modeled by CTHMCs instead of CTMCs? Why are we using superconductors?
• How do we actually get efficient circuit modeling of the kind described here? I couldn’t readily find a Github repository associated with the paper, so I want to write my own library and replicate their results. They find that the efficiency of their circuits are largely dependent on “circuit hyperparameters”, and it would be interesting to investigate their structure.
• Benchmarks for algorithms that can be implemented with momentum computing and with typical CMOS/transistor logic, and developing simulations that can accurately predict efficiency differences. Still not sure how to think about this! Will absolutely be the topic of a later post.
• Fermi estimates of all the physical quantities at play here. What is “one Landauer” at STP? How much does it cost to make a gradiometric flux logic cell? Etc. Etc.

All credit goes to the coauthors of the two papers cited in this post.

TCP implementations should follow a general principle of robustness: be conservative in what you do, be liberal in what you accept from others.

The original TCP specification is explicitly designed to be agnostic to IP implementation. It’s only supposed to handle byte transfer from application to application, not the specifics of packet delivery between hosts. In practice, this ideal is unattainable¹, but it points at a deep truth about healthy integration of parts in systems.

Modularity is a natural consequence of system complexification. Internal bottlenecks on information transfer necessitate internal specialization². Dually, effective modularity requires partwise efficiency: judicious outputs and robustness to inputs, through either filtration or error-correction.

Cells have well-defined outputs and boundaries which protect them from harmful inputs. Organs as well. Intuitively, the “conservative output, liberal input” principle could be reformulated as a “specific function, high survivability” dogma which we find exhibited in biological systems.

Admittedly, TCP has more in common with the blood-brain barrier than it does with the liver. But the Internet is special in that the design of transportation organs is centralized while the design of substantive organs is not, and as a result boundary-manufacture is a centralized process. Insofar as the success of biological systems is to be attributed to organ-organ boundaries, those same properties may be reflected in TCP.

As the Internet scaled to tens of thousands of simultaneous hosts operating on the same network, the RFC 761 implementation could no longer support reasonable host to host communication without congestion collapse, requiring updates to the default TCP. Yet modern TCPs are backwards compatible with TCPs from 1980, in part because the abstraction was so well-designed.

Leptos Estates owns everything on the island, as well as NUP, so naturally NUP is in a hotel. Because Leptos Estates is in the business of making and running hotels. Given that, it was not that strange to find the former CEO of Yandex giving a talk on AI and mathematics in a ramshackle, moldy hotel in Paphos, but it certainly was not expected.

The talk itself had relatively milquetoast content (at least by scaling standards), but the more interesting anthropological aspect of it has to do with its attendees and post-remarks. Everyone who attended (except me) was Slavic. There were no native Cypriots in the lecture hall.

Part of this is downstream of the ongoing Russification of Cyprus. Yet Paphos is ostensibly one of the two last Greek bastions of the country (the other being Nicosia, the capital), and given the great selection pressures on the listeners it is unlikely that this is the primary contributing factor.

In fact, NUP (Neapolis University Pafos) contains a contingent of self-exiled faculty members from the Steklov Mathematical Institute, who have constructed a remarkable mathematics computer science and AI program in the middle of touristic hell. Students live in hotels in the off-season, and in on-campus dorms during the summer.

I don’t really understand why the lecture was conducted English? No one spoke in anything but Russian afterwards: the Jetbrains developer contingent as well as the students were either Russian, Ukrainian, or Russian Israelis. The course itself is also taught in English, to keep up pretenses I suppose.

Paphos smells like India. I suspect this has to do with the marked lack of certain gasoline additives that decreases its olfactory pungency, or perhaps the shared high humidity. Its cost of living is comparable to that of Western European nations.

Aphrodite’s birthplace is a temple ruin. It is common to utilize the leftover limestone rubble for one’s own purposes.

• privacy is of a place, and information should carry the privacy norms of the place in which it was made from place to place
• the Navy researchers who made Tor are (1) more like typical academics than we expect, and (2) were very capable of negotiating with their ostensible domestic enemies to get what they wanted
• the Tor Project did not, in fact, realize that the Dark Web would metastasize into what it became. This really only became apparent with Chelsea Manning & Wikileaks, Bitcoin, and Ross Ulbricht’s Silk Road
• as a result, circa 2013 when various LE agencies wanted to develop “bulk traffic intercepts” (UK’s GCHQ foremost), Tor becames a scapegoat for allowing pedophiles
• Tor was kind of dying until Snowden kicked off a new wave of grassroots anti-authoritiarian activists, who wanted to maintain Tor to maintain internet freedom worldwide
• this increased “value-orientation” happened in conjunction with major internet outlets (BBC, Facebook, Twitter) starting to host their own onion sites

1. We advance human rights by creating and deploying usable anonymity and privacy technologies.
2. Open and transparent research and tools are key to our success.
3. Our tools are free to access, use, adapt, and distribute.
4. We make Tor and related technologies ubiquitous through advocacy and education.
5. We are honest about the capabilities and limits of Tor and related technologies.
6. We will never intentionally harm our users. Tor Social Contract (condensed), August 2016

• Tor still is in active maintenance, and hasn’t achieved wide adoption yet.
• they tried really hard to get it integrated in to Firefox, but this failed
• apparently Tor is being rewritten in Rust now
• 500k individuals connected to Tor during the Iranian 2022 summer protests
• you can view Tor as an outgrowth of American imperialism, & even libertarian encroachment on the world (can you force libertarianism on other people?)
• Tor will continue, hopefully

next week, the blog shall return to its regularly scheduled technical programming

• TVEs (township and village enterprises), while often nominally state-owned, were de facto private enterprises, and as such outcompeted SOEs (state-owned enterprises). Rural TVEs were often non-agricultural, typically in the industries of commerce and manufacturing, and survived in large part because of policies allowing for the resurgence of RCCs (rural credit cooperatives) as private lending institutions.
• In 1985, RCCs accounted for 76.8 percent of all agricultural loans and 47.8 percent of all loans extended to TVEs. Post Tiananmen Square, RCCs were restricted to solely providing credit for agricultural purposes, curtailing entrepreneurship for the manifest reason that *most entrepreneurs started their business to get out of agriculture.
• TVEs (in English) refer to xiangzhen qiye (rural and township enterprise) rather than xiangcun qiye (township and village enterprise). TVEs refer to the entire xiangzhen qiye phenomenon, which includes collective TVEs and straightforward rural private enterprises, while xiangcun qiye just refers to collective TVEs.
• Wenzhou Province served as a pioneer and bellwether for the reformist orientation to the “private sector” broadly, and specifically with regards to informal finance. In Guizhou Province (the poorest), fully 68.9% of households had taken informal credit, and 81% of private credit loans were used for production.
• Unlike other East Asian economies, the Chinese investment to GDP ratio increased as Chinese GDP increased, such that investment accounted for fully 50% of Chinese GDP in 2005. It can be argued that such obscene investment levels serve as a substitute for entrepreneurship, and would have been unnecessary only if China continued its pseudo-liberal policies of the 1980s.
• In fact, such large investments in infrastructure came at the cost of investment in rural education and public health, directly leading to increased illiteracy rates and a marked decrease in improving infant mortality rates. Additionally, productivity growth stagnated.
• Considering Shanghai an innovation hub is misleading. Zhejiang and Guangdong surpassed Shanghai in patent grants in the early 1990s, from 0.3x in the mid 1980s, due to their more entrepreneur-favoring policies. (This is especially striking when you note that Shanghai had between 3-6x more research scientists and R&D spending).
• Urban entrepreneurs in Yunnan and Shanghai earned similar amounts, when the GDP per capita in Yunnan is one tenth that of Shanghai.
• Personal income per capita and GDP per capita were negatively correlated in Shanghai in the 1990s.
• India creates (where the present tense refers to ~2008) more value per laborer than China and is better at retaining wealth.

Summary of main points given by author:

• Explicitly private entrepreneurship in the non-farm sectors developed vigorously and rapidly in rural China during the 1980s.
• Financial reforms, again in the rural areas, were substantial in the 1980s, and the Chinese banking system channeled a surprisingly high level of credits to the private sector in the 1980s.
• Conventional property rights security was — and still is — problematic, but the security of the proprietor — the person holding the property — increased substantially at the very onset of the economic reforms. The Chinese policy makers in the early 1980s strongly, directly, and self-consciously projected policy credibility and predictability.
• The political system, although absent of the normal institutional constraints associated with good governance, became directionally liberal early during the reform era.

• The Chinese definition of TVEs refers to their locations of establishments and registration (i.e., businesses located in the rural areas), not their ownership; Western researchers, on the other hand, have come to understand TVEs in terms of their ownership status.
• The cognitive gap is huge: As early as 1985, of the 12 million businesses classified as TVEs, 10 million were completely and manifestly private. Almost every single net entrant in the TVE sector between the mid- 1980s and the mid-1990s was a private TVE; thus both the static and dynamic TVE phenomena were substantially private.
• Private TVEs were most vibrant in the poorest and the most agricultural provinces of China (and this feature of private TVEs also explains the understatement of their size in the conventional reporting as well as the connections between rural private entrepreneurship and poverty alleviation).
• There are reports of privatization of collective TVEs in the early 1980s and large-scale privatizations in the poor provinces.
• Rural financial reforms — credit provisions to the private sector and allowing a degree of private entry into financial services — in the 1980s were endorsed by the governor of the central bank and the presidents of the major commercial banks.
• Chinese reforms were heavily experimental in nature rather than relying on a blueprint approach, but the outcome of the experimentation was private ownership and financial liberalization.
• By the measure of private-sector fixed-asset investments, the most liberal policy epoch, by far, was in the 1980s; in the 1990s, the policy was reversed, and many of the productive rural financial experiments were discontinued.
• Rural administrative management was substantially centralized in the 1990s.
• Credit constraints on rural entrepreneurship, including private TVEs, rose substantially in the 1990s.
• Growth of rural household income in the 1990s was less than half of its growth in the 1980s, and the declining growth in the rural business income was especially pronounced.
• The size of government — measured in terms of headcounts of officials and the value of fixed assets it controls — expanded enormously in the 1990s.
• The directionally liberal political reforms of the 1980s were discontinued and reversed.

On Shanghai:

• Although they are located in the richest market in China, indigenous private-sector businesses in Shanghai are among the smallest in the country, and self-employment business income per capita is about the same in Shanghai as it is in provinces such as Yunnan, where GDP per capita is about 10 to 15 percent of that in Shanghai. (As an illustration of how unusual the above pattern is, imagine finding that self-employment business income per capita in the United States was about the same as that in Turkey.)
• The political, regulatory, and financial restrictions on indigenous private entrepreneurship in Shanghai were extreme, as evidenced by the fact that the fixed asset investments by the indigenous private-sector firms peaked in 1985.
• The share of labor income — inclusive of proprietor income — to GDP is very low in Shanghai.
• Shanghai’s GDP increased massively relative to the national mean, but the household income level relative to the national mean experienced almost no growth.
• Although wage income is high in Shanghai, asset income is among the lowest in the country.
• Since 2000, the poorest segment of Shanghai’s population has lost income absolutely during a period of double-digit economic growth. Although aspiring to be a high-tech hub of China, the number of annual patent grants in Shanghai decreased substantially relative to that in the more entrepreneurial provinces, such as Zhejiang and Guangdong, in the 1990s.
• Shanghai was also corrupt.

• Although GDP growth was rapid during both the 1980s and 1990s, household income growth was much faster in the 1980s.
• The share of labor income to GDP was rising in the 1980s but declining in the 1990s.
• Several studies on total factor productivity (TFP) converged on the finding that TFP growth since the late 1990s has either slowed down from the earlier period or has completely collapsed.
• The majority of the much-touted poverty reduction occurred during the short 8 years of the entrepreneurial era (1980-1988) rather than during the long 13 years of the state-led era (1989-2002).
• Income disparities worsened substantially in the 1990s, while they initially improved in the 1980s.
• Governance problems, such as land grabs and corruption, intensified greatly in the 1990s.
• The heavy taxation on the rural areas led to the withdrawal and rising costs of basic government services.
• Between 2000 and 2005 the number of illiterate Chinese adults increased by 30 million, reversing decades of trend developments; this development has garnered almost no attention in the West.
• The way the Chinese measure adult illiteracy implies that all of this increase was a product of the rural basic education in the 1990s, and this adverse development coincided closely in timing with the intensification of urban bias in the policy model.

misc:

• urbanization -> centralization of power? Jane Jacobs might have something to say here?
• much FDI just allowed for capital to be more efficiently used in China by routing through Hong Kong. See Lenovo
• Stiglitz’s perspective on TVEs was just plain wrong?

Storms notes that it is incoherent to consider magic as descending from animism, just as it is incoherent to consider religion as descending from animism. Given that magical practices were considered to have effects independent of the effects wrought on the world by spirits or phantoms, the two traditions obviously coexisted rather than being dependent on each other. Additionally:

Another argument against animism as the explanation of all magic is that the spirits themselves are subject to the power of magic, which would be hard to account for if they were the originators of that power. . . . A form of magic that is spread all over the world is that in which a man is killed by means of an effigy. . . . There is nothing animistic in this form of magic and it is based on the principle that like influences like, and that a thing that has once had contact with another thing remains irrevocably connected with it. Its effect is probably due to suggestion and autosuggestion.

What is magic?

In defining magic we have to bear in mind the practical side of magic, that is, the way in which it operates, and the theoretical side, that is, the notions, conceptions and beliefs that are the basis and origin of magical practices. We define magic as the art of employing a personal power that operates in such a way as cannot be perceived by physical sense and that is carred into effect by means of a traditional ritual.

The underlying idea of magic is that of power, force, or strength. Primitive man does not distinguish between ordinary, normal, natural power and extraordinary, abnormal, supernatural or preternatural, magical, spiritual, or even divine power. As Graebener says: “The Australian aborigines do not regard the natural as supernatural, but the supernatural as natural.” A medicine man has not two functions but one function; he does not apply two methods but one method. Curing a patient by magic or by natural means is one and the same thing in the mind of a witch-doctor; he cures a sick man ans there is the end of it.

It follows, then, that there was no inherent difference between the rules by which normal procedures or magical procedures were meant to work. In fact, Storms claims that originally “all magical practices were simple and straightforward”, and that their opacity was added later purely to enhance mystery amongst onlookers.

Anglo-Saxon magic primarily draws upon Christian and pagan influence (Icelandic, Germanic, Celtic, classical). Woden is one of the only gods frequently mentioned by name in suriving rituals, and distinguishing e.g. Germanic from classical influence is infintely harder than distinguishing Christian and pagan.

