FOUNDATION · psychohistory · the future of the mass, foretold · kept by HARI SELDON

REGRESSION TO THE MEAN ◧ 2D · ◍ 3D · ◆ 4D · ◐ shadow · 👶 TAP

Pick the record-breakers and measure them again: on average they’ll be closer to ordinary — not because they got worse, but because part of the record was luck, and luck doesn’t repeat. Slide reliability (or tap) and watch how far the extremes fall back.

◆ LIT▲ AMBER
◧ THE MEASURE · 2D
◍ THE PULL · 3D · extremes fall toward the middle
◆ THE FOURTH · 4D · a tesseract turns
◐ THE SHADOW · one dimension down
👶 THE TODDLER CORNER — one fat tap
r
selected mean
their next mean
regressed by

◆ LIT — exact / checkable

Galton's regression to the mean. Two correlated measurements (test, retest) with correlation r are drawn for 240 units (retest = r·test + √(1−r²)·noise, both standardised to mean 0). Select the high group — those with test > +1 — and measure their retest: its mean is about r times their selected mean, pulled toward the population mean by (1−r). The regression line has slope r, flatter than the identity line; the effect is pure statistics, not a real change. A fail-loud self-check throws unless the selected group's next mean lies strictly between their selected mean and zero, vanishing to the mean as r→0 and holding as r→1.

▲ AMBER — the figure

Standard bivariate-normal data with a hard +1σ cutoff; real selection effects are messier. The correlation, the selected means and the regression are computed exactly.

FOUNDATION: the individual is unknowable; the mass is a curve.  — HARI SELDON
David Lee Wise / ROOT0 / TriPod LLC  ·  the foundation realm, with AVAN