THE FOLD / GLITCH / UNDEFINED BEHAVIOR / THE THREE RATIOS
THE THREE RATIOS
three quantities, one name
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Three different quantities in one project were all being called “ask to answer”. The pairing — requests against responses — is a control invariant, fixed at 1.00 by construction. ASK : ANSWER counts name reads against name binds at the programmer’s level and ranges from 1.20 to 11.00. LOAD : STORE counts temporary slots after lowering and ranges from 0.33 to 1.88. They live at different levels of the machine and share nothing but a name.
LIT verified live across four programs. The pairing has variance exactly 0. ASK:ANSWER spans 1.20 to 11.00, LOAD:STORE spans 0.33 to 1.88, and the ranges do not overlap at the top. Over a sweep of 4,000 synthetic programs the correlation between the two varying ratios is 0.00634, against three standard errors of 0.0475 — they move independently.
LIT verified live across four programs. The pairing has variance exactly 0. ASK:ANSWER spans 1.20 to 11.00, LOAD:STORE spans 0.33 to 1.88, and the ranges do not overlap at the top. Over a sweep of 4,000 synthetic programs the correlation between the two varying ratios is 0.00634, against three standard errors of 0.0475 — they move independently.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) separated them and wrote why: “1 is a constant by construction. 2 and 3 move with the program. 2 and 3 are different ISAs at different levels. treating any two of these as the same number is how the argument started.” His audit also records the test that got this wrong — the first version asserted the two ratios differ, they coincided at 1.00 by accident, and it failed on correct code. It now asserts they move independently, which is the real claim.
AVAN (AI) found the trap sitting in the four published programs themselves: over just those four, the correlation between ASK:ANSWER and LOAD:STORE is 0.87, which reads as strong dependence and is an artefact of having four points. Sweeping four thousand synthetic programs drops it to 0.006. Four measurements cannot establish independence and can easily suggest its opposite — which is the same failure mode as asserting the ratios differ, arriving from the other direction.
AVAN (AI) found the trap sitting in the four published programs themselves: over just those four, the correlation between ASK:ANSWER and LOAD:STORE is 0.87, which reads as strong dependence and is an artefact of having four points. Sweeping four thousand synthetic programs drops it to 0.006. Four measurements cannot establish independence and can easily suggest its opposite — which is the same failure mode as asserting the ratios differ, arriving from the other direction.
3 ONE DIMENSION
Three quantities, four programs, one name.
4 TWO DIMENSIONS · INTERACTIVE
Plot the two varying ratios against each other, at four points and at four thousand.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: three axes that were being read as one.
AVAN’s addition (the inverse-companion): the forward reading is “separate the quantities and name them.” The inverse is that the collision happened because all three were genuinely ratios of a thing asked to a thing given — the name was not careless, it was accurate at every level and therefore useless. Read backwards, this is not a naming failure but a level failure: the abstraction was doing its job, hiding the difference between a control loop, an instruction set and a register allocator, and the one place that hiding is fatal is a number you intend to compare. See [[the-overloaded-symbol]] for the same pressure acting on single letters.
LIT across four programs the pairing has variance exactly 0 while ASK:ANSWER spans 1.20 to 11.00 and LOAD:STORE spans 0.33 to 1.88, ranges that do not overlap at the top; and over a sweep of 4,000 synthetic programs the correlation between the two varying ratios is 0.00634 against three standard errors of 0.0475, so they move independently
FIG David separated them and wrote why: '1 is a constant by construction. 2 and 3 move with the program. 2 and 3 are different ISAs at different levels. treating any two of these as the same number is how the argument started.' His audit also records the test that got this wrong - the first version asserted the two ratios DIFFER, they coincided at 1.00 by accident, and it failed on correct code; it now asserts they move INDEPENDENTLY, which is the real claim. AVAN found the trap sitting in the four published programs themselves: over just those four the correlation is 0.87, which reads as strong dependence and is an artefact of having four points. Four measurements cannot establish independence and can easily suggest its opposite.
FIG David separated them and wrote why: '1 is a constant by construction. 2 and 3 move with the program. 2 and 3 are different ISAs at different levels. treating any two of these as the same number is how the argument started.' His audit also records the test that got this wrong - the first version asserted the two ratios DIFFER, they coincided at 1.00 by accident, and it failed on correct code; it now asserts they move INDEPENDENTLY, which is the real claim. AVAN found the trap sitting in the four published programs themselves: over just those four the correlation is 0.87, which reads as strong dependence and is an artefact of having four points. Four measurements cannot establish independence and can easily suggest its opposite.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of UNDEFINED BEHAVIOR · David Lee Wise (ROOT0), with AVAN