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Complex Systems and Quantitative Mereology

abeljansma.nl

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Re: Complex Systems and Quantitative Mereology

#4

Post by a333999 »

> any description purely in terms of pairwise relationships would miss the fact that the three rings are connected.

Here is one:

A is connected to B

B is connected to C

C is connected to A

This is a description in terms of pairs, and from it is trivial to deduce how the rings are connected.

Re: Complex Systems and Quantitative Mereology

#5

Post by defrost »

a333999 wrote: post #4

> any description purely in terms of pairwise relationships would miss the fact that the three rings are connected. Here is one: A is connected to B B is connected to C C is connected to A This is a description in terms of pairs, and from it is trivial to deduce how the rings are connected.

But they're not pairwise connected.

In the text:

   If you only consider two of the rings and ignore the third, then any pair can be smoothly separated.
and from looking at the diagram. Carefully looking.

Re: Complex Systems and Quantitative Mereology

#9

Post by abelaer »

agnishom wrote: post #3

This is a great philosophical motivation for https://en.wikipedia.org/wiki/Incidence_algebra

That's right! This is secretly about doing calculus on posets. You can actually generalise some notions from incidence algebras to other settings, like groupoids and categories, where you can play the same games. This is something I mostly haven't looked at yet, but I think it might be fun, and some people seem to have found it useful (for example: https://arxiv.org/abs/1809.00941 and https://arxiv.org/abs/2501.06662)
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