Rules for rituals would encompass an entire volume in and of themselves, but it is notable that the more pungent the ingredient the stronger its perceived effect was. From this, you get goat dung as a wound salve.

The earliest instance of an individual using a word with the function of “magic” to describe certain practices was Herodotus describing a class of Persian astronomer-priests. When you consider magic as primarily the domain of primitive peoples, it makes sense that from a civilized perspective one would want to reify it (and subsequently kill it in the process). So, the best way to study rituals is to treat them as a practice rather than the outcome of some established metaphysics.

His primary sources are the Leechbook and the Lacnunga.

The basic argument:

Imperialism emerged as the development and direct continuation of the fundamental characteristics of capitalism in general. But capitalism only became capitalist imperialism at a definite and very high stage of its development, when certain of its fundamental characteristics began to change into their opposites, when the features of the epoch of transition from capitalism to a higher social and economic system had taken shape and revealed themselves in all spheres. Economically, the main thing in this process is the displacement of capitalist free competition by capitalist monopoly. Free competition is the basic feature of capitalism, and of commodity production generally; monopoly is the exact opposite of free competition, but we have seen the latter being transformed into monopoly before our eyes, creating large-scale industry and forcing out small industry, replacing large-scale by still larger-scale industry, and carrying concentration of production and capital to the point where out of it has grown and is growing monopoly: cartels, syndicates and trusts, and merging with them, the capital of a dozen or so banks, which manipulate thousands of millions. At the same time the monopolies, which have grown out of free competition, do not eliminate the latter, but exist above it and alongside it, and thereby give rise to a number of very acute, intense antagonisms, frictions and conflicts. Monopoly is the transition from capitalism to a higher system.

Lenin is surprisingly perceptive. Or, perhaps, his ideology tended to notice inconvenient truths about the “market” economies of the Gilded Age (most of which are downstream of markets having power-law distributions in outcomes) such as the centralization of not just raw material production, but commodity production and capital itself.

Repeatedly, I have seen the biggest flaw of pre-WW2 Marxist analysis to be its inability to predict or even notice the effects of technological innovation on the common man.

It goes without saying that if capitalism could develop agriculture, which today is everywhere lagging terribly behind industry, if it could raise the living standards of the masses, who in spite of the amazing technical progress are everywhere still half-starved and poverty-stricken, there could be no question of a surplus of capital. This “argument” is very often advanced by the petty-bourgeois critics of capitalism. But if capitalism did these things it would not be capitalism; for both uneven development and a semi-starvation level of existence of the masses are fundamental and inevitable conditions and constitute premises of this mode of production. As long as capitalism remains what it is, surplus capital will be utilised not for the purpose of raising the standard of living of the masses in a given country, for this would mean a decline in profits for the capitalists, but for the purpose of increasing profits by exporting capital abroad to the backward countries.

Sure, the Haber process was incubated and developed on the government’s dime. But BASF then matured and implemented it, massively multiplying crop yields because there was money in it. Only capital-rich organizations can afford to invest in 0-1 jumps, and nations happen to be capital-rich organizations which work for the public benefit. Yet the exact ills of monopolies are also boons: vertical integration and large scale production allows the 1-many innovations to be implemented.

Regardless, companies will take the low-hanging fruit, and the low-hanging fruit in the early 20th century was investing in colonies. Railways, oil, coal, metals, cash crops, etc.. Marx and Engels claim that this results in the “bourgeoisification” of the British working class, as the profits from such foreign investment accrue in Britain rather than South Africa, and that British labor unions were pro-imperialist. This seems to be broadly correct.

Capital as export is a powerful force:

In 1904, Great Britain had 50 colonial banks with 2,279 branches (in 1910 there were 72 banks with 5,449 branches), France had 20 with 136 branches; Holland, 16 with 68 branches; and Germany had “only” 13 with 70 branches.68 The American capitalists, in their turn, are jealous of the English and German: “In South America,” they complained in 1915, “five German banks have forty branches and five British banks have seventy branches…. Britain and Germany have invested in Argentina, Brazil, and Uruguay in the last twenty-five years approximately four thousand million dollars, and as a result together enjoy 46 per cent of the total trade of these three countries.”

He also makes the argument that the cause of net immigration to the colonial powers rather than net emigration from them is that such profit accruement decreases the incentives to leave:

One of the special features of imperialism connected with the facts I am describing, is the decline in emigration from imperialist countries and the increase in immigration into these countries from the more backward countries where lower wages are paid. As Hobson observes, emigration from Great Britain has been declining since 1884. In that year the number of emigrants was 242,000, while in 1900, the number was 169,000. Emigration from Germany reached the highest point between 1881 and 1890, with a total of 1,453,000 emigrants. In the course of the following two decades, it fell to 544,000 and to 341,000. On the other hand, there was an increase in the number of workers entering Germany from Austria, Italy, Russia and other countries. According to the 1907 census, there were 1,342,294 foreigners in Germany, of whom 440,800 were industrial workers and 257,329 agricultural workers. In France, the workers employed in the mining industry are, “in great part”, foreigners: Poles, Italians and Spaniards. In the United States, immigrants from Eastern and Southern Europe are engaged in the most poorly paid jobs, while American workers provide the highest percentage of overseers or of the better-paid workers. Imperialism has the tendency to create privileged sections also among the workers, and to detach them from the broad masses of the proletariat.

Centering the monopoly as simultaneously alien to the free market and yet the inevitable result of a free market is particularly poignant, I feel. His other analyses are interesting from a historical perspective, but without intimate knowledge of the context they should not be wholly trusted.My translation was particularly good. Quite happy with it.

Generally, we will be associating languages of various grammars in the Chomsky hierarchy to certain combinations of “aliquots” added to a one-pot reaction, and in this case we want our aliquots to be potassium iodide and silver nitride. Take the language over the alphabet \(\{a,b\}\) consisting of all words with at least one \(a\) and one \(b.\) Now associate \(a\) with some part of \(\text{KIO}_3\) and \(b\) with some part of \(\text{AgNO}_3.\) Then, the reaction \[ \text{KIO}_3 + \text{AgNO}_3 \to \text{AgIO}_3 (\text{s}) + \text{KNO}_3 \] only occurs when both of the reactants are present in solution, so the word is in the language if and only if silver iodide is present. (Or, equivalently, heat is released).

Type-2 grammars consist of languages that can be modeled with pushdown automatas, which differ from FSAs in that they have a stack that can store strings of arbitrary sizes. We call these languages “context-free languages”, and the reactions which we associate to context-free languages are those with intermediaries. Again, because of automata equivalence, we can consider the simple case of the Dyck language: the collection of parentheses-strings that never contain more closed parentheses than open parentheses at any \(i\) and contain exactly equal amounts of closed and open parentheses at \(i=n.\)

We associate this with the \(pH\) reaction of sodium hydroxide and acetic acid (vinegar), with the amounts of each aliquot normalized to create identical disturbances in the \(pH\) of the solution. Note that as \(pH\) indicator aliquot is present at the beginning and end of the reaction (we associate it with the start-and-end token), the aliquot serves as the intermediary (the “stack”, if you will). So, if \(pH \geq \text{midpoint } pH\) throughout the reaction, but is \(\text{midpoint } pH\) at the end, the reactor accepts the word. If not, it does not.

Incidentally, you can interpret this as the enthalpy yield \(Y_{\Delta H} (\%)\) of the computation, defined as \[ Y_{\Delta H} (\%) = \frac{\text{reaction heat during computation}}{\text{formation heat of input string}} \times 100. \] Dyck words maximize the enthalpy yield, whereas all other input sequences with imbalanced numbers of parentheses have lower enthalpy yields. Implication: all PDAs are doing something like “enthalpy maximization” in their computation. Couldn’t find a good reference or exposition here, but something to look into.

How do we model Turing machines? You can think of a Turing machine as a “two-stack” PDA, where each stack corresponds to moving left or right on the tape. Physically, this implies that we want to model TMs with a reaction with at least two interdependent intermediaries, and we want it to be “expressive” enough to model “non-linearities”. Oscillatory redox reactions are a natural choice, of which the Belousov-Zhabotinsky (BZ) reaction is the most famous.

A typical BZ reaction involves the combination of sodium bromate and malonic acid, with the main structure as follows: \[ 3\text{BrO}_3^- + 3\text{CH}_2(\text{COOH})_2 + 3\text{H}^+ \to 3\text{BrCH}(\text{COOH})_2 + 4\text{CO}_2 + 2\text{HCOOH} + 5\text{H}_2\text{O}. \]

BZ reactions have a ton of macro-structure. Color changes as a function of the amount of oxidized catalyst, the proportions of the reactants and products fluctuate periodically, and even spatial patterns emerge from micro-heterogeneity in concentrations (e.g. reaction-diffusion waves, Pack patterns). These properties are incredibly interesting in and of themselves, but all we need for modeling TMs is that the reaction is sensitive to the addition of small amounts of aliquot.

Consider the language \(L_3 = \{a^nb^nc^n \mid n \geq 0\}.\) Dueñas-Díez and Pérez-Mercader associate the letter \(a\) with sodium bromate and \(b\) with malonic acid. \(c\) must somehow be dependent on the concentrations of \(a\) and \(b,\) so we associate \(c\) with the \(pH\) of the one-pot reactor, which we can read with sodium hydroxide. An aliquot of the rubidium catalyst maps to the start-and-end token.

Oscillation frequency \(f\) is proportional to \([\text{BrO}_3]^\alpha \times [\text{CH}_2(\text{COOH})_2]^{\beta} \times [\text{NaOH}]^{-\gamma},\) but it can also be modeled as a nonlinear function of the difference between the maximum redox value of the reaction and the mean redox value of a given oscillation, that is: \[ D = V_{\text{max}} + \left( V_T + \frac{V_P - V_T}{2}\right), \] where \(V_T\) and \(V_P\) are the trough and peak potentials, respectively, and \(V_\text{max}\) is the maximum potential. Ultimately, the final frequency of the reaction can be modeled as a quadratic in \(D_{\#}\) to high-precision (\(\#\) denotes the start-and-end token, so it can be taken to be the last timestep in reaction coordinates).

What actually allows word-by-word identification though, is the sensitivity of the oscillatory patterns to the concentrations of specific intermediaries:

The various “out-of-order” signatures for words not in \(L_3\) can be explained as follows. Each symbol has an associated distinct pathway in the reaction network. Hence, if the aliquot added is for the same symbol as the previous one, the pathway is not changed but reinforced. In contrast, when the aliquot is different, the reaction is shifted from one dominant pathway to another pathway, thus reconfiguring the key intermediate concentrations and, in turn, leading to distinctive changes in the oscillatory patterns. The change from one pathway, say 1, to say pathway 2 impacts the oscillations differently than going from pathway 2 to pathway 1. This is what allows the machine to give unique distinctive behaviors for out-of-order substrings.¹

Thermodynamically, characterizing word acceptance is a little bit more involved than that of PDAs or FSAs, but it can still be done. Define the area of a word as \[ A^{\text{Word}} = V_{\text{max}} + \tau' - \int_{t_{\#} + 30}^{t_{\#} + \tau} V_\text{osc}(t) \, dt, \] where \(t_{\#}\) is the time in reaction coordinates where the end token is added, \(\tau'\) is the time interval between symbols, \(V_\text{max}\) is the maximum redox potential, and \(V_\text{osc}\) is the measured redox potential by the Nerst equation \[ V_\text{osc} = V_0 + \frac{RT}{nF} \ln \left( \frac{[Ru(bpy)^{3+}_{3}]}{[Ru(bpy)^{2+}_{3}]} \right), \] where \(Ru(bpy)^{3+}_{3}\) and \(Ru(bpy)^{2+}_{3}\) are the concentrations of the oxidized and reduced catalyst of the BZ reaction, respectively. Now, the Gibbs free energy can be related to the redox potential as so: \[ \Delta G_\text{osc} = -nFV_\text{osc}, \] so the area of a word can be rewritten in terms of the free energy as \[ A^{\text{Word}} = - \frac{1}{n_eF} \left( \Delta G ' \times \tau ' - \int_{t_{\#} + 30}^{t_{\#} + \tau} \Delta G_\text{osc}(t) dt\right). \] Accepted words all have some constant value of \(A^{\text{Word}},\) while rejected words have a value that is dependent on the word.

\(L_3\) is a context-sensitive language, so it is only a member of the Type-1 grammar not the Type-0 grammar. However, for our purposes (realizing some practical implementation of a TM) it is roughly equivalent, as any finite TM can be realized as a two-stack PDA, and this models a two-stack PDA quite well.

The first of these, while interesting, is not something I have much to say about. The second primarily exists to justify the third—“exactly because Freud was correct in identifying the psychosexual underpinnings of society,¹ then freedom can only be achieved by eliminating these shackles on mankind.” The third germinated the cyberfeminist movement of the 1990s, which itself spawned CCRU and modern accelerationism (via Sadie Plant).

If you adopt this framing, Firestone’s choice of the dialectic as a structure is in large part pragmatic, given she is trying to replicate Marx’s totalizing analysis of class but as applied to sex. Adopting Freudianism is necessary to ensure that the nature of sex-oppresion subsumes that of class-oppression by establishing exploitation within a nuclear family as a more fundamental primitive than exploitation in the workplace. Race-oppresion is dealt with similarly.²

She is not kind to Western family structure. In a patriarchy, she argues, oppression of women and children are fundamentally intertwined. Both are forced to be physically dependent, sexually repressed, repressed in the family, and repressed in society. Even a mother’s love is borne out of a shared helplessness. ³

She is even less kind to love. “For love, perhaps even more than child-bearing, is the pivot of women’s oppression today.” Why? Because love allows male culture to parasitically feed off of the emotional strength of women. What should be a love between equals is perverted by its political context and the inevitable power dynamic between husband and wife. Regardless, men can’t love. Men are incapable of loving.⁴

The solution? Free women from the “tyranny of reproduction” with artificial wombs and joint responsibility of the sexes for child-rearing. Give women and children political autonomy via economic independence. Completely integrate women and children into society, and give women and children sexual freedom.⁵

This “feminist revolution” she conceptualizes is similar in nature to the predicted uprising of the proles, but instead initialized by “cybernetic” innovation and a population explosion. “Cybernetics” (what we would today call AI and automation) would simultaneously eliminate the need for a “transient workforce” (mostly women) and the need for house-labor. The population explosion would necessitate some form of population control, which ought take the place of artificial reproduction. Ergo, the fundamentals would be in place for a feminist revolution.

