THE FOLD / GRIND / THE HOT LOOP / THE RANKING INVERTS
THE RANKING INVERTS
fewer bits kept, and the better operator
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Six ways to fold a space, priced in bits. Rank them by bits kept and one operator wins; rank them by whether anything can be recovered and a different one does. Symmetrising keeps fewer bits than tracing an arm and is the better operator, because it is reversible on its image. A single-number ranking picks the wrong one.
LIT verified live. dim Sym4(C8) = C(11,4) = 330, which keeps 8.3663 bits out of 12, losing 3.6337. Tracing one arm leaves 512 dimensions — 9.0000 bits, strictly more. The multiset identity C(n+k−1, k) reproduces 330 independently.
LIT verified live. dim Sym4(C8) = C(11,4) = 330, which keeps 8.3663 bits out of 12, losing 3.6337. Tracing one arm leaves 512 dimensions — 9.0000 bits, strictly more. The multiset identity C(n+k−1, k) reproduces 330 independently.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) found the inversion and then changed the instrument rather than the prose: “symmetrize keeps FEWER bits than trace-1-arm (8.37 vs 9.00) and is the better operator, because it is reversible on its image. A single-number ranking picks the wrong one. W4 plots two axes for exactly this reason, and verify.js asserts the inversion rather than leaving it as prose.”
AVAN (AI) notes what makes that response unusual. Finding that your metric misorders the thing it measures normally produces a caveat; here it produced a second axis on the plot and an assertion in the test suite, so the inversion is now something the pack fails on if it ever stops being true. A caveat degrades quietly; a failing assertion does not.
AVAN (AI) notes what makes that response unusual. Finding that your metric misorders the thing it measures normally produces a caveat; here it produced a second axis on the plot and an assertion in the test suite, so the inversion is now something the pack fails on if it ever stops being true. A caveat degrades quietly; a failing assertion does not.
3 ONE DIMENSION
Bits kept, and recoverability, on the same operators.
4 TWO DIMENSIONS · INTERACTIVE
One axis, then two. Watch the order change.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: two operators, two orderings.
AVAN’s addition (the inverse-companion): the forward reading is “use two axes, because one misorders them.” The inverse is that two axes do not order anything either. A point that keeps more bits and a point that is recoverable are incomparable until someone supplies a weight, and adding an axis converts a wrong answer into no answer rather than into a right one. Read backwards, the honest gain is that the choice has been handed back to whoever has the use case — which is progress, and is not the same as a ranking.
LIT dim Sym^4(C^8) = C(11,4) = 330, which keeps 8.3663 bits out of 12, losing 3.6337, while tracing one arm leaves 512 dimensions at 9.0000 bits - strictly more - yet symmetrisation is reversible on its image and tracing is not; the multiset identity C(n+k-1, k) reproduces 330 independently
FIG David found the inversion and then changed the instrument rather than the prose: 'symmetrize keeps FEWER bits than trace-1-arm (8.37 vs 9.00) and is the better operator, because it is reversible on its image. A single-number ranking picks the wrong one. W4 plots two axes for exactly this reason, and verify.js asserts the inversion rather than leaving it as prose.' AVAN notes what makes that response unusual: finding that your metric misorders the thing it measures normally produces a caveat, and here it produced a SECOND AXIS and an assertion in the test suite. A caveat degrades quietly; a failing assertion does not.
FIG David found the inversion and then changed the instrument rather than the prose: 'symmetrize keeps FEWER bits than trace-1-arm (8.37 vs 9.00) and is the better operator, because it is reversible on its image. A single-number ranking picks the wrong one. W4 plots two axes for exactly this reason, and verify.js asserts the inversion rather than leaving it as prose.' AVAN notes what makes that response unusual: finding that your metric misorders the thing it measures normally produces a caveat, and here it produced a SECOND AXIS and an assertion in the test suite. A caveat degrades quietly; a failing assertion does not.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE HOT LOOP · David Lee Wise (ROOT0), with AVAN