Working models

Things that
do not add up

Quantities that multiply, bets that repeat, and games where the other side is thinking too — each one built as something you can operate rather than read.

Operate

The four rooms

Each is a site of its own. Nothing here is a slide deck: every page has a knob, a run button or an opponent.

Log Space Four games about quantities that multiply

OctaveLogdriveDecibanErgodic

An arena shooter whose rings are decades, a five-sector campaign where nothing adds, a Bayesian rail you stack evidence onto, and 240 years of a merchant dynasty in which the dead are struck out of the average. Plus an AM/GM demonstration you can drag, and a cross reference of eighteen ideas against the exact sector or case that teaches each one. When outcomes multiply, the average of the outcomes is not the outcome you get. The gap is worth −σ²/2 per step, and all four games are ways of making it visible. Enter → The Long/Short Desk Hedge-fund decisions, seven pages deep Sizing, hedging, carry and the decisions that follow from them, worked as a desk rather than described. Every symbol on the page is clickable and opens the worked example behind it, so the notation never becomes the obstacle. Includes the Black–Scholes derivation in full, a portfolio sheet, a strategy book and the volatility-drag page the rest of the site argues with. Take the desk → The Mediator's Advantage Correlated equilibrium against Nash, in thirteen games A Nash equilibrium makes players randomize independently. A correlated equilibrium lets one shared device whisper a private recommendation to each of them, and nobody is forced to listen. Thirteen games from two players to four, every payoff editable, all of it solved live — Nash by enumeration, the correlated equilibria by linear programming. In Aumann's 1974 example the mediator reaches a total of 6⅔ where every Nash equilibrium sums to 6. Run the mediator, then try disobeying it. Play the mediator → Living in Log Space 29 models on one master knob Turn a single control and watch twenty-nine separate systems respond together — the argument being that volatility drag is a fact about curvature rather than a fact about markets. The companion drill, Log Ladder, puts order-of-magnitude intuition on one logarithmic ruler. Paired with Log Ladder, linked below. Turn the knob →

Drawing the Hulls A companion to the game theory page: how its two regions are actually computed — one from a finite list of points, the other from inequalities with no points to list. Four draggable figures, and a linear program solved live as you turn the direction. Go deeper

Read

Probability, written out

The mathematics in order, the working that produced the numbers, and the one case where the intuition does not survive being generalized.

A Primer on Log Space The mathematics in order, from the multiplicative setup to the drag term — with five things you can work by hand rather than only read. Start here Working Notes Every number on the site that had to be settled and how it was settled, including the claims that did not survive being checked. The workings Drag in the Complex Plane What volatility drag becomes when the multiplying quantity is complex: one identity covering both cases, a sign flip that is only i² = −1, and the intuition that does not make the trip. Further out Log Ladder Order-of-magnitude intuition drilled on a single logarithmic ruler. Short, and harder than it looks. Drill

Built as static pages on Cloudflare. The single idea underneath most of it: when outcomes multiply rather than add, the average of the outcomes is not the outcome you get.