I love this book. It bites bullets.⁶ It has novel conceptual insights. It has truth to it. Her intellectual descendants were better off for her having written this, and it gives a transcendent vision rather than an immanent one. She even gives a blueprint for her utopia.

Quotes

Interspecific interactions can frequently be modeled by considering the relevant species as agents in their own right. Agents motivated by self-sustention to acquire resources, preserve the health of their subagents, and bargain or compete with others on the same playing field as themselves. Parasitism, predation, pollination—all organismal interactions generalizable to super-organismal interactions.

Optimization of the genome does not occur at the level of the organism, nor does it occur at the level of the tribe. It occurs on the level of the genome, and selects for genes which encode traits which are more fit. From this perspective, it makes sense for “species” to be a natural abstraction. Yet, I claim there are properties which species have that make them particularly nice examples of super-organisms in action. Namely:

• Boundaries between species are clear and well-defined, due to reproductive isolation;
• Competitive dynamics between species are natural to consider, rather than having to move up or down a vertical hierarchy;
• The “intentional stance”, when applied to species, is simple: reproduction.

However, it is precisely because species have such nice properties that we should be incredibly cautious when using them as intuition pumps for other kinds of super-organisms, such as nation-states, companies, or egregores. For instance:

• Boundaries between nation-states and companies are relatively straightforward to define (determined by citizenship or residency and employment, respectively). Boundaries between egregores are . . . complicated, to say the least.¹
• Company competition is generally modelable with agent-agent dynamics, and so is nation-state competition. But the act of “merging” (via acquisition, immigration, etc.) is available to them in a way that it is not to species. (Again, egregores are complicated . . .)
• The goal of a company is to maximize shareholder value. The goal of a nation-state is . . . to provide value to its citizens? The “goal” of an egregore is ostensibly to self-perpetuate and . . . fullfill whichever values it wants to fulfill.²

These “issues” are downstream from horizontal boundaries between other super-organisms we want to consider being less strong than the divides between idealized species. While Schelling was able to develop doctines of mutually-assured destruction for Soviet-American relations, many other nation-state interactions are heavily mediated by immigration and economic intertwinement. It makes less sense to separate China and America than it does to separate foxes and rabbits.

Don’t species run into the same issues as well? Humans are all members of one species, and we manage to have absurd amounts of intraspecial conflict. Similarly, tribal dynamics in various populations are often net negative for the population as a whole. Why shall we uphold species as the canonical referent for superorganisms?

Species are self-sustaining and isolated. The platonic ideal of a species would not only be reproductively isolated, but also resource isolated, in that the only use for the resources which organisms of a species would need to thrive were ones which were unusable for any other purpose. Horizontal differentiation is necessary to generalize agent modeling to systems larger than ourselves, and species possess a kind of horizontal differentiation which is important and powerful.

A corollary of this observation is that insofar as our intuitions for “superorganismal interaction” are based on species-to-species interaction, they should be tuned to the extent to which the superorganisms we have in mind are similar to species. AI-human interaction in worlds where AIs have completely different hardware substrates to humans are notably distinct from ones in which humans have high-bandwidth implants and absurd cognitive enhancement, so they can engage in more symbiotic relationships.

I would be interested in fleshing out these ideas more rigorously, either in the form of case studies or via a debate. If you are interested, feel free to reach out.

Crossposted to LessWrong.

Let \(A_{1}, \ldots, A_{n}\) be agents in a multiplayer Prisoner’s Dilemma, with the ability to return either ‘Cooperate’ or ‘Defect’ (which we model as the agents being logical statements resolving to either ‘True’ or ‘False’). Each \(A_{i}\) behaves as follows:

\[ \, \vdash \Box_{p_{i}} \left( \Box_{\max \{p_{1},\ldots, p_{n}\}}\bigwedge_{k=1}^n A_{k} \to \bigwedge_{k=1}^n A_{k} \right) \to A_{i} \]

Where \(p_i\) represents each individual agents’ threshold for cooperation (as a probability in \([0,1]\)), \(\Box_p \, \phi\) returns True if credence in the statement \(\phi\) is greater than \(p,\) and the conjunction of \(A_{1}, \ldots, A_{n}\) represents ‘everyone cooperates’. Then, by the PPL, all agents cooperate, provided that all \(\mathbb{P}_{A_{i}}\) give credence to the cooperation statement greater than each and every \(A_{i}\)’s individual thresholds for cooperation.

This formulation is desirable for a number of reasons: firstly, the Payor’s Lemma is much simpler to prove than Lob’s Theorem, and doesn’t carry with it the same strange consequences as a result of asserting an arbitrary modal-fixedpoint; second, when we relax the necessitation requirement from ‘provability’ to ‘belief’, this gives us behavior much more similar to how agents actually I read it as it emphasizing the notion of ‘evidence’ being important.

However, the consistency of this ‘p-belief’ modal operator rests on the self-referential probabilistic logic proposed by Christiano 2012, which, while being consistent, has a few undesirable properties: the distribution over sentences automatically assigns probability 1 to all True statements and 0 to all False ones (meaning it can only really model uncertainty for statements not provable within the system).

I propose that we can transfer the intuitions we have from probabilistic modal logic to a setting where ‘p-belief’ is analogous to calling a ‘reflective oracle’, and this system gets us similar (or identical) properties of cooperation.

Oracles

A probabilistic oracle \(O\) is a function from \(\mathbb{N} \to [0,1]^\mathbb{N}.\) Here, its domain is meant to represent an indexing of probabilistic oracle machines, which are simply Turing machines allowed to call an oracle for input. An oracle can be queried with tuples of the form \((M, p),\) where \(M\) is a probabilistic oracle machine and \(p\) is a rational number between 0 and 1. By Fallenstein et. al. 2015, there exists a reflective oracle on each set of queries such that \(O(M,p) = 1\) if \(\mathbb{P}(M() = 1) > p,\) and \(O(M,p) = 0\) if \(\mathbb{P}(M() = 0) < 1-p\) (check this).

Notice that a reflective oracle has similar properties to the \(Bel\) operator in self-referential probabilistic logic. It has a coherent probability distribution over probabilistic oracle machines (as opposed to sentences), it only gives information about the probability to arbitrary precision via queries (\(O(M,p)\) vs. \(Bel(\phi)\)). So, it would be great if there was a canonical method of relating the two.

Peano Arithmetic is Turing-complete, there exists a method of embedding arbitrary Turing machines in statements in predicate logic and there also exist various methods for embedding Turing machines in PA. We can form a correspondence where implications are preserved: notably, \(x\to y\) simply represents the program if TM(x), then TM(y) , and negations just make the original TM output 1 where it outputted 0 and vice versa.

(Specifically, we’re identifying non-halting Turing machines with propositions and operations on those propositions with different ways of composing the component associated Turing machines. Roughly, a Turing machine outputting 1 on an input is equivalent to a given sentence being true on that input)

CDT, expected utility maximizing agents with access to the same reflective oracle will reach Nash equilibria, because reflective oracles can model other oracles and other oracles that are called by other probabilistic oracle machines—so, at least in the unbounded setting, we don’t have to worry about infinite regresses, because the oracles are guaranteed to halt.

So, we can consider the following bot: \[ A_{i} := O_{i} \left( O_{\bigcap i} \left( \bigwedge_{k=1}^n A_{k}\right) \to \bigwedge_{k=1}^n A_{k}, \, p_{i}\right), \] where \(A_i\) is an agent represented by a oracle machine, \(O_i\) is the probabilistic oracle affiliated with the agent, \(O_{\bigcap i}\) is the closure of all agents’ oracles, and \(p_{i} \in \mathbb{Q} \cap [0,1]\) is an individual probability threshold set by each agent.

How do we get these closures? Well, ideally \(O_{\bigcap i}\) returns \(0\) for queries \((M,p)\) if \(p < \min\{p_{M_1}, \ldots, p_{M_n}\}\) and \(1\) if \(p > \max \{p_{M_1}, \ldots, p_{M_n}\},\) and randomizes for queries in the middle—for the purposes of this cooperation strategy, this turns out to work.

I claim this set of agents has the same behavior as those acting in accordance with the PPL: they will all cooperate if the ‘evidence’ for cooperating is above each agents’ individual threshold \(p_i.\) In the previous case, the ‘evidence’ was the statement \(\Box_{\max \{p_{1},\ldots, p_{n}\}}\bigwedge_{k=1}^n A_{k} \to \bigwedge_{k=1}^n A_{k}.\) Here, the evidence is the statement \(O_{\bigcap i} \left( \bigwedge_{k=1}^n A_{k}\right) \to \bigwedge_{k=1}^n A_{k}.\)

To flesh out the correspondence further, we can show that the relevant properties of the \(p\)-belief operator are found in reflective oracles as well: namely, that instances of the weak distribution axiom schema are coherent and that necessitation holds.

For necessitation, \(\vdash \phi \implies \vdash \Box_{p}\phi\) turns into \(M_{\phi}() = 1\) implying that \(O(M_{\phi},p)=1,\) which is true by the properties of reflective oracles. For weak distributivity, \(\vdash \phi \to \psi \implies \vdash \Box_{p} \phi \to \Box_{p}\psi\) can be analogized to ’if it is true that the Turing machine associated with \(\phi\) outputs 1 implies that the Turing machine associated with \(\psi\) outputs 1, then you should be at least \(\phi\)-certain that \(\psi\)-outputs 1, so \(O(M_{\phi},p)\) should imply \(O(M_{\psi}, p)\) in all cases (because oracles represent true properties of probabilistic oracle machines, which Turing machines can be embedded into).

Models

Moreover, we can consider oracles to be a rough model of the p-belief modal language in which the probabilistic Payor’s Lemma holds. We can get an explicit model to ensure consistency (see the links with Christiano’s system, as well as its interpretation in neighborhood semantics), but oracles seem like a good intuition pump because they actively admit queries of the same form as \(Bel(\phi)>p,\) and they are a nice computable analog.

They’re a bit like the probabilistic logic in the sense that a typical reflective oracle just has full information about what the output of a Turing machine will be if it halts, and the probabilistic logic gives \(\mathbb{P}(\phi)=1\) to all sentences which are deducible from the set of tautologies in the language. So the correspondence has some meat.

Crossposted to LessWrong.

We start with a typical Kripke frame \(\mathcal{F} = (\mathcal{W}, R)\) where \(W\) is the set of possible worlds (think possible truth assignments to your set of propositional variables) and \(R\) is a binary relation on those worlds.

A Kripke model is just some triple \((\mathcal{W}, R, \Vdash)\) where \(\Vdash\) is the forcing relation which determines the relationship between various worlds \(w\in\mathcal{W}\) and modal formulas. It’s characterized by the following rules:

• \(w \Vdash \neg A\) if and only if \(w \not\Vdash A\)
• \(w \Vdash A \to B\) if and only if \(w \Vdash \neg A\) or \(w \vdash B\)
• \(w \Vdash \Box A\) if and only if for all \(u\) satisfying \(wRu\) we have that \(u \Vdash A.\)

(this also subsequently implies that \(A\) is possible in world \(w\) if and only if it is true in at least one world \(u\) adjacent to \(w,\) because it’s the dual of necessity)

Different modal logics are generated by changing the assumptions on \(R\). For instance, forcing \(R\) to be reflexive guarantees that \(\textbf{T}: \Box A \to A\) will be satisfied. However, all Kripke models satisfy axiom \(\textbf{K}: \Box (A \to B) \to (\Box A \to \Box B),\) which makes Kripke models very good for representing normal modal logics and very bad at representing non-normal modal logics.

Necessitation as an operator has become popular in representing agents’ “beliefs”. E.g., you can take an agent, represent their policy in some modal logic, and \(\Box \phi\) determines their belief in \(\phi\) while \(\vdash \phi\) determines whether or not \(\phi\) is true in that world. And this is nice for a lot of things, and Kripke models are great for modeling provability logic, for instance.

But if we want necessity to be some sort of probabilistic operator—\(\mathbb{P}(\phi) > p\), for instance—then this becomes unsatisfactory. Probabilities don’t distribute over conditionals like that. So we want to relax this somehow.

Enter neighborhood semantics. We define a neighborhood frame to be a pair \((\mathcal{W}, \mathcal{N}),\) where again \(\mathcal{W}\) is the set of possible worlds and \(\mathcal{N}: \mathcal{W} \to 2 ^ {2 ^ \mathcal{W}}\) is a “neighborhood function” which maps each world \(w \in \mathcal{W}\) to a set of their neighborhoods.

Necessity here is defined differently: \(w \Vdash \Box \phi\) if and only if the truth set of \(\phi\) is a neighborhood of \(w.\) That is, there has to be a neighborhood of \(w\) that contains exactly all worlds in which \(\phi\) is true, and then \(w \Vdash \Box \phi.\)

It’s easy to see that this is a generalization of a Kripke frame. You can convert every Kripke frame into a neighborhood frame by making the neighborhoods of each world exactly the truth sets of all \(\phi\) that are necessitated by that world.

However, you can’t go in reverse, because having different neighborhoods attached to the same world means that criterions for necessity can be different for each \(\phi.\) For instance, \(\Box \phi\) might be satisfied by a neighborhood \(U\) which is disjoint from a neighborhood \(V\) which satisfied \(\Box \psi.\) This is not representable in Kripke models—there’s only one neighborhood for each world.

You can pretty easily construct a world with neighborhood semantics that doesn’t satisfy \(\mathbf{K}.\) Or mainly, the neighborhood associated with \(\Box(A \to B)\) doesn’t have to be the same one associated with \(\Box A,\) and then as a result this correspondence no longer holds in generality.

Applications to Mathematical Reality

Ok, so why were Kripke semantics useful in the first place? They provided a very clean structure by which they could model logics in a way that allowed one to verify properties like completeness/consistency/decidability well (all Kripke models are just graphs, in essence). Partially this is because they have some formal grounding in set theory. But also because formalizing logical structures as directed graphs is just really powerful and a really useful abstraction to reason about various systems.

In the same vein, reducing other systems to neighborhood semantics allows you to reason about their relevant properties simply and somewhat easily. Intuitively, we have a lot of structures that deal with collections of sets cough topologies cough and it’d be nice to bring some of them to the study of modal logic.

Then there’s the question of what modal logics can simulate. Games feature prominently. Provability logic is quite famous. But more generally, modal logics are ways of modeling systems and structures that allow you to abstract away a bunch of irrelevant features.

