Explore
Three ways into the writing: the ideas that keep coming back and how they connect, the simulations built to test them, and the data behind them.
Ideas
The same ideas keep coming back in different places. Each node is an idea; two ideas are joined when the same pieces use both. Pick one to see where it appears.
- Technology
- Capital
- Culture
Ergodicity
7 pieces
- Power Laws, Extremistan, and Non-Ergodicity
- Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
- Markets as Reflexive Fixed Points
- Notes on permanence, time, and ergodicity
- Life as a Double Fixed Point
- The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
- Number Theory and the Arithmetic of Recurrence
Fat tails
8 pieces
- Detecting Crashes with Fat-Tail Statistics
- Power Laws, Extremistan, and Non-Ergodicity
- Markets as Reflexive Fixed Points
- The Limits of Knowing
- Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
- Twenty Centuries of Financial Data: What 240 Countries and 2,000 Years Reveal
- The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
- Crashes Without a Cause: Markets as Phase Transitions
Power laws
7 pieces
- Power Laws, Extremistan, and Non-Ergodicity
- Markets as Reflexive Fixed Points
- Sandpiles and Crashes: How Systems Tune Themselves to the Brink
- Life as a Double Fixed Point
- Detecting Crashes with Fat-Tail Statistics
- Faster Than Exponential: Can You See a Crash Coming?
- Twenty Centuries of Financial Data: What 240 Countries and 2,000 Years Reveal
Criticality
8 pieces
- Crashes Without a Cause: Markets as Phase Transitions
- Life as a Double Fixed Point
- Sandpiles and Crashes: How Systems Tune Themselves to the Brink
- Markets as Reflexive Fixed Points
- Why the Calm Is Dangerous
- Power Laws, Extremistan, and Non-Ergodicity
- Reflexivity by the Numbers
- Faster Than Exponential: Can You See a Crash Coming?
Feedback loops
7 pieces
Crashes
8 pieces
- The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
- Detecting Crashes with Fat-Tail Statistics
- Crashes Without a Cause: Markets as Phase Transitions
- Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
- Faster Than Exponential: Can You See a Crash Coming?
- Sandpiles and Crashes: How Systems Tune Themselves to the Brink
- Markets as Reflexive Fixed Points
- Reflexivity by the Numbers
Leverage
6 pieces
Convexity
4 pieces
Compounding
6 pieces
- Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
- The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
- Faster Than Exponential: Can You See a Crash Coming?
- Power Laws, Extremistan, and Non-Ergodicity
- Notes on permanence, time, and ergodicity
- Detecting Crashes with Fat-Tail Statistics
Risk models
5 pieces
Building companies
4 pieces
Money
8 pieces
- Twenty Centuries of Financial Data: What 240 Countries and 2,000 Years Reveal
- The Tail Hedge Debate: Spitznagel Is Right, AQR Is Answering the Wrong Question
- Detecting Crashes with Fat-Tail Statistics
- The missing institution of the Internet
- The new financial backend of the world
- Finance Is Geometry, and It All Comes Back to Jensen’s Inequality
- Crypto doctrine
- What Actually Moves Prices
Fixed points
8 pieces
- Fixed Points and Attractors
- Logic, Self-Reference, and Category Theory
- Markets as Reflexive Fixed Points
- Chaos, Fractals, and Renormalization
- Life as a Double Fixed Point
- Number Theory and the Arithmetic of Recurrence
- Crashes Without a Cause: Markets as Phase Transitions
- Power Laws, Extremistan, and Non-Ergodicity
Chaos
5 pieces
Self-reference
5 pieces
Proof
16 pieces
- Programming a Mini-Lean in Julia’s Type System
- A Proof Is Only as Good as Its Spec
- Writing Your First Proofs in Lean
- Can I prove Concrete programs in Lean?
- Logic, Self-Reference, and Category Theory
- Propositions Are Types, Proofs Are Programs
- Fede’s Guide to Type Systems: From Generics to Dependent Types
- Building a Tiny Theorem Prover in Python
- When the Compiler Is the Oracle
- Nutrition Labels for Trust
- Why Concrete Exists
- Markets as Reflexive Fixed Points
- A Fact-Producing Compiler
- CommitLLM: How to Verify an LLM Inference
- Fixed Points and Attractors
- Designing a Programming Language for the AI Era
Types
10 pieces
- Fede’s Guide to Type Systems: From Generics to Dependent Types
- Programming a Mini-Lean in Julia’s Type System
- Propositions Are Types, Proofs Are Programs
- The Rust Effects Debate and Concrete’s Case for a Smaller Language
- Building a Tiny Theorem Prover in Python
- Logic, Self-Reference, and Category Theory
- Self-Replicating Programs Emerge from Random Noise
- Writing Your First Proofs in Lean
- Can I prove Concrete programs in Lean?
- When the Compiler Is the Oracle
Capabilities
6 pieces
Compilers
13 pieces
- When the Compiler Is the Oracle
- Fede’s Guide to Type Systems: From Generics to Dependent Types
- Why Concrete Exists
- A Fact-Producing Compiler
- Nutrition Labels for Trust
- Can I prove Concrete programs in Lean?
- Propositions Are Types, Proofs Are Programs
- What Concrete Makes Worse
- Designing a Programming Language for the AI Era
- The Rust Effects Debate and Concrete’s Case for a Smaller Language
- A Proof Is Only as Good as Its Spec
- Programming a Mini-Lean in Julia’s Type System
- Self-Replicating Programs Emerge from Random Noise
Ethereum
4 pieces
AI
10 pieces
- When Civilization Escapes the Human
- Designing a Programming Language for the AI Era
- CommitLLM: How to Verify an LLM Inference
- When the Compiler Is the Oracle
- Friction as Luxury: What We Lose When AI Gives Us What We Want
- China is trying to commoditize the complement
- A Fact-Producing Compiler
- When Risk Models Create Risk
- The missing institution of the Internet
- Legibility Kills What It Measures
Computation
6 pieces
Trust
9 pieces
Institutions
7 pieces
Coordination
3 pieces
Legibility
3 pieces
Tacit knowledge
4 pieces
Friction
3 pieces
The long run
3 pieces
Meaning
2 pieces
Simulations
The interactive models from the essays, to change the assumptions and see what happens. They are models, not measurements: each one generates its own data and none of them reads a market.
Systems where an event makes the next event more likely: sandpile avalanches, the branching ratio, self-exciting Hawkes events, herding on an Ising lattice, reflexive feedback, volatility clustering, risk models creating risk, leverage cascades, and inelastic markets.
What iteration does: contraction to a fixed point, cobweb diagrams, losing stability, the logistic map, Feigenbaum's constant, the tent map, the Cantor set, the Waddington landscape, the Gauss map and continued fractions, small divisors, recursive data types, the diagonal argument, and Lawvere's fixed-point theorem.
What you can and cannot know from data: recognizing power-law tails, when sample averaging stops converging, time versus ensemble averages and ergodicity, the Hill tail-index estimator, critical slowing down, and faster-than-exponential LPPLS bubble shape.
Data
Datasets assembled for the writing and published openly. Each page pins a specific commit, so what you cite and what you download are the same bytes, and states where every series came from and under whose terms.
Exchange rates, precious metals, interest rates, commodity prices, inflation, GDP, real wages and sovereign debt, from 1 CE to 2026, assembled from 26 sources into one reproducible build.