[godelski]

Working with different objects doesn't make it any less of math. Just because you can derive calculus from set theory (analogous to assembly or even binary here) doesn't make calculus "not math".

Math is about abstractions and relations. See the Poincare quote again.

Plus, the Programming Languages people would like to have a word with you. Two actually: Category Theory. But really, if you get them started they won't shut up. That's either a great time or a terrible time, but I think for most it is the latter.

[GoblinSlayer]

Wheeler: It from bit. Otherwise put, every it—every particle, every field of force, even the space-time continuum itself—derives its function, its meaning, its very existence entirely—even if in some contexts indirectly—from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. It from bit symbolizes the idea that every item of the physical world has at bottom—at a very deep bottom, in most instances—an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes–no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe.

[godelski]

That is not in contention with what I said, now is it?

Wheeler is arguing that if a tree falls in the forest, and there is nobody to hear it, that it still makes a sound because there are things that interact with the sound. But if the tree fell in a forest and there was nothing else in the universe then there is no sound because there is no observation.

It helps to read the whole thing[0] and to understand the context of the discussion. This is meta-physics and a deep discussion into what the nature of reality is. Ian Hacker has a good introduction to the subject but I find develop grave misunderstandings when they also do not have the strong math and physics background necessary to parse the words. Even people who understand the silliness of "The Secret" and that an observer need not be human often believe that this necessitates a multi-verse. A wildly convoluted solution to the problem of entropy not being invertible. Or closer to computer terms, a solution that insists that P = NP. There is information lost.

If you wanna argue that there's no difference between the word cup and a cup itself because there is no word without the observer who has the language, then yeah.

[0] https://historyofinformation.com/detail.php?id=5041

[GoblinSlayer]

If nature is information theoretic, then physics is mathematics.