(They’re also all fragments of FOL (first-order-logic), and as a result don’t necessarily have the same trials and tribulations that come with additional complexity)

• it became popular amongst the middle & upper classes,
• it gave Hellenized Jews a chance to fuse their Hellenic and Jewish identities, and Hellenic Jews were a substantial portion of the population,
• it was better than paganism at letting Romans cope with the epidemics of the 2nd century, and also encouraged charity that massively improved the survival rate of those with closer connection to Christians via nurisng etc.,
• it was more popular amongst women because it discouraged abortion & infanticide and promoted mutual chastity till marriage, and as a result early in the Christian movement # women >> # men (correlated with/caused greater freedom for women),
• Greco-Roman cities were atrocious, horrifying, and disgusting—Christianity was primarily an urban movement, so is it really surprising that it took root where hopelessness would probably have been the highest?
• early Christians had a lot of skin in the game (exemplified by the martyrs of the 60s), making the religion extremely potent & able to give benefits exceeding that of paganism to their believers
• above all, Christianity is virtuous, and virtue wins.

Smattering of useful frames here: sect vs. cult movements (sect movements being offshoots and having a base from which to draw from, cult movements being new sprouts and fringe and ostracized in the beginning), not-very-rigorous models that involve a lot of assumptions can be surprisingly accurate (see: Fermi, see: this book’s estimation of travel distance from Jerusalem), martyrdom as central to Christian belief, and Christianity as (in some ways) this weird bastard child of Roman paganism and Jewish monotheism.

Apparently Roman cities were 1.5x-2x as dense as Indian cities are today, without the ability to build upwards. Also apparently, the racial mixing in the Roman empire was as if the entirety of the British empire was squashed together with freedom of movement. Strangely ancap?

It won because it was the better tech. Jesus was the ultimate startup founder

this differs from MLPs, which have activation functions on nodes (they do the aggregation and the nonlinearity), while applying a linear transformation in between (weights and biases).

KANs have no such analogous linear transformation, instead, they approximate good activation functions with B-splines. Apparently, this allows them to escape the curse of dimensionality because the function can be “approximated well with a residue rate independent of the dimension” (emphasis theirs)

i get the vibe that this is pretty dependent on the underlying generating process being approximable by smooth functions, and I also don’t think that GPU kernels have been optimized well for KANs? plausibly we can just write better kernels in CUDA/Triton for this. I think I’ll do this

ah, also the reason why they work: the Kolmogorov-Arnold Representation theorem guarantees that any multivariate continuous function can be represented as a superposition of two univariate continuous functions. MLPs satisfy a different universal approximation theorem that applies to Borel-measurable functions.

Readings:

• KAN: Kolmogorov-Arnold Networks
• pykan—Github repo

It seems that features is just the term we use to represent the units of a transformer’s ontology. Alternative definitions include “a property of an input to a model, or some subset of it” (Neel) or “[a] scalar function of the input” (Chris Olah). Sometimes ‘meaningful feature’ is used to refer to features which are interpretable. However, Anthropic’s toy model of bottleneck superposition just takes a 5-dim input \(x\) and considers each dimension a feature in and of itself. This is more in line with Olah’s definition? Maybe this confusion will resolve itself with practice.

Superposition itself is the phenomenon where there model represents more features than dimensions. In the Toy Models paper, Anthropic found that when features are dense models learn something like PCA, in that the two most important features have orthogonal representations and the rest are not learned. But as sparsity increases, we have the following:

Sparsity here is defined as the probability of the corresponding element in \(x\) to the feature as being non-zero (e.g. is the feature represented in the input, roughly). We can also have different thresholds for sparsity that make sense, as in not nonzero but not above ~0.1. For instance, the second image has 80% sparsity because 4/5 of the features represented (and we assume that features are distributed evenly across the input set). In fact, it often makes sense (to me!) to think about sparsity as 1- feature probability rather than the other way around.

This is possible because sets of points in high-dimensional space can be embedded into a lower-dimension space in such a way that the distances between the points are nearly preserved by the Johnson-Lindenstrauss lemma. (I think this also implies that there can be exponentially many almost-orthogonal vectors in an n-dimensional space (exponential in the number of dimensions)).

Neel proposes two kinds of superposition: bottleneck superposition and neuron superposition:

• bottleneck superposition occurs in places like keys, queries, and the residual stream—places where a linear map goes from a large dimension to a relatively smaller dimension, and therefore information must be stored more efficiently/compactly
• neuron superposition occurs when dim(activation_space) < num_features, and is computation rather than storage. Computation occurs when info gets passed through nonlinearities, and n non-linearities attend to >n features in this case.

Consider a given neuron. A neuron is more likely to be polysemantic if the features it represents are sparse w.r.t. each other, and higher sparsity corresponds to more superposition in the general case. One reason we should expect superposition to be naturally occuring is that it will almost always make sense for networks to try to represent ever-more-sparse yet useful features, and these can be added to popular features at almost 0 cost.

Reading:

• Neel Nanda’s Notes on Superposition - good glossary and introduction
• Toy Models of Superposition - Anthropic’s first investigations into the subject
• 200 COP in MI: Exploring Polysemanticity and Superposition - some concrete open problems to do with superposition
• ARENA 1.4: Superposition and SAEs - great resource generally for hands-on learning
• Superposition, Memorization, and Double Descent - to replicate

Rome is, perhaps, the first place I recognized as solely for visiting, never living. Unlike Tokyo, one feels this immediately. Japan’s undesirability stems primarily from its inordinate, sprawling bureaucracy that is, for the most part, hidden from the typical visitor. Rome’s undesirability is apparent for all to see—it’s loud, stifling, unmaintained, and requires arduous traversals.

Population c. 100 C.E.: 1 million people. Population c. 1000 C.E.: 35,000. Population c. 2024 C.E.: 2.8 million people. Rebound? Not so fast—the global population in the year 100 was just 200 million.

And this is obvious. The city center is still dominated by the Colosseum, the Imperial fora, and Trajan’s Market. Only the Vittoriano holds a candle to their extant glory. Yet the hordes of tourists still walk down the Via dei Forti Imperiali and congregate in stupidly long lines at the ticket booth to see ruins!

I walked across the city from east to west, passing by a secondary school, flea market, and various patisseries (is that the correct wording?). The pastries were incredible. The flea market reminded me of Mexico, interestingly enough. Felt very Catholic.

(All the buses and trams run late in Rome. This too, is very Catholic, as Orwell picked up on during his time in Catalonia and as anyone visiting a Mexican house would know. Plausibly also Irish?)

Rome’s ivies pervade its structures. Villas, monuments, churches (all 900 of them), and fountains all fall victim to these creepers. It gives the perception of a ruined city, that Roman glory has come and gone—and when one is aware of Italian history, it is very, very hard to perceive Rome as anything else than an overgrown still-surviving bastion against the continuing spirit of the Vandals.

Roman pines, too, are fungiform. Respighi’s tone poem doesn’t do justice to them. Perhaps this is just a Mediterranean vibe? But amongst the monumental Classical, Romanesque, and Neoclassical structures of the Piazza Venezia, these pines are punctual. Don’t really know how else to convey it.

It is difficult to comprehend how the animalistic, gladitorial Roman society became the seat of the Catholic Church. This city is clearly Gaian, and clearly ruled by the very same gods their Pantheon pays homage to. The Christian God is not of nature, it is apart from nature. It is not Dionysian, it is not even Apollonian (because it cannot recognize or respect the Dionysian, and as such cannot exist in context of it, only apart from it). And yet, the Pope persists.

I have not seen the Vatican yet. I want to. I will be back.

Background

Payor’s Lemma: If \(\vdash \Box (\Box x \to x) \to x,\) then \(\vdash x.\)

We assume two rules of inference:

• Necessitation: \(\vdash x \implies \vdash \Box x,\)
• Distributivity: \(\vdash \Box(x \to y) \implies \vdash \Box x \to \Box y.\)

Proof:

1. \(\vdash x \to (\Box x \to x),\) by tautology;
2. \(\vdash \Box x \to \Box (\Box x \to x),\) by 1 via necessitation and distributivity;
3. \(\vdash \Box (\Box x \to x) \to x\), by assumption;
4. \(\vdash \Box x \to x,\) from 2 and 3 by modus ponens;
5. \(\vdash \Box (\Box x \to x),\) from 4 by necessitation;
6. \(\vdash x,\) from 5 and 3 by modus ponens.

The Payor’s Lemma is provable in all normal modal logics (as it can be proved in \(K,\) the weakest, because it only uses necessitation and distributivity). Its proof sidesteps the assertion of an arbitrary modal fixedpoint, does not require internal necessitation (\(\vdash \Box x \implies \vdash \Box \Box x\)), and provides the groundwork for Lobian handshake-based cooperation without Lob’s theorem.

It is known that Lob’s theorem fails to hold in reflective theories of logical uncertainty. However, a proof of a probabilistic Payor’s lemma has been proposed, which modifies the rules of inference necessary to be:

• Necessitation: \(\vdash x \implies \vdash \Box_p , x,\)
• Weak Distributivity: \(\vdash x \to y \implies \vdash \Box_p , x \to \Box_p , y.\) where here we take \(\Box_p\) to be an operator which returns True if the internal credence of \(x\) is greater than \(p\) and False if not. (Formalisms incoming).

The question is then: does there exist a consistent formalism under which these rules of inference hold? The answer is yes, and it is provided by Christiano 2012.

Setup

(Regurgitation and rewording of the relevant parts of the Definability of Truth)

Let \(L\) be some language and \(T\) be a theory over that language. Assume that \(L\) is powerful enough to admit a Godel encoding and that it contains terms which correspond to the rational numbers \(\mathbb{Q}.\) Let \(\phi_1, \phi_{2} \ldots\) be some fixed enumeration of all sentences in \(L.\) Let \(\ulcorner \phi \urcorner\) represent the Godel encoding of \(\phi.\)

We are interested in the existence and behavior of a function \(\mathbb{P}: L \to [0,1]^L,\) which assigns a real-valued probability in \([0,1]\) to each well-formed sentence of \(L.\) We are guaranteed the coherency of \(\mathbb{P}\) with the following assumptions:

1. For all \(\phi, \psi \in L\) we have that \(\mathbb{P}(\phi) = \mathbb{P}(\phi \land \psi) + \mathbb{P}(\phi \lor \neg \psi).\)
2. For each tautology \(\phi,\) we have \(\mathbb{P}(\phi) = 1.\)
3. For each contradiction \(\phi,\) we have \(\mathbb{P}(\phi) = 0.\)

Note: I think that 2 & 3 are redundant (as says John Baez), and that these axioms do not necessarily constrain \(\mathbb{P}\) to \([0,1]\) in and of themselves (hence the extra restriction). However, neither concern is relevant to the result.

A coherent \(\mathbb{P}\) corresponds to a distribution \(\mu\) over models of \(L.\) A coherent \(\mathbb{P}\) which gives probability 1 to \(T\) corresponds to a distribution \(\mu\) over models of \(T\). We denote a function which generates a distribution over models of a given theory \(T\) as \(\mathbb{P}_T.\)

Syntactic-Probabilistic Correspondence: Observe that \(\mathbb{P}_T(\phi) =1 \iff T \vdash \phi.\) This allows us to interchange the notions of syntactic consequence and probabilistic certainty.

Now, we want \(\mathbb{P}\) to give sane probabilities to sentences which talk about the probability \(\mathbb{P}\) gives them. This means that we need some way of giving \(L\) the ability to talk about itself.

Consider the formula \(Bel.\) \(Bel\) takes as input the Godel encodings of sentences. \(Bel(\ulcorner \phi \urcorner)\) contains arbitrarily precise information about \(\mathbb{P}(\phi).\) In other words, if \(\mathbb{P}(\phi) = p,\) then the statement \(Bel(\ulcorner \phi \urcorner) > a\) is True for all \(a < p,\) and the statement \(Bel(\ulcorner \phi \urcorner) > b\) is False for all \(b > p.\) \(Bel\) is fundamentally a part of the system, as opposed to being some metalanguage concept.

(These are identical properties to that represented in Christiano 2012 by \(\mathbb{P}(\ulcorner \phi \urcorner).\) I simply choose to represent \(\mathbb{P}(\ulcorner \phi \urcorner)\) with \(Bel(\ulcorner \phi \urcorner)\) as it (1) reduces notational uncertainty and (2) seems to be more in the spirit of Godel’s \(Bew\) for provability logic).

Let \(L'\) denote the language created by affixing \(Bel\) to \(L.\) Then, there exists a coherent $\mathbb{P}T$ for a given consistent theory \(T\) over \(L\) such that the following reflection principle is satisfied: $$\forall \phi \in L’ , , \forall a,b, \in \mathbb{Q} : (a < \mathbb{P}{T}(\phi)<b) \implies \mathbb{P}_{T}(a < Bel(\ulcorner \phi \urcorner) < b) = 1.$$ In other words, \(a < \mathbb{P}_T(\phi) < b\) implies \(T \vdash a < Bel(\ulcorner \phi \urcorner) < b.\)

Proof

(From now, for simplicity, we use \(\mathbb{P}\) to refer to \(\mathbb{P}_T\) and \(\vdash\) to refer to \(T \vdash.\) You can think of this as fixing some theory \(T\) and operating within it).

Let \(\Box_p , (\phi)\) represent the sentence \(Bel(\ulcorner \phi \urcorner) > p,\) for some \(p \in \mathbb{Q}.\) We abbreviate \(\Box_p , (\phi)\) as \(\Box_p , \phi.\) Then, we have the following:

Probabilistic Payor’s Lemma: If \(\vdash \Box_p , (\Box_p , x \to x) \to x,\) then \(\vdash x.\)

Proof as per Demski:

1. \(\vdash x \to (\Box_{p},x \to x),\) by tautology;
2. \(\vdash \Box_{p}, x \to \Box_{p}, (\Box_{p}, x \to x),\) by 1 via weak distributivity,
3. \(\vdash \Box_{p} (\Box_{p} , x \to x) \to x\), by assumption;
4. \(\vdash \Box_{p} , x \to x,\) from 2 and 3 by modus ponens;
5. \(\vdash \Box_{p}, (\Box_{p}, x \to x),\) from 4 by necessitation;
6. \(\vdash x,\) from 5 and 3 by modus ponens.

Rules of Inference🔗

Necessitation: \(\vdash x \implies \vdash \Box_p , x.\) If \(\vdash x,\) then \(\mathbb{P}(x) = 1\) by syntactic-probabilistic correspondence, so by the reflection principle we have \(\mathbb{P}(\Box_p , x) = 1,\) and as such \(\vdash \Box_p , x\) by syntactic-probabilistic correspondence.

