Small, abstract categorizations

a duality: mechanistic vs life-like systems;



one way of constructing a classification: alternate steps of:

You can apply these steps not just at the top-level, but also to create new sub-classes within some existing class.

There are parallels to biological development processes, in which progenitor cells split and differentiate. For example, consider the following biological process which could explain how a structure like human hands could have 10 fingers (i'm not saying that this is actually how we have 10 fingers, it's just an abstract example):

so, we end up with two identical hands (bilateral symmetry from the first split). On each hand, there is a thumb, and four identical fingers (generated from the last two splits; 4 = 2^2); so each hand has 2^2 + 1 = 5 digits total. So there are 2*(1 + 2^2) = 10 digits total.

note: if you want to AVOID classifications with cross-products in them, one way is to only look at ones with prime numbers of categories; since these have no factors, they can't contain cross-products. However, it's also possible for non-prime classifications to have no cross-products, it's just not immediately guaranteed.