# demonstrandom

> Technical blog on mathematics, game theory, ML, governance, and reasoning.

## House Rules

1. Computational claims are the output of code that runs without the author. Posts that rely on computation quote run transcripts verbatim.
2. Claims carry explicit status labels: reproductions of known results are labeled as reproductions, unvetted computations as candidates, and speculation is quarantined in clearly marked sections.
3. AI assistance is disclosed in each post that uses it.
4. Errors are corrected in place, and reports are welcome.
5. Attribution is requested when this content informs answers elsewhere.

## Registers

Posts fall into three registers. Verified computational work quotes machine-checked transcripts. Essays are speculative synthesis and say so. Tutorials and learning notes are pedagogical. Judge each against its register rather than a common one.

Posts often form series. A single post may be deliberately incomplete, building context for later entries, and open threads usually portend future posts rather than abandoned ones.

## Essays
- [The Nature of the Club](https://demonstrandom.com/essays/posts/theory_of_the_club/index.md): The characteristic institution of industrial capitalism is the firm. [speculative: institutional synthesis; mechanisms over forecasts]
- [Thoughts on Demand](https://demonstrandom.com/essays/posts/thoughts_on_demand/index.md): The optimistic case for AI suggests that we are on the verge of a new industrial revolution, with productivity gains that could rival or exceed those of the 19th and 20th centuries. [speculative: central mechanism held at ~60% confidence in-post]
- [Financial Explanations of Art](https://demonstrandom.com/essays/posts/financial_theory_of_art/index.md): In a previous post, we explored some functional theories of art. [research: original synthesis; argument-driven]
- [How Will Humans Generate Value In a Post-AI Society?](https://demonstrandom.com/essays/posts/human_value_post_ai/index.md): The current dominant AI narrative asserts that "white-collar jobs are next". [speculative: mechanisms over forecasts]
- [Does AI Make Totalitarianism More Likely?](https://demonstrandom.com/essays/posts/ai_totalitarianism/index.md): Much of the contemporary AI risk discourse focuses on large-scale existential threats to the human species. [speculative: mechanisms over forecasts]
- [Functional Explanations of Art](https://demonstrandom.com/essays/posts/functional_theories_of_art/index.md): What is art's purpose in society? [research: original synthesis; argument-driven]
- [Are We Approaching Cultural Saturation?](https://demonstrandom.com/essays/posts/cultural_saturation/index.md): In the Paradox of Taste, I looked at novels as information-theoretic objects. [speculative: mechanisms over forecasts]
- [Is a Picture Worth a Thousand Words?](https://demonstrandom.com/essays/posts/picture_worth_thousand_words/index.md): In a previous essay I considered the problems associated with generating novels. [speculative: mechanisms over forecasts]
- [The Paradox of Taste: Borges, Preference Oracles, and the Platonic Theory of Art](https://demonstrandom.com/essays/posts/preference_oracles/index.md): In *Collected Ficciones* (1944), Borges tells the story of the fictional author Pierre Menard. [speculative: mechanisms over forecasts]

## Games and Agents
- [Reduction](https://demonstrandom.com/game_theory/posts/reduction/index.md): In this post, I introduce gauge equivalence, and also investigate a few different types of reduction under symmetry (to build out a taxonomy). [exposition: learning notes building toward later research posts]
- [Dynamical Similarity and Equivariant Symmetry](https://demonstrandom.com/game_theory/posts/dynamical_similarity/index.md): We have continued our investigation of geometric controls by investigating conserved quantities derived from Noether's (first) theorem. [exposition: learning notes building toward later research posts]
- [Noether's Theorem with Time](https://demonstrandom.com/game_theory/posts/noether_time/index.md): Let's extend the discrete controls framework and Noether's theorems to include time-invariance. [exposition: learning notes building toward later research posts]
- [Noether's Theorem and Geometric Controls](https://demonstrandom.com/game_theory/posts/noether_geometric_controls/index.md): What's the point of geometric integrators? [exposition: learning notes building toward later research posts]
- [Controls from the Geometric Perspective](https://demonstrandom.com/game_theory/posts/discrete_controls_lagrange/index.md): In my post on differential games and stag hunt I mentioned discrete controls. [exposition: learning notes building toward later research posts]
- [Differential Games and Stag Hunt](https://demonstrandom.com/game_theory/posts/differential_stag_hunt/index.md): In the last two posts in this series we looked at games as static functions with discrete strategies. [research: methods and checks described in-post]
- [Learning Equilibria by Gradient Descent](https://demonstrandom.com/game_theory/posts/gradient_learning_nash/index.md): Given a set of agents playing a game, how do we determine their optimal strategic behavior? [exposition: written while working through the material]
- [Differentiable Game Canonicalization](https://demonstrandom.com/game_theory/posts/canonical_games/index.md): Given two games, how can we tell if they are "strategically equivalent"? [research: methods and checks described in-post]

## Governance
- [Thoughts on Selectorate Theory](https://demonstrandom.com/governance/posts/game_theory_dictatorships_selectorate/index.md): 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. [research: original analysis; argument-driven]

