[FRIAM] To repeat is rational, but to wander is transcendent

[Jon Zingale]

Let me see if I can add some context. One of Nick's obsessions is that of
emergence, and in particular, he concerns himself with a possible
relationship between emergence and Simpson's paradox. I started to wonder
what there is generally to say about the paradox. As a first approximation,
I think that there is nothing especially "statistical" about the paradox,
rather, it appears to be a consequence of geometry and mereology. I can
imagine a few worms each stretched to the southeast corner of a graph and
yet their aggregate appears to stretch northeast. This leads me to wonder
about the qualities of quantities. When can one expect there to exist such
a disconnect between individuals and wholes? This leads me to think about
intensive versus extensive quantities as they are conceived in
thermodynamics (and now everywhere).

Extensive quantities like magnitudes, counts, volumes, and mass have the
property that when you put two or more individuals together with the same
value as one another, that same property wrt the whole will likely be
different. This case should be especially likely when the number of
dimensions where the extensive quantity manifests is high. On the other
hand, for intensive quantities (density, color, temperature, hardness,
viscosity...) this is not the case.

I feel that there may be something here worth connecting. To reframe
Simpson's paradox in terms of what kinds of quantities remain invariant
when moving from the individual to aggregate *level*.
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