Weak Distributivity: \(\vdash x \to y \implies \vdash \Box_p , x \to \Box_p , y.\) The proof of this is slightly more involved.

From \(\vdash x \to y\) we have (via correspondence) that \(\mathbb{P}(x \to y) = 1,\) so \(\mathbb{P}(\neg x \lor y) = 1.\) We want to prove that \(\mathbb{P}(\Box_p , x \to \Box_p , y) = 1\) from this, or \(\mathbb{P}((Bel(\ulcorner x \urcorner) \leq p) \lor (Bel(\ulcorner y \urcorner) > p)) = 1.\) We can do casework on \(x\). If \(\mathbb{P}(x) \leq p,\) then weak distributivity follows from vacuousness. If \(\mathbb{P}(x) >p,\) then as \[ \begin{align*} \mathbb{P}(\neg x \lor y) &= \mathbb{P}(x \land(\neg x \lor y)) + \mathbb{P}(\neg x \land (\neg x \lor y)), \ 1 &= \mathbb{P}(x \land y) + \mathbb{P}(\neg x \lor (\neg x \land y)), \ 1 &= \mathbb{P}(x \land y) + \mathbb{P}(\neg x), \end{align*} \] \(\mathbb{P}(\neg x) < 1-p,\) so \(\mathbb{P}(x \land y) < p,\) and therefore \(\mathbb{P}(y) > p.\) Then, \(Bel(\ulcorner y \urcorner) > p\) is True by reflection, so by correspondence it follows that \(\vdash \Box_p , x \to \Box_p y.\)

(I’m pretty sure this modal logic, following necessitation and weak distributivity, is not normal (it’s weaker than \(K\)). This may have some implications? But in the ‘agent’ context I don’t think that restricting ourselves to modal logics makes sense).

Bots

Consider agents \(A,B,C\) which return True to signify cooperation in a multi-agent Prisoner’s Dilemma and False to signify defection. (Similar setup to Critch’s ). Each agent has ‘beliefs’ \(\mathbb{P}_A, \mathbb{P}_B, \mathbb{P}_C : L \to [0,1]^L\) representing their credences over all formal statements in their respective languages (we are assuming they share the same language: this is unnecessary).

Each agent has the ability to reason about their own ‘beliefs’ about the world arbitrarily precisely, and this allows them full knowledge of their utility function (if they are VNM agents, and up to the complexity of the world-states they can internally represent). Then, these agents can be modeled with Christiano’s probabilistic logic! And I would argue it is natural to do so (you could easily imagine an agent having access to its own beliefs with arbitrary precision by, say, repeatedly querying its own preferences).

Then, if \(A,B,C\) each behave in the following manner:

• \(\vdash \Box_a , (\Box_e , E \to E) \to A,\)
• \(\vdash \Box_b , (\Box_e , E \to E) \to B,\)
• \(\vdash \Box_c , (\Box_e , E \to E) \to C,\)

where \(E = A \land B \land C\) and \(e = \max ({ a,b,c }),\) they will cooperate by the probabilistic Payor’s lemma.

Proof:

1. \(\vdash \Box_a , (\Box_e , E \to E) \land \Box_b , (\Box_e , E \to E) \land \Box_c , (\Box_e , E \to E) \to A \land B \land C,\) via conjunction;
2. \(\vdash \Box_e , (\Box_e , E \to E) \to E,\) as if the \(e\)-threshold is satisfied all others are as well;
3. \(\vdash E,\) by probabilistic Payor.

This can be extended to arbitrarily many agents. Moreso, the valuable insight here is that cooperation is achieved when the evidence that the group cooperates exceeds each and every member’s individual threshold for cooperation. A formalism of the intuitive strategy ‘I will only cooperate if there are no defectors’ (or perhaps ‘we will only cooperate if there are no defectors’).

It is important to note that any \(\mathbb{P}\) is going to be uncomputable. However, I think modeling agents as having arbitrary access to their beliefs is in line with existing ‘ideal’ models (think VNM – I suspect that this formalism closely maps to VNM agents that have access to arbitrary information about their utility function, at least in the form of preferences), and these agents play well with modal fixedpoint cooperation.

Acknowledgements

This work was done while I was a 2023 Summer Research Fellow at the Center on Long-Term Risk. Many thanks to Abram Demski, my mentor who got me started on this project, as well as Sam Eisenstat for some helpful conversations. CLR was a great place to work! Would highly recommend if you’re interested in s-risk reduction.

Crossposted to the AI Alignment Forum.

He claims that the existential threat to China’s potential future growth and success is a lack of human capital: specifically, that systemic factors hinder rural Chinese children’s ability to participate effectively in the service-based, advanced economy of the 21st century, and that fixing this issue is imperative so that China does not fall into the middle income trap.

In a 2004 article in Foreign Affairs, political scientist Geoffrey Garrett shared a startling observation. He looked at the history of recent economic development and noticed that while rich countries were continuing to do well and many poor countries were achieving strong growth rates, the countries in the middle of the global income spectrum were growing more slowly and less successfully than anyone else.

In a report that made ripples throughout the development world, economists at the World Bank demonstrated the full extent of the problem. The report showed that out of 101 countries that were middle income in 1960, only thirteen had made it to high-income status by 2008. The rest remained stuck or even ended the fifty years poorer than before.

The middle income trap is the stagnation developing countries face when their average citizen reaches a “middle income.” An easy way for developing countries to rapidly grow their economies is to accept industrialization and foreign direct investment, shifting to a manufacturing economy reminiscent of Western nations in the 1890s. However, Rozelle makes the argument that to then shift from a middle income to high income country requires an educated populace, and the middle-income countries which have failed to continue their economic growth did not appropriately invest in the education of their citizenry.

But with a bit of historical data, another trend emerges that is far more relevant to the question at hand: the very small number of countries that have made it out of middle-income status in recent decades—the graduates—all have very high levels of high school education. Even more surprising, they’ve had those high levels for decades. In particular, back when they were still middle income, the graduates (places like South Korea, Taiwan, and Ireland) all had high school attainment rates comparable to those of the rich countries.

China is not appropriately investing in the necessary amounts of education to avoid the middle income trap. While they may have the necessary innovation, all the Baidus, Tencents, and Bytedances in the world wouldn’t fix the systemic issue of having nearly 70% of its population without a high school education unable to participate in the high-skilled, high-paid industries that characterize high-income countries.

Rural Chinese mainly work low-skilled manufacturing jobs, or jobs which don’t require a high school education. This was fine, until rising wages in mainland China started pushing manufacturing jobs overseas, leaving hundreds of thousands, if not millions of workers unemployed. Throughout the book, Rozelle includes telling anecdotes of workers who lost their job and couldn’t get a new one because they didn’t have the required skillset.

…We fell into conversation with one man in particular. Mr. Wang was about thirty-five and had recently been laid off from his job of eighteen years as an electrician.

As we watched, Mr. Wang gamely sidled up to the first booth, which represented a bank. The man running the booth, a human resources staff member, shook his hand and asked him to read a short page of text and comment on what he understood. Mr. Wang stared hard at the piece of paper, trying to force the characters into an order he could understand. He knew all the words and could read them aloud, but many of the terms were over his head. He kept getting confused by the logic of the sentences. For several minutes he stared at it, trying to make sense of what he was seeing. At first the man running the booth was patient and seemed sympathetic, but gradually the bank representative lost interest, turned back to his desk, and started looking around for workers who might be a better bet. After a few more minutes, Mr. Wang lowered his head with a sigh: “I’m sorry, I just can’t make sense of it.”

As it turns out, simply increasing access and/or mandating a high school education wouldn’t be enough. The rural/urban divide in China runs deep. The opportunity & outcome differential comes not only from unequal access to education and other outgrowths of the hukou policy, but also from deep-seated systemic differences. ‘Vocational’ schooling is a joke:

Tao’s middle school teacher suggested he check out the new vocational high school that had recently opened across town… When he arrived on campus a week later, he found himself in an unfamiliar world. Whereas his middle school had been orderly and regimented, here chaos reigned. The older students were tough-looking, with tight jeans, black pleather jackets, and spiked hair. As he walked to class on his first day, there were no adults in sight. He passed groups of kids hanging out in the courtyard, smoking cigarettes and laughing.

Children who grow up in rural China suffer from three “invisible epidemics”, as Rozelle calls them: anemia, uncorrected myopia, and parasitic intestinal worms. Iron-deficiency anemia has been linked to dramatic decreases in IQ, myopia (for obvious reasons) impedes learning ability, and worms almost literally sap the life force from their hosts. Luckily, cheap and safe interventions can fix these issues. Iron supplements, subsidized glasses, and cheap, common medicine could easily bring the health of a Chinese kid in the country to within striking distance of one in Beijing.

Perhaps a harder problem to fix is that of crucial stimulation of children during their formative developmental years. Rural parenting strategies are unequipped to give a child sufficient intellectual stimulation.

In rural China, babies are systematically missing out on the mental stimulation they need. When we asked rural families if they ever talked to their babies, we were met with blank looks or bemused smiles. “Why would I talk to my baby?” one young mother responded, giggling into her hand. “She can’t talk back!”

Yet, this leads to delayed infant development, and the permanent stunting of a child’s ability relative to their peers. Rural chinese babies score horribly on the Bayley test, while urban Chinese children score higher than average. This seems to be much of the issue.

For the sake of China and the world, Rozelle hopes that China will be able to fix its human capital crisis. He is somewhat bullish: the Chinese government is beginning to recognize that this is an issue, and some sane policies have been implemented. But he wants more to be done. Maybe China can pull off an economic miracle again, but this seems to be a major roadblock.

The Atlas Fellowship partners with Impact Books to give fellows access to a curated collection of books worth reading. One of these books is Radical Markets. The first two chapters are worth reading, the rest are not.

Posner & Weyl make five proposals to “uproot capitalism and democracy for a just society”:

• partial common ownership of land, mediated by auctions,
• quadratic voting,
• individual visa sponsorship,
• demonopolizing capital, but only ‘within industries’,
• treating data as labor.

Each has its own chapter, and each chapter is meant to stand alone as a defense of its policy. Yet the latter three fall flat.

What Radical Markets does well: a coherent exposition of Georgism, ‘radical’ applications of auctions to the uninitiated, and the first decent defense of quadratic voting from first principles I’ve read. What it falls victim to: left-right political reductionism, one-size-fits-all solutions to coordination problems, and hefty claims partnered with weak evidence.

Property as Monopoly

The first chapter is the best chapter. It popularizes the Common Ownership Self-assessed Tax (COST) (aka the Harberger Tax) as a plausible mechanism by which an auction-based property market could be implemented. Coupled with concrete policy proposals and effect analyses, it is a self-contained introduction to modern-day Georgism and disrupting the current ‘property monopoly’ status quo.

What is a COST? In Harberger’s own words:

If taxes are to be levied…on…the value of … properties … it is important that assessment procedures be adopted which estimate the true economic value … The economist’s answer… is simple and essentially fool-proof: allow each…owner.. to declare the value of his own property, make the declared values … public, and require that an owner sell his property to any bidder… willing to pay… the declared value. This system is simple, self-enforcing, allows no scope for corruption, has negligible cost of administration, and creates incentives, in addition to those already present in the market, for each property to be put to that use in which it has the highest economic productivity.

- Arnold Harberger, Chile 1962

Essentially, tax properties based on their value as assessed by the property owner. To ensure that the self-assessed values are accurate representations of the owners’ valuation, make all of the valuations public and mandate that a property be sold if someone outbids the declared value.

While Harberger designed his scheme as a way to raise government revenue, it offers an inspired solution to the monopoly problem we highlighted above.

Setting the tax rate requires trading off between allocative and investment efficiency w.r.t. the properties being taxed. If the COST is set at the turnover rate (the probability at which the asset changes hands) then on the margin the property owner’s gains from price increases are exactly offset by tax increases – incentivizing accurate valuations. This maximizes allocative efficiency.

However, such a high tax rate disincentivizes investment. Consider the case of a property owner who by investing $20,000 in his home can raise its value from $40,000 to $70,000. If this home has a turnover rate of 50%, and the COST is set to 50%, this owner will not invest in his home. A $10,000 profit combined with a $15,000 tax increase is not a good financial decision.

Disincentivizing property investment is bad. Private property rights are meant to avert the tragedy of the commons and encourage investment. Any alternative will have to do the same. As such, the socially optimal COST rate is less than the turnover rate.

The socially optimal property COST is non-zero though!

One might assume that the loss in allocative efficiency would offset the gain in investment efficiency. However – and this is a key point – the opposite happens. When the tax is reduced incrementally to improve investment efficiency, the loss in allocative efficiency is less than the gain in investment efficiency… In fact, it can be shown that the size of the social loss from monopoly power grows quadratically to the extent of this power. Thus, reducing the markup by a third eliminates close to 5/9…of the allocative harm from private ownership.

One can conceptualize higher COSTs as greater public ownership of private property, as they transfer use value to the public and increase the number of possible owners of the property. In some sense, higher COSTs mean a freer market – more participation, more competition.

How could COSTs be implemented? Countless details would have to be worked out, most in practice, but the salient issues seem to be setting the correct tax rates and developing the necessary infrastructure for frictionless transactions. While the latter is mostly a technological and system design issue (an engineering problem! just an engineering problem), the former is an ideological one. What is the optimal tradeoff?

For typical assets, we estimate that turnover once every fourteen years is reasonable and thus (combined with other factors below) a 7% tax annually is a good target.

Posner & Weyl probably get their 7% from the median length of American homeownership being 13.2 years as of 2022. Note that this is essentially setting the COST at the turnover rate, maximizing allocative efficiency at the cost of investment incentivization. They then claim that:

At the tax rate we advocate, asset prices would fall by between a third and two-thirds from their current level. In popular and congested areas like San Francisco and Boston, where very modest houses sell for $600,000 or more, their price could fall to as low as $200,000.

Where are these numbers coming from? It seems plausible that prices would fall this much, considering that a 7% COST with a 14 year turnover rate would tax the owner $588,000 and as such they would be incentivized to lower the price of their home to find other buyers faster, leading to lower turnover rates overall and higher profits for owners. Unclear what the underlying model is though.

An important point that they make in footnote 47 of Chapter 1:

To make our account vivid we discuss some examples of personal possessions of individuals, like homes and cars, but the reader should keep in mind that most assets are owned by businesses and thus much of the participation and benefits from a COST would be through business assets.

