Random musings
Introduction In previous essays I considered how value will change in a post-AGI society , and also thought about what happens when demand becomes a constraint on value rather than supply. I argued that if AI makes the supply side vastly more efficient, there will be both immediate term and long term constraints in how much demand is available. While it is difficult to imagine a total limit to…
Introduction In the dynamical similarity and allometry posts, we started with a group acting on a system and asked what survived the group action. For dynamical similarity, the survivors were quantities shared by whole families of similar trajectories, somewhat like the conserved quantities in Noether’s theorem. For allometry, they were the power laws relating an organism’s traits to its body…
D’Arcy Thompson’s method of transformations: Scarus (Fig. 519) on a rectangular grid deformed into Pomacanthus (Fig. 520), from On Growth and Form (1917). Introduction In the dynamical similarity post we looked at equivariant symmetries of the Lagrangian, which produce Noether-like quantities that are conserved not within a single trajectory but across families of similar trajectories. That is,…
Introduction In the post/paper draft here I wrote about using invariants to classify normal-form games. That post is a monster that I ultimately need to carve up and revise significantly; the purpose of this post is to explain a core set of the ideas, give some explanation of the ideas (so you don’t have to wait forever for me to revise) and motivate the project in the larger scheme of my…
Note Companion post For an accessible motivation and overview of this framework, see Games, Invariants, and Alignment . Draft Note : This is a (second) draft of a paper I will be potentially be further revising, reformatting, and submitting to ArXiv in the near future, and as such is written in that style ( previous draft ). Note that it is not yet reviewed/fully checked, and may contain errors or…
Introduction Robert Oppenheimer, when he had his security clearance questioned and then lifted when he was being punished for having resisted the development of the hydrogen bomb, was asked by the interrogator at this security hearing — “Well, Dr. Oppenheimer, if you’d had a hydrogen bomb for Hiroshima, wouldn’t you have used it?” And Oppenheimer said, “No.” The interrogator asked, “Why is that?”…
Introduction In a previous post, we explored some functional theories of art . However, we left open the question of specific financializations . In this post I’ll try to understand institutions of art, like auctions, museums, etc. to understand how the formal institutions actually impose a specific financial value on an object. How to Commit Tax Fraud with Art Imagine the following scenario:…
Introduction Now that we’ve investigated the basics of invariant theory , we can look at how to compute invariants with code. In this post, I’ll investigate computational invariant theory, with an emphasis on the algorithmic aspects. I’m vaguely following Derksen and Kemper’s book . This is once again a long post, mixing theory, algorithms, and code. I used Claude to help with the code and the…
Introduction Invariant theory is the study of how symmetries constrain the structure of mathematical objects (similar to Noether’s theorem ). In this post, I will give a brief introduction to invariant theory and its applications. Invariant theory is a vast field. I’m pulling mainly from the book Invariant Theory by Peter Olver (but with changes in order and notation), but will also thread in and…
Introduction The current dominant AI narrative asserts that “white-collar jobs are next”. This includes lawyers, software engineers, radiologists, writers, mathematicians, artists, and ultimately any job that can be done with a computer. Suppose this is true. Furthermore, suppose that robotics will eventually usher in a world of true abundance, where the production of goods and services is…
Introduction Much of the contemporary AI risk discourse focuses on large-scale existential threats to the human species. However, there are more mundane risks that are also worth considering, one of which is the possibility that AI could enable a new wave of totalitarianism. Background Throughout history, advances in communication and bureaucratic technology have enabled larger and more powerful…
Introduction Bruce Bueno de Mesquita and Alastair Smith’s The Dictator’s Handbook (2011) is one of the more successful pop-science books in political economics. Its central thesis is that to remain in power all leaders must maintain their coalition: this requirement creates certain incentives governing leaders’ behavior. Furthermore, the ratio between the number of members a leader needs in their…
Introduction Neither would it carry any Imputation of Falshood to our simple Ideas, if by the different Structure of our Organs, it were so ordered, That the same Object should produce in several Men’s Minds different Ideas at the same time; v.g. if the Idea, that a Violet produced in one Man’s Mind by his Eyes, were the same that a Marigold produced in another Man’s, and vice versa. - John Locke,…
Introduction What is art’s purpose in society? Why do we spend so much time and money consuming, producing, and criticizing it? What separates “good” art from “bad” art (is there even such a thing?), and why do we honor and esteem “good” artists while ridiculing the bad ones? Why do we read movie reviews or discuss movies we’ve seen on internet message boards (especially if we’ve already seen the…
Introduction In this post, I introduce gauge equivalence, and also investigate a few different types of reduction under symmetry (to build out a taxonomy). If you haven’t followed along, in the last few posts we introduced the Lagrangian in the context of geometric controls . We then proved Noether’s theorem with time and applied it to similar systems . Epistemic status: This post is still a bit…
Introduction Suppose we have a population of objects of different lifespans (starting at different times). Given a sample from a specific time point, we should expect “most” of the objects we see to be drawn from objects of longer life spans. Let’s briefly look into this phenomenon. All these results all well-known in the literature, under “renewal theory”, “Palm theory”, “length-based sampling”.…
Introduction We have continued our investigation of geometric controls by investigating conserved quantities derived from Noether’s (first) theorem . Here we look at a slight extension, where the Noether charge is not conserved for the system itself, but across classes of systems. Here, we will look at a particular case of this phenomenon: dynamical similarity. Note: Much of this material was…
Introduction In the Paradox of Taste , I looked at novels as information-theoretic objects. One question I asked was: what if all novels that could ever exist were enumerated and indexed in the Library of Babel? The Library of Babel is gigantic. A back-of-the envelope calculation shows that there are roughly to grammatical-ish English strings of novel length 1 . Even is a superastronomical number.…
Introduction Let’s extend the discrete controls framework and Noether’s theorems to include time-invariance. We’ll start with extending the continuous version, then discretize. Edit: I refactored this post on December 8th 2025, moving the discussion of homogeneous potentials and dynamical similarity to the subsequent post . Some symmetries (such as dynamical similarity) do not make the physical…
Introduction In a previous essay I considered the problems associated with generating novels. With the introduction of the new Nano-Banana Pro , let’s revisit those same basic information bottleneck argument with respect to pictures. All arguments are back-of-the-envelope. Count the Bits Consider the map: is Nano-Banana (or any other generative model that produces pictures). You feed it a sequence…