Figureiii

Collapse

a distribution refitted on its own output, generation after generation

Begin with a population — the grey curve, which has a wide, lumpy, uneven shape, because real populations do. Fit a model to it. Draw a finite sample from the model. Throw the population away. Fit the next model to the sample.

Grey: the original population, shown throughout for reference. Coloured: the current generation. Nothing here is scripted; the sampling is live and the run is different every time.
What this shows

A histogram of an original population is drawn in grey: broad, asymmetric, with three distinct modes and two long thin tails. A coloured curve shows the current generation — a mixture of at most four Gaussian components, fitted at each step to a finite sample of the generation before and to nothing else. A readout gives how much of the original spread survives and how many components are left; a control sets the sample size, which is the decisive number. At a sample of forty the tails are gone within two or three generations, because a finite sample rarely contains a rare value and what is not sampled cannot be refitted. Components then begin to be pruned, and a pruned component never returns, because there is no longer anything in the world it could be re-fitted from. Averaged over twelve runs, by generation ten the curve holds about three quarters of the original spread with under three components; by generation twenty, just over half; by generation forty, a little under two fifths of the spread and usually a single component. Raise the sample to three hundred and fifty and the same population survives the same forty generations with about six sevenths of its spread and three or four components still standing. The mechanism is identical in both runs. What differs is how much of the world each generation was permitted to see, and that is a budget, and somebody sets it.

Run it more than once. The endpoint is always the same shape and never in quite the same place, which is the part that should worry you: each collapse produces a confident, coherent, internally consistent world, and there is no way to tell from inside one which of them you are in.

Then raise the sample and watch the same population survive the same forty generations almost untouched. Nothing about the mechanism changed. What changed is how much of the world each pass was allowed to look at — and that is a budget, and somebody sets it, and it is set by what it costs.