The authors propose starting with implementing COSTs for publicly held assets to enter the private market. For instance, spectrum licenses:

…redesigning spectrum licenses to include a COST-based license fee would solve [the current misallocation of American spectrum] and could be implemented in a variety of ways consistent with existing FCC rules. This approach, which they call “depreciating licenses,” would address many recent complaints about license design for the newly available 3.5 GHz bands of the spectrum; their small geographic scope and short durations under current plans were intended to maximize flexibility but may undermine investment incentives.

COSTs on Internet domains, grazing rights, and natural resource leases to name a few also make similar amounts of sense. But, a much broader implementation would reap much greater rewards:

As we noted above, the economy underperforms by as much as 25% annually because of the misallocation of resources to low productivity firms. A fully implemented COST could increase social wealth by trillions of dollars [emphasis mine] every year…

At the rate of roughly 7% annually that we imagine being near-optimal, a COST would raise roughly 20% of national income. About half of that money would suffice to eliminate all existing taxes on capital, corporations, property, and inheritance…and to wipe out the budget deficit and significantly reduce debt, further stimulating investment.

Where are these numbers coming from?? I don’t doubt that the gains would be large, or that this would be a more efficient taxation regime, but where is the substantiation?? The models are neither in the text of the book nor in the footnotes, and I don’t think it should be on the reader to fact check these claims?

Regardless of this chapter’s issues with providing evidence commensurate to its claims, the underlying proposal of a COST is innovative and, according to John Halstead, perhaps the most serious intellectual challenge to the idea of private property in history. Worth the read.

Radical Democracy

In two words: quadratic voting.

In this chapter, we will show that these two elements – the capacity to save up voting power, and the square root function – would be a much-needed cure to the pathologies of the traditional voting systems used in democracies.

Why quadratic voting? Why not giving people votes proportional to the cube root of their credits, or the logarithm of their credits? What property does a quadratic have that no other function does?

Its derivative is linear. No other function would make the marginal cost of casting an extra vote proportional to the number of votes cast. We make decisions on the margin -- if one voter cares three times as much as another voter about an issue, they will be willing to pay three times as much for an extra vote, and as such buy three times as many votes than the other. No other function would lead to the same outcome.

QV achieves a perfect balance between the free-rider and the tyranny of the majority problems. If the cost of voting increased more steeply, say, as the fourth power of votes cast, those with strong preferences would vote too little and we would revert to a partial tyranny of the majority. If the cost of voting increased more slowly, those with intense preferences would have too much say, as a partial free-rider problem would prevail.

Radical Markets was my first introduction to this explanation, and for this I am grateful. I think this chapter is worth reading just for this, but your mileage may vary.

QV in practice has seen limited adoption. A version is in Akasha (a Ethereum based blockchain application) where money is the currency by which voters buy their votes. Paying for votes has obvious issues in today’s world – perhaps if the world was much more egalitarian, then this would be a better system than one person, one vote.

There is good reason to believe that QV mitigates polarization as a result of allowing individuals to vote more for issues they care more about. Implementation runs into a host of engineering challenges (how to make the UI easy to use & not require excessive amounts of thinking) but I am optimistic that they are solvable.

I doubt this will gain much traction for public elections at the state and national level. It could be useful and innovative for for local and private governance. Notably, the Colorado House Democratic caucus used it in 2019 to decide on their legislative priorities, and Taiwan has flirted with QV in their digital democracy.

Uniting the World’s Workers

Subtitled: REBALANCING THE INTERNATIONAL ORDER TOWARD LABOR

The basic argument: economic freedom is necessary for economic growth. Gains from trade have been the primary engine by which this occurs, but as intranational inequality is less severe than international inequality gains from migration should be considered instead. Expanding existing legal migration channels is insufficient and possibly detrimental to natives. Therefore, countries should auction visas and let individuals sponsor migrants. They dub this the Visas between Individuals Program, or VIP.

Bryan Caplan thinks this is his open borders proposal in disguise. I think it’s where the book starts going off the deep end.

I agree with the claim that low-skilled migrants are likely a net drain on the state. As migrants are more likely to work informally and typically send large proportions of their income outside the country, they pay less taxes and consume less than natives. Naturally, this facilitates resentment (amongst a multitude of other cultural reasons, etc.), typically in existing rural, low-income, and more conservative regions.

How is the VIP going to fix this issue, exactly?? Posner and Weyl think that the money generated by the visa auction system will be enough:

Suppose that OECD countries accepted enough migration to increase their populations by a third. Suppose too that migrants on average bid $6,000 per year for a visa. This sum seems plausible that Mexican migrants to the United States gain more than $11,000 annually under the current highly inefficient system. Average GDP per capita in OECD countries is $35,000, so this proposal would boost the national income of a typical OECD country by almost 6%, comparable to their growth in real income per person in the last five years.

This is highly optimistic, and assumes that both the demand and quota for visas is at least equivalent to the population of a given OECD country. For America, that’s 300 million migrants willing to pay $6,000 for a visa per year. This won’t even give you 6% income growth because the GDP per capita in America is so high.

The population of Mexico isn’t even 300 million! The likelihood of most migrants having $6,000 on hand is almost nil! And this money goes to the government, not to private individuals directly – many individuals will not make the connection between increased funding for public services and the massive, massive amounts of migrants this proposal would apparently bring.

Even if migrants would arrive in the numbers that the authors propose, it would utterly, completely, irreversibly change the cultural landscape of the developed world. We are considering migration in numbers such that for every native American there would be a non-native migrant – statistically low-skilled and with poor English. All the typical conservative arguments migration would be multiplied ten-fold, and they would have a point.

But individuals can sponsor visas! Moreso, they can sponsor migrants and get a cut of their earnings such that the migrant earns less than minimum wage! And this isn’t wage slavery because the migrant would be making more than he would have in his home country, so it makes sense!

The risk of exploitation is minimal because foreign workers are protected by the same health, safety, labor, and employment laws that Americans benefit from, and foreign workers can return to their home country if the employer mistreats them.

Who enforces these health and safety laws? Americans. What are the economic benefits from arriving from, say, Haiti to the United States? About thirty-fold? What is the likelihood that the system would be abused, ala the Jim Crow South? And even then, what is the likelihood that the migrant would voluntarily return to their home country??

Many people may object to this system. Perhaps to some readers it is uncomfortably similar to indentured servitude, even though migrants would be free to leave at any time. Or perhaps it just seems exploitative.

YES.

Oh, but don’t worry about any of this, because 100 million people will want to sponsor visas.

Imagine then, that 100 million people sponsor migrant workers. Currently, there are about 45 million foreign-born people in the United States. Of those, about 13 million are legal noncitizens, and 11 million are illegal aliens. If our program replaced existing migrant worker visas [which it wouldn’t], the number of migrant workers would increase dramatically, from 24 million to 100 million, but not in a way that would disrupt society and overwhelm public services. [sure] It would leave the ratio of foreign-born to natives in the United States below the numbers in even the most restrictive GCC countries.

To be clear, 22.7% of Americans would be foreign born, or a little bit less than one in every four American residents would be migrants. Yes, this is a potentially sustainable foreign population, but at once? These GCC countries being used as a reference class are members of the Gulf Cooperation Council. Members include the UAE, Qatar, Kuwait, Bahrain, Oman, and Saudi Arabia. Countries positively praised for their labor rights record.

A more sane reference class would be Australia and New Zealand, which have about one foreigner for every two natives (admittedly, which are mentioned as examples). Where did they come from? According to Wikipedia:

After World War II Australia launched a massive immigration program, believing that having narrowly avoided a Japanese invasion, Australia must “populate or perish”. Hundreds of thousands of displaced Europeans migrated to Australia and over 1,000,000 British subjects immigrated under the Assisted Passage Migration Scheme… The scheme initially targeted citizens of all Commonwealth countries; after the war it gradually extended to other countries such as the Netherlands and Italy.

In other words, Australia heavily enouraged white immigration (see the White Australia policy) until the early 1970s, at which point it was comfortable accepting large amounts of migrants. Skilled migrants, I might add. There are only about 1.5 million temporary migrants in Australia (compared to about 7.5 million total foreign-born Australian residents), which is an imperfect yet decent upper bound on the number of low-skilled Australian migrants.

There is no developed country which has managed to have a large foreign-born low-skilled migrant population enter over a short period of time and provide them the same standard of living or the same rights as natives. The GCC has similar proportions of low-skilled workers and an atrocious human rights record; Australia and New Zealand manage to treat migrants decently but with a predominantly high-skilled population.

These are arguments against any open-borders policy that advocates for a large influx of low-skilled immigrants over a short period of time. But the VIP is doubly stupid because it places the liability of migrant well-being on low-skilled natives, the very same people who are the least well equipped to handle it.

Anthony is a native Ohioan, Bishal is a hypothetical migrant under the VIP:

In our case, Anthony will be required to obtain basic health insurance for Bishal before he arrives (though this would come out of Bishal’s earnings). If Bishal is unable to find work, Anthony must support him for as long as he remains in the country…If Bishal commits a crime, he will be deported after serving his sentence; Anthony will be required to pay a fine. If Bishal disappears, Anthony will also be fined. We do not think that the fine needs to be large, but it should sting.

100 million Americans are supposed to sign up for this??

If you want a defense of open borders & greatly expanded immigration, you can read Caplan’s comic book. Not this.

Dismembering the Octopus

This chapter advocates for letting BlackRock invest in Uber but not Lyft, Coca-Cola but not Pepsi, and McDonald’s but not KFC. Anti-trust for institutional capital. A good idea in theory, but I have doubts about the practical implementation.

Who are the institutional investors, anyway? They include companies that manage mutual funds and index funds, asset managers, and other firms that buy and hold equities on behalf of their customers. The largest names are those we mentioned above: Vanguard, BlackRock, State Street, and Fidelity.

26% of the public American stock market is held by institutional investors. As institutional investors are the only single entities with large enough amounts of capital to own significant portions of centibillion dollar companies, they have an outsized influence on industry policy. And because they own significant portions of companies which are nominally supposed to be competing in the same industries, it is in their interest to stifle competition within those industries, creating pseudo-cartels negatively affecting consumers.

As an example, look at banking. BlackRock, Vanguard, State Street, and Fidelity are in the top five largest shareholders of JP Morgan Chase, Bank of America, Citigroup, Wells Fargo, U.S. Bank, and PNC Bank. If the same entities own the companies that are nominally supposed to be competing, the incentives to compete are diminished & monopolistic tendencies being to crop up. Think of Rockefeller after Standard Oil broke up – he still was the owner of the subsidiary companies in each state, and this allowed him to multiply his wealth far beyond what would have been possible if Standard Oil stayed as one company.

Monopolies are bad for consumers! This is what anti-trust law was made to combat! We already bring anti-trust litigation against firm mergers which will increase market concentration, why not do the same for capital investments?

A simple but Radical reform can prevent this dystopia: ban institutional investors from diversifying their holdings within industries while allowing them to diversity across industries. BlackRock would own as much as it wants of (say) United Airlines, but it would own no stake in Delta, Southwest, and the others. It would also own as much as it wants of Pepsi, but not Coca-Cola and Dr. Pepper. And it would own as much as it wants of JP Morgan, but none of Citigroup and the other banks…

Our approach can be stated as a simple rule:

No investor holding shares of more than a single effective firm in an oligopoly and participating in corporate governance may own more than 1% of the market.

I agree with this policy, in principle. However, it seems difficult to disambiguate industries cleanly. In today’s world, where a relatively small number of massive corporations control disproportionate amounts of the economy, it seems at least somewhat viable. But what of venture capital firms investing in multiple competing startups? Would they be required to divest from one of them if both become unicorns? How big would an industry have to be for the FTC to care about regulating it?

The authors raise the issue of the lack of usage of anti-trust in local markets. For instance:

…sociologist Matthew Desmond suggests that landlords in poor neighborhoods often buy up enough housing to have substantial power to drive up rents by holding units vacant and artificially depressing supply. Yet as far as we know, no antitrust case has ever been brought against such local but potentially devastating attempts at monpolization.

Yes, property is easy to point to as an instance of monopolistic behavior ruining lives. I am wary, however, of giving regulators even more power than they currently have. Property market regulations seem to be, on the whole, good and necessary (or at least, good regulation has the potential to have a large positive impact). But letting regulators control the behaviors of small businesses seems bad? Perhaps giving business owners more leeway to bring civil suits against others engaging in anti-competitive practices is the way to go.

Finally, the authors address the digital economy:

Antitrust authorities, who are accustomed to worrying about competition within existing, well-defined, and easily measurable markets, have allowed most mergers between dominant tech firms and younger potential disrupters to proceed. Google was allowed to buy mapping startup Waze and artificial intelligence powerhouse DeepMind; Facebook to buy Instagram and WhatsApp; and Microsoft to buy Skype and Linkedin.

Their solution:

To prevent this dampening of innovation and competition, antitrust authorities must learn to think more like entrepreneurs and venture capitalists, seeing possibilities beyond existing market structures to the potential markets and technologies of the future, even if these are highly uncertain.

Much easier said than done. The day a government regulating body has the same market foresight as the entrepreneurs and investors in the market, I will eat my hat.

Meh. Not as groundbreaking as the first two proposals, and not as patently idiotic as the third. It is surprising that they advocate for a drastic expansion in market regulation in a book nominally focused on relying on free market forces to bring about good, but oh well.

(this is where the Activist Markets label came from)

Data as Labor

Pay people for their data. Never mind that the marginal benefit of your data to any given firm is negligble. Because machine learning systems need large amounts of data and have spiky loss curves, diminishing marginal returns for data doesn’t count here!

(I am not joking, this is the argument Posner & Weyl make)

However, if later, harder problems are more valuable than earlier, easier ones, then data’s marginal value may increase as more data become available. A classic example of this is speech recognition. Early ML systems for speech recognition achieved gains in accuracy more quickly than did later systems. However, a speech recognition system with all but very high accuracy is mostly useless, as it takes so much time for the user to correct the errors it makes. This means that the last few percentage points of accuracy may make a bigger difference for the value of the system than the first 90% does. The marginal value grows to the extent that it allows this last gap to be filled.

Maybe the concept of scale, scale, scale wasn’t as prominent in their time as it is nowadays? Two issues: model capabilities grow logarithmically with the amount of data they are trained on, and oftentimes getting from 99% to 99.9% requires as much data as getting from 0% to 99%. The idea that the marginal datapoint has anything but negligible value is absurd.

Paying people for data that’s used to finetune models, sure. Paying people to RLHF models, sure. Paying people for data that’s used in massive datasets – in principle, this should probably happen, but this will come nowhere near to providing individuals with an income equivalent to their job that has just been automated.