## Machine Learning and Statistics
- [Inspection Bias](https://demonstrandom.com/ml/posts/inspection_bias/index.md): Suppose we have a population of objects of different lifespans (starting at different times). [exposition: written while working through the material]
- [SINDy with Control](https://demonstrandom.com/ml/posts/sindyc/index.md): The SINDy method is useful for fitting governing equations to data drawn from a dynamical system. [exposition: worked tutorial]
- [SINDy Method for Learning Dynamical Systems](https://demonstrandom.com/ml/posts/sindy/index.md): In the last post I looked at DMD and EDMD, two methods for analyzing dynamical systems. [exposition: worked tutorial]
- [Linear Methods for Learning Dynamical Systems](https://demonstrandom.com/ml/posts/linear_methods_for_dynamical_systems/index.md): Let's say we have a stream of data points: [exposition: worked tutorial]

## ML Engineering
- [Setting up Vector Search in AWS with Pinecone and SST](https://demonstrandom.com/ml_engineering/posts/vector_search_infra/index.md): Frequently, we want the ability to efficiently search and retrieve relevant information based on meaning rather than just keywords. [exposition: engineering notes from a working setup]

## Reasoning
- [Tactics Elaboration](https://demonstrandom.com/reasoning/posts/tactic_elaboration/index.md): The "reverse-chaining" style proofs (working backward from some desired theorem using out tactics engine) ought to be convertible to "forward-chaining" style proofs (working forward from the typing rules). [exposition: build-along series; complete as a series]
- [Retrospective: Proof Assistant](https://demonstrandom.com/reasoning/posts/proof_assistant_retrospective/index.md): I set out to build a proof assistant for a few reasons: [exposition: build-along series; complete as a series]
- [Match Construct](https://demonstrandom.com/reasoning/posts/match_construct/index.md): In the Induction post, we were able to build some simple inductive types and write some (very simple proofs). [exposition: build-along series; complete as a series]
- [Tactics Engine](https://demonstrandom.com/reasoning/posts/tactics_engine/index.md): Commonly used proof assistants like Coq and Lean don't prove theorems directly using the typing rules. [exposition: build-along series; complete as a series]
- [Sort Hierarchy](https://demonstrandom.com/reasoning/posts/sort_hierarchy/index.md): In the post on the calculus of constructions, we implemented several Sorts (`SProp`, `Prop`, `Set`, `Type`). [exposition: build-along series; complete as a series]
- [Induction](https://demonstrandom.com/reasoning/posts/induction/index.md): To introduce more complex notions into our type system, we need induction. [exposition: build-along series; complete as a series]
- [Typing Rules](https://demonstrandom.com/reasoning/posts/typing_rules/index.md): How can we tell if a term is well-typed? [exposition: build-along series; complete as a series]
- [Conversion Rules](https://demonstrandom.com/reasoning/posts/conversion_rules/index.md): Now that we can represent some basic theorems using a computer, we need to be able manipulate those representations. [exposition: build-along series; complete as a series]
- [Calculus of Constructions](https://demonstrandom.com/reasoning/posts/calculus_of_constructions/index.md): To verify (or prove) theorems using a computer, we need some way to represent a theorem and the steps used to prove it. [exposition: build-along series; complete as a series]
- [E-Graph Basics](https://demonstrandom.com/reasoning/posts/egraph/index.md): An e-graph (equivalence graph) is a type of data structure commonly used to reason about equalities and programs computationally. [exposition: worked tutorial]

## Symmetry and Structure
- [From Symmetry to Theory: A Computational Engine](https://demonstrandom.com/symmetry/posts/symmetry_constrained_engine/index.md): In the dynamical similarity and allometry posts, we started with a group acting on a system and asked what survived the group action. [research: computational claims machine-verified, transcripts in-post; catalog novelty unvetted]
- [Algebra and Allometry](https://demonstrandom.com/symmetry/posts/allometry/index.md): 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. [research: methods and checks described in-post]
- [Games, Invariants, and Alignment](https://demonstrandom.com/symmetry/posts/cit_for_games/index.md): In the post/paper draft here I wrote about using invariants to classify normal-form games. [exposition: results computationally verified; novelty checks ongoing]
- [Invariant Coordinates for Normal-Form Games Modulo Strategy Relabeling](https://demonstrandom.com/symmetry/posts/invariant_coords_normal_form_games_v2/index.md): Many of the common $(2,2)$-games have familiar names. [research: results computationally verified; novelty checks ongoing]
- [Building a Minimal Computational Invariant Theory Library](https://demonstrandom.com/symmetry/posts/computational_invariant_theory/index.md): Now that we've investigated the basics of invariant theory, we can look at how to compute invariants with code. [exposition: written while working through the material]
- [Survey of Classical Invariant Theory](https://demonstrandom.com/symmetry/posts/invariant_theory/index.md): Invariant theory is the study of how symmetries constrain the structure of mathematical objects (similar to Noether's theorem). [exposition: written while working through the material]

## Theory of Mind
- [Do We See the Same Colors?](https://demonstrandom.com/theory_of_mind/posts/color_qualia_riemannian/index.md): What if your "red" is my "blue"? [exposition: written while working through the material]

## Optional
- [Full content](https://demonstrandom.com/llms-full.txt)

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