Yes that’s what we try here. Generalize the property we investigate (asymmetry) by quantifying it via how rare a given arrangement is for an isotropic model. We then test how often similarly rare systems are found in sims; no requiring a specific arrangement, just having the same isotropic frequency - ThreadSky

8minutesold.bsky.social • 46 days ago

Yes that’s what we try here. Generalize the property we investigate (asymmetry) by quantifying it via how rare a given arrangement is for an isotropic model. We then test how often similarly rare systems are found in sims; no requiring a specific arrangement, just having the same isotropic frequency

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astromikemerri.bsky.social•46 days ago

Just to clarify, as far as I can tell your generalisation is limited to other forms of *asymmetry*, so would not identify an empty shell or a planar distribution or a prolate pencil or, indeed, a rude word as in any way weird.

8minutesold.bsky.social•46 days ago

In Michael‘s example with the balls, this would count all cases of oddly-colored balls as similarly rare. So if there are 20 single balls each with a different color and 80 red ones, observing e.g. a purple one would result in a simulation analog frequency of 20%. We wouldn’t call that a challenge.

astromikemerri.bsky.social•46 days ago

Only if strange colour is associated with asymmetry, rather than, as I clearly intended, any other peculiar property.

8minutesold.bsky.social•46 days ago

Though the analogy is limited because we need a base comparison model (isotropy in our case) to compare both the observed and simulated systems against. We need that to define what we call the isotropic frequency, which essentially quantifies the „unlikeliness“ of a given system.

8minutesold.bsky.social•46 days ago

Of course there can be many more properties, which I think is the point Michael wants to make. To stick with the balls, that’s like suggesting to not only look for color, but also whether a ball is too big, of a different material, less massive, in fact a cube not a ball, or whatever.

8minutesold.bsky.social•46 days ago

If course there are infinite possibilities then, and thus one could always find something that sticks out. But as I tried to argue before, we didn’t set out to search for a weird feature,but focus on one that is established and rather fundamental.

astromikemerri.bsky.social•46 days ago

This is simply not true. You observed the property and *then* tried to establish how unlikely it was. When there are many other such properties (including arguably even better established ones like flattening and central concentration), such a posteriori analysis is statistically flawed.

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