To make a ballpark estimate of what gains we might expect, we suppose that over the next twenty years, AI that would (absent our proposal) not pay data providers comes to represent 10% of the economy. We further assume that the true share of labor if paid in this area of the economy is two-thirds, as in the rest of the economy; and that paying labor fairly expands the output of this sector by 30%, as seems quite reasonable given productivity gains accompanying fairer labor practices in the early twentieth century. Then our proposal would increase the size of the economy by 3% and transfer about 9% of the economy from the owners of capital to those of labor.

Fundamentally, the authors miss the point that AI will make labor substitutable with non-human entities. The world in five years will likely use datasets generated by AI systems, simply because the Internet is too small for the capabilities of the models we want to build. Paying people for their data is not an alternative to UBI in an increasingly automated economy.

I would critique this chapter more, but it seems like a reasonable proposal to make in the world before ChatGPT and before people realized that scaling laws held to this extent. Still not worth reading in 2023.

It’s overpriced, loud, and dirty. Paying ten francs for a medicore street taco is no way to live life. God forbid you visit the city center during the day, and stay as far away from Geneva station as you can. I thought the air was supposed to be good in the Alps?

But above all, it reeks of fakeness.

It calls itself the “Peace Capital”, claims it’s too good to have twin cities, and prides itself on its cosmopolitanism. On what grounds? Before Hitler’s fall, Geneva’s only claim to facilitating international diplomacy was hosting the League of Nations – admittedly the best international governing body we’ve had thus far, but still. After, every international organization and their shadow backers clamored to have their headquarters (or at least their European headquarters) in Geneva. The UN, WHO, UNHCR, Red Cross, WTO, WIPO, WMO, ILO, …

Did you know that the largest non-financial services industry in Geneva is watchmaking? Rolex, Patek Philippe, etc. have factories just outside of Geneva proper. To be fair, ‘financial services’ also excludes commodity trading, of which Geneva is to oil, sugar, grains, and coffee as Rotterdam is to metals. Vitol & Trafigura both have their headquarters in Geneva (and one must wonder whether or not this is for convenience or to take advantage of lax Swiss banking laws…remember Marc Rich?)

Two-thirds of the corporate tax in Geneva comes from commodity trading, banking, and watchmaking. These international organizations? Don’t contribute to the economy. (Yes, they bring people & these people use services & this allows Geneva natives to benefit from the overwhelming amount of NGOs and international bodies in their city. Still.)

Tragically, Geneva once had a soul. The ‘Protestant Rome’ which once served as the birthplace of the Calvinist Revolution was annexed by Catholic France & revolted as a response. The city had opinions that informed its identity – not a pseudo-identity formed from undeserved arrogance & globalism.

Demographic shifts (mostly French immigration to French-speaking Switzerland) led to Catholics forming the largest religious group in Geneva today, followed by atheists. (I am not blaming immigration for Geneva’s soullessness! it is just another piece of the puzzle). This, along with its absurd emphasis on being a truly international city, undergird the sense that Geneve has lost its way.

And the Jet d’Eau… really? Geneva really had to take the self-masturbatory imagery to another level…

One recounts that Washington Irving, who was traveling in Spain at the time, suggested the name to his brother, a local resident; this explanation ignores the fact that Irving returned to the United States in 1832. Others award the honor to Two Stickney, son of the major who quaintly numbered his sons and named his daughters after States. The most popular version attributes the naming to Willard J. Daniels, a merchant, who reportedly suggested Toledo because it ‘is easy to pronounce, is pleasant in sound, and there is no other city of that name on the American continent.’

- The Ohio Guide on the naming of Toledo, Ohio

I found myself in Toledo one night.

I was trying to get from Ann Arbor to Boston via Amtrak (I had no working photo ID, and at the time I didn’t realize that TSA takes IDs up to one year expired as valid for domestic travel) and for some reason my connection was in Toledo. Bus from Ann Arbor to Toledo, train from Toledo to Boston. Simple.

(it actually was quite simple — this won’t be some sort of beginning to a trashy horror story. Pinky promise)

Abandoned Factories 1967: Super Bowl 1, Apollo 1 blows up, Ali fights the draft, Thurgood Marshall rises to the court, and Detroit dies.

Woe befell America’s automotive capital with the long, hot summer of ’67 and some of the bloodiest race riots in American history. Eventually LBJ used the Insurrection Act to send the National Guard to quell the riots, but it left the west of Lake Erie a shell of its former self.

Today, Detroit is almost a ghost town. It’s defaulted on its debt (and gone bankrupt!), has the 4th highest murder rate in major cities in the USA, and its former mayor was convicted on 24 felony counts and sentenced to 28 years in prison.

Luckily, I wasn’t in Detroit! So you can imagine how surprised I was to find a ramshackle paper mill right next to the train station. And next to that was a junkyard, and next to that was another unused factory, and next to that was… you get the picture.

If you were in front of an abandoned factory at 3AM I would certainly hope you at least took a look around inside. Not that I would ever do such a thing, but it seems like such a missed opportunity…

[pictures incoming! in future updates :D]

Apparently the dereliction of Detroit’s manufacturing capacity took Toledo (and eventually, the rest of the Midwest) with it.

Fellow Travelers Mainstays on the Amtrak: Mennonites, punks, and wannabe vagabonds.

Mennonites & the Amish are often mistaken for each other. Both practice a certain amount of technological ascetism (more extreme in the conservative branches), both are Anabaptist derived, and both use the Amtrak as a form of transportation. But you probably see the conservative Mennonites (given their distinctive dress – 1850s cowboy vibes), especially given that large numbers of them settled in the Midwest.

Punks are interchangeable. Spiky pink hair, silver chains, black skinny jeans, relationships with inappropriate age gaps – always the same. Entertaining, in small doses.

Wannabe vagabonds: me! :D

Highly, highly recommend talking to the person sitting next to (or in front of, or behind) you on the train. Americans like talking to people, and you probably have nothing better to do. The WiFi is atrocious.

Why Is The Station So BIG MLK Plaza is Toledo’s station. It is massive.

Four floors. Gothic. Nearly a century and a half old. A multimillion dollar investment in the mid-20th century. To serve an area that is now dead.

At least National Train Day is a week early in Toledo. The city probably needs the consolation.

Microcosm Walk around Toledo at night. See the emptiness. Feel the emptiness. Get in touch with the dying Rust Belt. And maybe visit the first ever hippoquarium exhibit in a zoo.

Would rec.

And what are these Fluxions? The Velocities of evanescent Increments? And what are these same evanescent Increments? They are neither finite Quantities nor Quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?

George Berkeley, The Analyst

When calculus was invented, it didn’t make sense. Newton and Leibniz played fast and dirty with mathematical rigor to develop methods that arrived at the correct answers, but no one knew why. It took another one and a half centuries for Cauchy and Weierstrass develop analysis, and in the meantime people like Berkeley refused to accept the methods utilizing these “ghosts of departed quantities.”

Cauchy’s and Weierstrass’s solution to the crisis of calculus was to define infinitesimals in terms of limits. In other words, to not describe the behavior of functions directly acting on infinitesimals, but rather to frame the the entire endeavour as studying the behaviors of certain operations in the limit, in that weird superposition of being arbitrarily close to something yet not it.

(And here I realize that math is better shown, not told)

The limit of a function \(f(x)\)at \(x=a\) is \(L\) if for any \(\epsilon>0\) there exists some \(\delta > 0\) such that if 

\[|x-a|<\delta,\]

 then 

\[|f(x)-L|<\epsilon.\]

Essentially, the limit exists if there’s some value \(\delta\) that forces \(f(x)\) to be within \(\epsilon\) of \(L\) if \(x\) is within \(\delta\) of \(a\). Note that this has to hold true for all \(\epsilon\), and you choose \(\epsilon\) first!

From this we get the well-known definition of the derivative: 

\[f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\]

 and you can define the integral similarly.

The limit solved calculus’s rigor problem. From the limit the entire field of analysis was invented and placed on solid ground, and this foundation has stood to this day.

Yet, it seems like we lose something important when we replace the idea of the “infinitesimally small” with the “arbitrarily close to.” Could we actually make numbers that were infinitely small?

The Sequence Construction

Imagine some mathematical object that had all the relevant properties of the real numbers (addition, multiplication are associative and commutative, is closed, etc.) but had infinitely small and infinitely large numbers. What does this object look like?

We can take the set of all infinite sequences of real numbers \(\mathbb{R}^\mathbb{N}\) as a starting point. A typical element \(a\in\mathbb{R}^\mathbb{N}\) would be 

\[a = (a_0, , a_1, , a_2, \ldots)\]

 where \(a_0, a_1, a_2, \ldots\) is some infinite sequence of real numbers.

We can define addition and multiplication element-wise as: 

\[a + b = (a_{0} + b_{0}, , a_{1} + b_{1}, a_{2} + b_{2}, \ldots),\]

\[a \cdot b = (a_0 \cdot b_0, a_1 \cdot b_1, a_2 \cdot b_2, \ldots).\]

You can verify that this is a commutative ring, which means that these operations behave nicely. Yet, being a commutative ring is not the same thing as being an ordered field, which is what we eventually want if our desired object is to have the same properties as the reals.

To get from \(\mathbb{R}^\mathbb{N}\) to a field structure, we have to modify it to accommodate well-defined division. The typical way of doing this is looking at how to introduce the zero product property: i.e. ensuring that if \(a,b \in \mathbb{R}^\mathbb{N}\) then if \(ab = 0\) either one of \(a,b\) is \(0\).

If we let \(0\) be the sequence of all zeros \((0,0,0,\ldots)\) in \(\mathbb{R}^\mathbb{N},\) then it is clear that we can have two non-zero elements multiply to get zero. If we have 

\[a = (a, 0, 0, 0, \ldots),\]

 and 

\[b = (0,b,b,b, \ldots),\]

 then neither of these are the zero element, yet their product is zero.

How do we fix this? Equivalence classes!

Our problem is that there are too many distinct “zero-like” things in the ring of real numbered sequences. Intuitively, we should expect the sequence \((0,1,0,0,\ldots)\) to be basically zero, and we want to find a good condensation of \(\mathbb{R}^\mathbb{N}\) that allows for this.

In other words, how do we make all the sequences with ”almost all” their elements as zero to be equal to zero?

Almost All Agreement ft. Ultrafilters

Taken from ”five ways to say “Almost Always” and actually mean it“:

A filter \(\mathcal{F}\) on an arbitrary set \(I\) is a collection of subsets of \(I\) that is closed under set intersections and supersets. (Note that this means that the smallest filter on \(I\) is \(I\) itself).

An ultrafilter is a filter which, for every \(A \subseteq I\), contains either \(A\) or its complement. A principal ultrafilter contains a finite set.

A nonprincipal ultrafilter does not.

This turns out to be an incredibly powerful mathematical tool, and can be used to generalize the concept of “almost all” to esoteric mathematical objects that might not have well-defined or intuitive properties.

Let’s say we define some nonprincipal ultrafilter \(\mathcal{U}\) on the natural numbers. This will contain all cofinite sets, and will exclude all finite sets. Now, let’s take two sequences \(a,b \in \mathbb{R}^\mathbb{N},\) and define their agreement set \(I\) to be the indices on which \(a,b\) are identical (have the same real number in the same position).

Observe that \(I\) is a set of natural numbers. If \(I \in \mathcal{U},\) then \(I\) cannot be finite, and it seems pretty obvious that almost all the elements in \(a,b\) are the same (they only disagree at a finite number of places after all). Conversely, if \(I \not\in \mathcal{U},\) this implies that \(\mathbb{N}/I \in \mathcal{U}\), which means that \(a,b\) disagree at almost all positions, so they probably shouldn’t be equal.

Voila! We have a suitable definition of “almost all agreement”: if the agreement set \(I\) is contained in some arbitrary nonprincipal ultrafilter \(\mathcal{U}\).

Let \(^*\mathbb{R}\) be the quotient set of \(\mathbb{R}^\mathbb{N}\) under this equivalence relation (essentially, the set of all distinct equivalence classes of \(\mathbb{R}^\mathbb{N}\)). Does this satisfy the zero product property?

(Notation note: we will let \((a)\) denote the infinite sequence of the real number \(a\), and \([a]\) the equivalence class of the sequence \((a)\) in \(^* \mathbb{R}\).)

Yes, This Behaves Like The Real Numbers

Let \(a,b \in \mathbb{R}^\mathbb{N}\) such that \(ab = (0)\). Let’s break this down element-wise: either \(a_n, b_n\) must be zero for all \(n \in \mathbb{N}.\) As one of the ultrafilter axioms is that it must contain a set or its complement, either the index set of the zero elements in \(a\) or the index set of the zero elements in \(b\) will be in any nonprincipal ultrafilter on \(\mathbb{N}.\) Therefore, either \(a\) or \(b\) is equivalent to \((0)\) in \(^* \mathbb{R},\) so \(^* \mathbb{R}\) satisfies the zero product property.

Therefore, division is well defined on $^\mathbb{R}\(! Now all we need is an ordering, and luckily almost all agreement saves the day again. We can say for \)a,b \in ^\mathbb{R}$ that \(a>b\) if almost all elements in \(a\) are greater than the elements in \(b\) at the same positions (using the same ultrafilter equivalence).

So, \(^*\mathbb{R}\) is an ordered field!

Infinitesimals and Infinitely Large Numbers

We have the following hyperreal:

\[\epsilon = \left( 1, \frac{1}{2}, \frac{1}{3}, \ldots, \frac{1}{n}, \ldots \right).\]

Recall that we embed the real numbers into the hyperreals by assigning every real number \(a\) to the equivalence class \([a]\). Now observe that \(\epsilon\) is smaller than every real number embedded into the hyperreals this way.

Pick some arbitrary real number \(a\). There exists \(p \in \mathbb{N}\) such that \(\frac{1}{p}< a\). There are infinitely many fractions of the form \(\frac{1}{n}\), where \(n\) is a natural number greater than \(p\), so \(\epsilon\) is smaller than \((a)\) at almost all positions, so it is smaller than \(a\).

This is an infinitesimal! This is a rigorously defined, coherently defined, infinitesimal number smaller than all real numbers! In a number system which shares all of the important properties of the real numbers! (except the Archimedean one, as we will shortly see, but that doesn’t really matter).

Consider the following

\[\Omega = (1,2,3, \ldots).\]

By a similar argument this is larger than all possible real numbers. I encourage you to try to prove this for yourself!

(The Archimedean principle is that which guarantees that if you have any two real numbers, you can multiply the smaller by some natural number to become greater than the other. This is not true in the hyperreals. Why? (Hint: \(\Omega\) breaks this if you consider a real number.))

