Series are subjects that are, unlike articles, too long to fit in one page. They spread over multiple episodes for more pleasure.

Les Circuits Longs Les Circuits Longs in progress

Dissolution runs at computational speed. Construction runs at biological speed. Friction was the governor that kept them in sync. This series traces a single mechanism from several angles: what happens when optimization outpaces formation.

Leptokurtic Leptokurtic in progress

Financial returns have fat tails. Crashes that Gaussian models call impossible happen regularly. This series assembles twenty centuries of financial data, builds a crash-detection toolkit from 17 methods, tests tail hedging with real options data, and then explains the geometric logic tying the whole picture together.

Ethereum Ethereum in progress

Modern economic systems rest on two foundations: tools that expand productive capacity and institutions that define who controls their output. The internet transformed how information moves, but it did not reconstruct the institutional machinery that governs ownership and exchange. Digital economic life therefore expanded without a durable system of rights, enforcement, or jurisdiction. Blockchain networks, and Ethereum in particular, address this gap by embedding institutional functions in software and enforcing them through economic incentives and cryptographic verification.

Theorem Proving Theorem Proving complete

A four-part series on the connection between types and proofs: the Curry-Howard correspondence, a tiny prover implemented explicitly in Python, a mini-Lean embedded in Julia’s type system, and writing proofs in Lean.

Concrete Concrete in progress

Concrete is a series about a systems language designed so the compiler can say more than pass or fail.

If you are new to the series, start with Why Concrete Exists. If you want the most practical demonstration first, read When the Compiler Is the Oracle. If you want the living reference material, use Concrete Spec.

Suggested reading order:

  1. Why Concrete Exists
  2. The Rust Effects Debate and Concrete’s Case for a Smaller Language
  3. The AI Training Data Trap for Programming Languages Has an Exit
  4. Can I prove Concrete programs in Lean?
  5. When the Compiler Is the Oracle
  6. What Concrete Makes Worse
  7. A Fact-Producing Compiler