Discussion about this post

User's avatar
Will's avatar

The description of math axioms is not so good an illustration of your point. In mathematics there is a phenomenon where we can interpret one system of axioms within another, so every piece of mathematics done in one system of the axioms carries over to the other. (This is in contrast to physical systems where there is always some cost to interfacing two different systems.)

Setting aside the issue of axiom systems mathematicians haven't thought up yet, we understand pretty well which systems can be interpreted within which other systems.

Instead a much bigger issue is with mathematical concepts and definitions. We define fields of mathematics around mathematical concepts, and study questions that can be simply expressed using those concepts. It is hard to move to new concepts because so much of our previous work is expressed using the old concepts.

Expand full comment
Overcoming Bias Commenter's avatar

Reminds me of Gall's Systemantics ( https://en.wikipedia.org/wi... ), in particular the principles- "As systems grow in size, they tend to lose basic functions."- "The larger the system, the less the variety in the product."

Points that you don't spell out explicitly but that clearly support your point:- "A complex system that works is invariably found to have evolved from a simple system that works."- "A complex system designed from scratch never works..."

While all of these principles are anecdotally (and often humorous) I think they draw on crucial insights into these kind of complex systems.

Expand full comment
11 more comments...

No posts