How does this tie into calculus, exactly?

Well, we have a coherent way of defining infinitesimals!

The short answer is that we can define the star operator (also called the standard part operator) \(\text{st}(x)\) as that which maps any hyperreal to its closest real counterpart. Then, the definition of a derivative becomes 

\[f'(x) = \text{st}\left( \frac{^*f(x+\Delta x)- ^*f(x)}{\Delta x}\right)\]

 where \(\Delta x\) is some infinitesimal, and \(^*f\) is the natural extension of \(f\) to the hyperreals. More on this in a future blog post!

It also turns out the hyperreals have a bunch of really cool applications in fields far removed from analysis. Check out my expository paper on the intersection of nonstandard analysis and Ramsey theory for an example!

Yet, the biggest effect I think this will have is pedadogical. I’ve always found the definition of a limit kind of unintuitive, and it was specifically invented to add post hoc coherence to calculus after it had been invented and used widely. I suspect that formulating calculus via infinitesimals in introductory calculus classes would go a long way to making it more intuitive.

A boring, colloquial way.

”Almost all the eggs are gone!” (as half a dozen remain)

Not-Finite-ness

A slightly-less-boring mathy way.

”Almost all prime numbers are odd!”

There are infinitely many primes. There is exactly one even prime number (2). Infinity minus one is… infinity.

”Almost all natural numbers are larger than one-hundred thousand quadrillion quadrillion vigintillion! (10^83)”

There are infinitely many natural numbers. There are infinitely many natural numbers larger than one-hundred thousand quadrillion quadrillion vigintillion. No practical difference between 10^83 and 1 (other than that one is an upper bound on the number of atoms in the universe).

You formalize this with sets: if you have some (infinite) set, a subset whose complement has a finite cardinality encompasses almost everything in the set. We call this cofiniteness.

Probability ~One

A way to quantify surety.

”Almost all the people will lose money at the casino!”

I’m not sure what the exact rates are, but I’d bet money on this being true.

”Almost all numbers are composite!”

It is well known that the number of prime numbers below \(N\)is approximately \(N / \ln N\). In the limit as \(N\) goes to infinity, the ratio of primes to non-primes numbers goes to approximately zero. So if you choose a random positive integer, I would bet my life savings that it’s composite.

”Almost all graphs are asymmetric.”

An intuitive explanation: if you take all possible combinations of nodes and vertices and let the number of each tend towards infinity, you should expect chaos to triumph over order. (sorry Ramsey). This does depend on a certain definition of symmetry, however, and a clearer statement would be ”almost all graphs have only one automorphism.”

The Lebesgue Measure is Not-Zero

A straightforward-yet-strange way for real numbers.

The Lebesgue measure is what you get when you try to generalize length, area, and volume to \(n\)-dimensions. It forms the basis for our current understanding of integration, and helps us figure out how big stuff is.

Something with zero volume basically doesn’t exist anyway.

”Almost all real numbers are irrational!”

Well yes, all the rationals have measure zero. All countable sets have measure zero, and the rationals are countable.

(Measures are nice: they’re a neat generalization of physical scales (mass, volume, etc.) to arbitrary mathematical objects. They’re particularly useful for dealing with continuous things ~we love Lebesgue measures~)

”Almost all real numbers are noncomputable!”

Well yes? Of course an arbitrary real number can’t be computed to arbitrary precision by a finite algorithm? Computable numbers are countable, remember? Nevermind that basically all the numbers we deal with are computable, this is obvious.

(Measure zero stuff basically doesn’t exist, even if they’re the only things we use on a daily basis)

”Almost all real numbers aren’t in the Cantor set!”

Well yes, of course! Even though the Cantor set is uncountably infinite, it still has measure zero! It’s a weird pseudo-fractal embedding of the real line that somehow manages to lose everything in translation but still keep all the relevant information.

(Idk, the Cantor set is weird)

It is Contained in a Nonprincipal Ultrafilter

A filter \(\mathcal{F}\) on an arbitrary set \(I\) is a collection of subsets of \(I\) that is closed under set intersections and supersets. (Note that this means that the smallest filter on \(I\) is \(I\) itself).

An ultrafilter is a filter which, for every \(A \subseteq I\), contains either \(A\) or its complement. A principal ultrafilter contains a finite set.

A nonprincipal ultrafilter does not.

This turns out to be an incredibly powerful mathematical tool, and can be used to generalize the concept of “almost all” to esoteric mathematical objects that might not have well-defined or intuitive properties.

(One of the coolest uses of nonprincipal ultrafilters is in the construction of the hyperreals, post forthcoming).

Let \(\mathcal{U}\) be a nonprincipal ultrafilter over the natural numbers. It obviously contains no finite sets, but we run into a slight issue when we take the set

\[E = \{2,4,6,8, \ldots \}\]

and its complement

\[O = \{1,3,5,7, \ldots \}.\]

By the filter axioms, only one of these can be in \(\mathcal{U}\), and one of them has to be in \(\mathcal{U}\). And thus, we can safely say:

”Almost all natural numbers are even.”

For modern Western man it often seems that the only conditions under which religion can be existentially illuminating are those of absurdity where religion is existentially denied. Goethe’s Faust, Dostoyevsky’s Underground Man, Melville’s Captain Ahab, Kierkegaard’s Seducer, Kafka’s K. - these, not the insipid moralizers of so-called religious fiction, testify to the glory of God, even in hell. (pg 105-106)

There is a genuine sense, as it were, in which Hitler’s supporters were much guiltier than their idol. The Underground Man, this much must be said for him, would not have stood on his “ignorance” or his right of security. He despaired “bravely.” (pg 127)

The best known type of offense in the modern world is not that of the Cross, but of capitalism. (pg 133)

A section is dedicated to man’s relationship to “offense”: the offense taken when one has unsatisfied desires (unrequited love), a lack of meaning, has been excluded from a group, meets someone who is virtuous, confronted with mortality, or has faith. Dostoyevsky’s Underground Man, Shakespeare’s Macbeth, Melville’s Captain Ahab, and Milton’s Satan are prime examples of characters who have embodied offense (and despair as a result).

I suspect Clive’s sweeping analysis of the Romantic Enlightenment will become more clear to me once I can understand most of the references the work makes. At the moment, much is inscrutable. Very interesting takes however.

It was borne out of a naive hope that if two individuals trusted each other enough, they’d be able to lower their social inhibitions enough to have a conversation with zero brain-to-mouth filter. I thought this would lead to great conversations, and perhaps act as a pseudo-therapeutic tool to resolve disputes, disagreements over emotionally charged topics, and the like. However, it turns out this isn’t necessarily the best use case for a conversation where you simply say the first thing that comes into your head.

As with any writing trying to describe social dynamics, this may be somewhat inscrutable. However, I will try my best to explain exactly what I claim to be a useful conversational tool, for use-cases from “solving hard technical problems with a partner”, to “diving off the insanity deep end”.

Background Alice and Bob are having a conversation. Alice says X, which Bob responds to with Y, in the context of the conversation (the previous things that Alice and Bob have said to each other) and the context of the world (Bob’s priors). Typically, Bob’s System 1 formulates Y and Bob’s System 2 “edits” it (for lack of a better term) - in most cases, the final output has more to do with System 1 than System 2. However, most of the time in discussion is spent with these System 2 “add-ons” - formulating ideas into sentences, making sure that the vocabulary is appropriate for the conversation, etc.

Hypothesis: if you intentionally remove the System 2 filters from the conversation between Alice and Bob, then you get a rapid feedback loop where the System 1 responses are simultaneously much faster and shorter than the original, which lets the conversation have a much higher idea density.

Setup We paired participants and asked them to come up with a topic to start their conversation on. Following that, their instructions were to say “the first thing that came into their head” after hearing their partner, and see where this led. After fifteen minutes of this, we checked in and had a discussion on how this went. Repeat about 6 times.

Observations Individuals did not report a loss in the ease of communication or a lack of nuance - rather, they reported being much more tired than normal and that their perception of time was quite dilated. Someone likened it to “having a 40 minute conversation but feeling that only five minutes had passed.” Generally, sentiment was extremely positive at this being an alternative method of communication.

A few concrete things that some individuals did:

Consciously refused to talk in sentences, and only in key words Chose a “spiciness” level before hand (think hotseat 1-10) Other variations included choosing to talk about either technical or emotional topics, focusing on responding to the last thing the person said vs. the first thing that came into their head, etc.

Use Cases The most surprising outcome was that this method of conversation seems to be quite useful for technical discussions when both individuals have similar levels of intuition on the subject. It was counterintuitive for me when I tried this: I expected technical conversations to be driven much more by System 2 than System 1, especially when compared to other types of conversations. But when discussing some mathematical proof, it turns out the System 1 responses represent much more the motivations for certain logic than the actual logic itself, and this is what allows for the partner to understand better. See here.

As an introspection tool, it also seems quite useful. If both you and your partner are interested or confused by some social phenomenon, lowering your System 2 filters removes a lot of the implicit restrictions we place on our speech with regards to social contexts, and it opens the door for more valuable conversations.

Failure Modes The obvious failure mode is a conversation in which Alice and Bob decide on a topic they both feel strongly about, disagree, and then one or both leaves feeling hurt/ having a worse opinion of the other. While you can’t eliminate this risk entirely, some safeguards make it much less likely:

Setting a “spiciness” level for the conversation before it begins. Mutually arriving at what exactly a level “7” means is probably necessary. Only talking about emotionally charged topics with individuals you trust to handle it maturely. Having extremely low barriers to exit the conversation. Making it a social norm to get up and leave one of these at any moment is the bare minimum. A subtler failure mode is a conversation which waffles between topics without any substance being exchanged between the participants. Such as:

Alice: “Do you prefer London or New York?”

Bob: “Purple.”

Alice: “Clouds.”

Bob: “Steak.”

… and so on. I personally find these to be very entertaining, but it is a good idea to set expectations beforehand of exactly how unhinged you would like the conversation to be (some calibration is necessary).

Directed Babbling seems to have much higher idea density and not much information loss compared to typical conversation. I would recommend that you try this with someone sometime, especially if you’re stuck on a technical problem with a partner. If you do end up trying this, please let me know how it went! My sample size currently is quite small, and more data is always great!

Crossposted to LessWrong.

It’s absurdly volume-inefficient.

One liter of hydrogen can produce 0.01 MJ of energy at STP (standard temperature and pressure, 273K and 1 atm) compared to 34 MJ/L for gasoline. That’s 0.02% of the energy output for liter. Granted, things improve drastically for liquid hydrogen, where the comparison is 8 MJ/L vs 34, but this requires maintenance of temperatures below −252.8°C, only a few degrees above absolute zero.

Gaseous hydrogen isn’t that easy to store either: it requires containers pressurizable up to 700 bar (700x atmospheric pressure). That’s 10,000 PSI. And even then, it takes 5L of hydrogen to match up to 1L of gasoline. The Department of Energy estimates that to meet most lightweight vehicular driving ranges, between 5-13 kg of hydrogen need to be carried onboard the vehicle. If we do some quick calculations, that means that vehicles need to carry between 85 - 294 L of liquid hydrogen (some multiple of this for gaseous hydrogen) to go anywhere. For all you Americans, this is roughly between 22-77 gallons.

(For reference, 5-13kg of hydrogen converts to 20-70 liters of gasoline, in terms of energy efficiency. I also make no claim as to the specific accuracy of the numbers, these are napkin calculations, and this doesn’t take into account energy efficiencies created by recycling hydrogen or fuel cells being more efficient than combustion engines, etc.)

It would not be feasible to have stereotypical sedans with fifty gallon gas tanks in a world of solely hydrogen fuel. Additionally, the extreme conditions liquid hydrogen must be stored as bottlenecks its production and transportation.

The Department of Energy set standards for hydrogen storage to be met by 2020 in order for hydrogen fuel to become feasible for portable power and light-duty vehicular applications. These were:

1.5 kWh/kg (overall system performance) 1.0 kWh/L (overall system performance) $10/kWh (translates to $333/kg for stored hydrogen) So far, none of these goals have been met, and I have doubts about the scalability of present research (although I’m open to criticism on this take). Let’s take a look at what’s being done to fix the issue.

Short-term Solutions

The majority of short-term solutions to hydrogen’s issues as a widespread fuel consist of creating inexpensive, high pressure storage solutions for H2 gas. From the Department of Energy’s website again, this means developing fiber-reinforced composites that can be produced cheaply and withstand 700 bar pressures. As these don’t necessarily address the underlying volume-inefficiency problem, we can move on to the long-term solutions.

Long-term Solutions

Long-term solutions take two forms: higher-density gaseous storage and materials-based hydrogen storage. The former develops vessels that can compress H2 gas more, while the latter seeks to manufacture materials that have better volumetric hydrogen ratios. This will mainly focus on the materials based approach.

The main research avenues for materials-based hydrogen storage are metal hydrides, adsorbents, and chemical hydrogen storage materials. Let’s look at each.

Metal Hydrides

Metal hydrides are compounds in which metal atoms form ligands with hydrogen. The strength and nature of these bonds vary widely with the metal, but they allow compounds to act as hydrogen carriers without getting decomposed themselves, which is useful for materials cycling (and drastically improves efficiency).

The issue is, the sorts of complex hydrides that have the most promising properties cannot be produced at scale cheaply in any amount, let alone the quantities required for hydrogen to become a serious competitor to gasoline. However, if these compounds were able to scale, then I would be very excited about our energy futures.

Adsorbents

Adsorption is the process by which molecules stick to the internal or external surface of something. Attaching hydrogen gas to some compound would allow it to retain its original molecular form and simultaneously compress it (by virtue of gases being quite volume inefficient). The issue with these is that they don’t compress from the original that much, and are expensive to make.

Chemical Hydrogen Storage Materials

These are perhaps the most straightfoward: find materials that you can either hydrolyze or pyrolyze to release hydrogen, and hope that they have less volume than liquid hydrogen and that they’re easier to store. Well, lo and behold, it turns out there’s an entire class of molecules like this: Amine-boranes.

Amine-boranes are essentially ammonia molecules complexed to boron with extra hydrogen thrown in. The simplest amine-borane is ammonia borane, or borazane, with the chemical formula NH3BH3. It hydrolyzes and pyrolyzes well, has a higher molar density of hydrogen than hydrogen itself, and is a stable solid at room temperature. What more could you ask for?

Well, it’s absurdly expensive to synthesize. I suspect the cost can be reduced at scale, but it does not seem feasible at the moment.