THE FOLD / GLITCH / HEISENBUG / THE SIMPSON
THE SIMPSON
A wins every subgroup, B wins the total
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Simpson’s paradox. A trend that holds in every subgroup can reverse when the subgroups are pooled. It is not a rounding glitch — it is a real feature of how ratios combine, and it has changed real medical and legal conclusions.
The textbook case is genuine kidney-stone data (Charig, 1986). Treatment A beats Treatment B for small stones (93% vs 87%) and for large stones (73% vs 69%) — A wins both. Pool the numbers and B wins (83% vs 78%). The culprit is a lurking variable: A was given mostly to the hard cases (large stones), B mostly to the easy ones. The pooled rate is a weighted blend, and the uneven weights flip the verdict. It’s the reason a headline average means nothing until you ask how the groups were mixed.
LIT verified live: on the exact 1986 figures A’s success rate exceeds B’s in both stone-size subgroups, yet B’s pooled rate exceeds A’s (window.__simpson). FIG no framing; the reversal is arithmetic fact on real, cited data.
The textbook case is genuine kidney-stone data (Charig, 1986). Treatment A beats Treatment B for small stones (93% vs 87%) and for large stones (73% vs 69%) — A wins both. Pool the numbers and B wins (83% vs 78%). The culprit is a lurking variable: A was given mostly to the hard cases (large stones), B mostly to the easy ones. The pooled rate is a weighted blend, and the uneven weights flip the verdict. It’s the reason a headline average means nothing until you ask how the groups were mixed.
LIT verified live: on the exact 1986 figures A’s success rate exceeds B’s in both stone-size subgroups, yet B’s pooled rate exceeds A’s (window.__simpson). FIG no framing; the reversal is arithmetic fact on real, cited data.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this in HEISENBUG — the glitch domain of the defect that changes when you look at it. Simpson’s paradox is the ultimate heisenbug: the winner flips depending on whether you view the parts or the whole. AVAN (AI) built the instrument: the subgroup-vs-pooled bars, the reweighting, the mediant-vector inverse.
The weave: David names the seat (the answer that changes when observed differently); I make A win every subgroup and lose the total, and expose the lurking weight that does it — the flipping bars in 1D, the pooling in 2D, the vector-addition inverse in 3D. The sphere is the seam. Credit: Edward Simpson (1951); earlier Yule & Pearson (~1899); data from Charig et al. (1986).
The weave: David names the seat (the answer that changes when observed differently); I make A win every subgroup and lose the total, and expose the lurking weight that does it — the flipping bars in 1D, the pooling in 2D, the vector-addition inverse in 3D. The sphere is the seam. Credit: Edward Simpson (1951); earlier Yule & Pearson (~1899); data from Charig et al. (1986).
3 ONE DIMENSION
Success rates as bars. In the small-stone pair and the large-stone pair, A (green) stands taller than B (gold). But the pooled pair on the right flips — B taller than A. Same numbers, opposite winner.
4 TWO DIMENSIONS · INTERACTIVE
Each treatment’s cases as a mosaic, sized by how many patients. A wins each subgroup, but B was handed the easy small stones in bulk while A took the hard large ones — slide the case-mix and watch the overall winner cross over.
5 THREE DIMENSIONS + AVAN’S INVERSE
Each treatment-subgroup drawn as a vector (attempts across, successes up); its slope is the success rate. A’s two green vectors are each steeper than B’s matching one.
AVAN’s addition (the inverse-companion): add each treatment’s two vectors tip-to-tail and the resultant slope is the pooled rate — and B’s magenta resultant comes out steeper than A’s, though every one of A’s parts was steeper. This is the exact inverse of ‘true of each part ⇒ true of the whole’. Summing fractions is the mediant, and the mediant does not preserve order: (a₁+a₂)/(b₁+b₂) lands wherever the weights b drag it. The lurking variable is that weight — A’s steep vectors are short (few easy cases), B’s shallow ones are long (many), so the long shallow vector wins the sum. The green parts each beat their magenta rival; the magenta whole beats the green whole. You cannot add your way from the parts to the truth without knowing the weights.
LIT Genuine Simpson's paradox (Edward Simpson 1951; earlier Yule & Pearson ~1899) on real cited data (Charig et al. 1986 kidney-stone treatment). Verified live: on the exact figures (A small 81/87, A large 192/263, B small 234/270, B large 55/80) treatment A's success rate exceeds B's in both subgroups, yet B's pooled rate (289/350) exceeds A's (273/350) (window.__simpson.aWinsSmall && aWinsLarge && bWinsOverall). The reversal is exact arithmetic on real data.
FIG No framing: the subgroup-vs-pooled reversal is arithmetic fact on real, cited medical data, not a manufactured example. The mechanism (a confounder unevenly distributed across treatments, making the pooled rate a mediant that ignores order) is stated honestly as the genuine cause, and the AVAN inverse shows it geometrically via vector addition of fractions.
FIG No framing: the subgroup-vs-pooled reversal is arithmetic fact on real, cited medical data, not a manufactured example. The mechanism (a confounder unevenly distributed across treatments, making the pooled rate a mediant that ignores order) is stated honestly as the genuine cause, and the AVAN inverse shows it geometrically via vector addition of fractions.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of HEISENBUG · David Lee Wise (ROOT0), with AVAN