mathematics

Files exploring the philosophy and foundations of mathematics.

• HeroClix
• Philosophy of Logic and Mathematics
• Computation and Information Theory
• The Multiplayer Coalition Problem
• The Nash Bargaining Problem
• Subgraph Investment Optimization
• D&D Spell Damage Model
• HoP Ep 5: Pythagoras
• The Equation of Exchange and the Transaction Multiplier
• A History of Logic
• Master of Magic — Economic Analysis
• Energy-Based Models — Aleph + Lean producing machine-checkable proofs at 99.4% on PutnamBench; formal verification as the bottom layer of the reasoning stack
• Catan — 47,000 Games of Empirical Findings — Catan as a multi-agent stochastic dynamic optimization problem; pip-weighting, graph board, 27% classifier accuracy on opening
• Catan 50-Game Validation — pip-weighted exposure analysis with archetype classification on the 50-game public dataset
• BattleTech Simulator — Monte Carlo combat simulator to derive empirical BattleValue for BattleTech mechs and find bargains in the official BV2 system.
• BattleValue — A Universal Combat Comparison Metric — BV = sqrt(Attack × HP).
• Emergence, Convergence, and the Strange Loop — The vault’s metaphysical position, stated explicitly: what logic is, why it works, why it doesn’t need God, and what it can’t prove about itself.
• Eric Weinstein on Gauge Theory Applied to Economics (w/ Bob Murphy) — The “price level” is a fiction.
• Gödel’s Incompleteness Theorems — No sufficiently powerful formal system can be both complete and consistent.
• Intuitionistic Logic — What if truth requires proof? Drop the excluded middle and logic becomes constructive — and accidentally invents the theoretical foundation of programming.
• Non-Classical Logics — What happens when you challenge the other axioms? Contradictions that don’t explode, truth that comes in degrees, and premises that must actually be relevant.
• Opposing Forces — Why Every Action Generates a Reaction — A metaphysical exploration of why concentrated power always produces counter-forces, and whether this is a fundamental feature of reality.
• Quantum Logic — The other non-classical logics were invented by philosophers.
• Symmetry Breaking — How Constitutive Features Emerge From Balanced Forces — If every action has an equal and opposite reaction, why isn’t reality stuck at zero? The answer isn’t a mysterious origin event — it’s that perfect balance is unstable, asymmetr…
• The Formal Revolution (1847–1931) — In 84 years, logic went from a philosophical discipline to the foundation of mathematics, computing, and the limits of knowledge itself.
• The Godel Governance Problem — Can a system be powerful enough to prevent monopoly without becoming one?
• The Technology-Governance Gap — When the systems we build exceed our ability to understand them, who governs?
• Battlezone (1980) — 3D Without a Multiply Instruction — fixed-point 1.15 trig without a multiply instruction: quarter-wave table folding, octant-folded arctangent via one division, and an octagonal-boundary distance approximation simplified to 0.375·min + 1.0·max so it costs two shifts and an add
• Arithmetic Scarcity and the 3D Problem — what a 3D pipeline does when multiplication costs ~25 additions; the transform collapses available when geometry is constrained
• Stellar 7 (1983) — The Same Game Without the Coprocessor — changing coordinate systems to delete an operation: polar storage turns a 4-multiply Y-axis rotation into one addition plus a 2-multiply polar→Cartesian conversion
• Arithmetic as a Purchase — Sixty Years of Paying for Multiply — four ways of coping with unaffordable multiplication (buy / memoize / restructure / parallelize), all four already visible in commercial hardware by 1964
• Hangman — Solving Both Sides — exact backward induction with an α-cap sandwich that certifies its bounds (unsolved lengths plotted in red); tractability is set by branching + path reconvergence, not nominal state-space size