Concept

Simplex

The set of lists of non-negative numbers adding to a fixed total, which for three numbers is a triangle. Distributions and divisions both live in one, so a claim about every distribution becomes a claim about a region of it.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The 91 histograms 12 draws can produce. A triangle whose points are the possible histograms of a fixed number of draws over three faces, each drawn as a dot shaded by how far it is from the true distribution.

When the whole histogram deviates

The rung below priced a rare average. Ask instead for the chance that the whole tally of outcomes comes out wrong, and the exponent is no longer a function of one number — it is a distance between two distributions, and every rare-average rate is a shadow of it.

probability · central limit

The splits no group can beat, for three partners. The triangle of ways to split a fixed total between three players, with each coalition's demand drawn as a straight cut across it, and the region surviving every cut shaded.

A split nobody can walk away from

Every way of dividing what a group earns is a point of a triangle, and every coalition's threat to leave cuts a straight line across it. What survives all the cuts is the set of stable divisions — and for one three-player game there is nothing left.

applied · the core

Named alongside it

The objects these essays reach for when they reach for this one.

Allocation Central limit theorem Coalition Constraint Cooperative game Core Counting argument Empirical distribution Entropy Exhaustive search Fairness Large deviations

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