I saw Wolfram give a live talk after launching his big ass book on cellular automata being the foundation of all things. It seemed far fetched and I don’t think anyone outside of his egosphere takes the concept seriously. Let alone understands it.
He may be off putting at times but when he gets in to it he can be very interesting to listen to.
(Constructivist mathematics is a thing, and it is pretty easy to formulate physics in a constructivist framework. Many serious quantum theoreticians do.)
- because if we had those tools we would not call them "compkex nonlinear phenomena".
- maybe, but what makes you think this one is the one?
However in the realm of applied math, linear functions rather uniquely have a set of standard algorithms which work on all classes of linear functions, which make them very, very easy to work with. And any non-linear function can be approximated to whatever level of detail you want just by adding more (linear) parameters. You can try solving your non-linear function slightly more exactly... but why bother?
It's like saying "why don't we have other models of computation besides a Turing machine?" to which the answer is: "we do. but every computation can be represented as a Turing machine, so why bother?"
This isn't perfect but something like, math express things while computation progresses things.
You could argue that a particular mathematical framework is computational but I'm just trying to exemplify a distinction.
I think your intuitions about how math works is an unfortunate side effect of how math is often taught, and not so much reflected in mathematics itself.
https://en.wikipedia.org/wiki/Constructivism_(philosophy_of_...