Is the Universe Made of Math?

[struggle4progress]

18. Abstractions are a useful trick we humans have learned, to handle the very real limits

on our ability to focus and to remember

One reason I like mathematics is simply that I don't have a great memory: so if I can "figure it out" instead of "recalling it," that's helpful to me

A cosmology "based solely on mathematics" would be profoundly unscientific: Max Tegmark cannot understand this world by pure thought --- and if he believes he can, he falls into a dangerous ideological error

The great insight from the era of the "natural philosophers" was that we can improve some of our abstractions by discarding those which fail observational or experimental tests and disregarding those which are untestable: that method works very well for a CERTAIN class of abstractions --- though not for ALL abstractions I consider important

The language of mathematics became part of the language of science because mathematics can be organized in a logical fashion and because some mathematics is associated with useful computational rules

But much of modern mathematics cannot be associated with useful computational rules; and so we might have cause to doubt the actual scientific value of much of mathematics

The computable fragment of mathematics is a rather strange and wild land: problems that can be solved by computation can, by very slight modification, become problems that are impossible to solve by computation

We should suspect such phenomena will occur in good physics as well: a rather satisfactory and computable theory might, by an reasonable modification, become a theory which does not admit a general solution by computation --- in which case, we might by a variety of clever attacks, be able to solve THESE special cases or THOSE special cases of the theory, without any hope of ever solving certain OTHER special cases