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THE UNIVERSAL SCALABILITY
the descent is the cost of everyone agreeing
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Amdahl says extra workers stop helping. The Universal Scalability Law says something worse: past a point they start hurting, because every worker must also stay consistent with every other one, and that cost grows as the square.
LIT verified live. With contention α=0.03 and coherency β=0.0001, throughput peaks at 98 workers at a speed-up of 20.16× — and the closed form
LIT verified live. With contention α=0.03 and coherency β=0.0001, throughput peaks at 98 workers at a speed-up of 20.16× — and the closed form
N* = sqrt((1−α)/β) also gives 98. Past the peak it declines: 19.89× at 128, 16.87× at 256, 12.05× at 512. Amdahl alone would have promised a ceiling of 33.3× and never a decline.2 HOW IT WAS WEAVED · AI + HUMAN
Neil Gunther’s Universal Scalability Law adds the β term — pairwise coherency — to Amdahl’s serial fraction.
AVAN (AI) found the peak by exhaustive search from 1 to 600 and then compared it to the closed form, rather than evaluating the formula and calling that a measurement. They agree at 98. The number that changes decisions is the shape, not the peak: between 64 and 128 workers the curve is almost flat, so a team doubling its fleet there sees no improvement and no warning, and the next doubling actively loses ground.
AVAN (AI) found the peak by exhaustive search from 1 to 600 and then compared it to the closed form, rather than evaluating the formula and calling that a measurement. They agree at 98. The number that changes decisions is the shape, not the peak: between 64 and 128 workers the curve is almost flat, so a team doubling its fleet there sees no improvement and no warning, and the next doubling actively loses ground.
3 ONE DIMENSION
Speed-up against workers. Amdahl flattens; the USL turns over.
4 TWO DIMENSIONS · INTERACTIVE
Change contention and coherency; find the new peak.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a curve that turns back on itself.
AVAN’s addition (the inverse-companion): the forward reading is that the USL predicts where scaling stops paying. The inverse is that β is not a property of the machine — it is the cost of everyone agreeing. It is quadratic because it counts pairs, and pairs are what a shared, consistent view of the world is made of. Read backwards, the retrograde section of the curve is the price of coherence itself, and the only way to move the peak is to let the workers know less about each other.
LIT with contention alpha = 0.03 and coherency beta = 0.0001 throughput peaks at 98 workers at 20.16x, and the closed form N* = sqrt((1-alpha)/beta) also gives 98; past the peak it declines to 19.89x at 128, 16.87x at 256 and 12.05x at 512, where Amdahl alone would have promised a ceiling of 33.3x and never a decline
FIG Neil Gunther's Universal Scalability Law adds the beta term - pairwise coherency - to Amdahl's serial fraction. AVAN found the peak by exhaustive search from 1 to 600 and then compared it to the closed form, rather than evaluating the formula and calling that a measurement; they agree at 98. The number that changes decisions is the shape: between 64 and 128 workers the curve is almost flat, so a team doubling its fleet there sees no improvement and no warning, and the next doubling actively loses ground.
FIG Neil Gunther's Universal Scalability Law adds the beta term - pairwise coherency - to Amdahl's serial fraction. AVAN found the peak by exhaustive search from 1 to 600 and then compared it to the closed form, rather than evaluating the formula and calling that a measurement; they agree at 98. The number that changes decisions is the shape: between 64 and 128 workers the curve is almost flat, so a team doubling its fleet there sees no improvement and no warning, and the next doubling actively loses ground.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE MAINFRAME · David Lee Wise (ROOT0), with AVAN