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PaperclipPerfector  5mo ago (text post)   3717 thread views

Friday Fun Thread for May 24, 2024

Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.

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This is also part of his criticism of 1x1=1, in that it assumes axiomatically a rectilinear universe, which is not the way the actual universe exists.

It is possible to build up a thorough and comprehensive axiomatic theory starting from a geometry without the parallel postulate. But what's described here seems like an extremely painful, sloppy, and intentionally confusing usage of notation. Possibly just wrong, probably not even wrong.

In terms of foundational mathematics, building up from geometric definitions like crossing lines is an extremely cumbersome method of defining your axioms. Even if you do not insist on using intentionally confusing notation like 1x1=2. As you said, you immediacy run into annoyances in terms of defining basic things like the irrationals in sqrt(2).

If you wanted to make a serious attempt at analyzing alternatives to the conventional axiomatic assumptions, it would be much more clear to begin with variations on Zermelo–Fraenkel set theory, with or without the axiom of choice and the continuum hypothesis. This would be a much more rigorous and clear way of showing how your systems produces a non-Peano arithmetic. If someone is unwilling to go through that work, it seems extraordinarily unlikely that they are producing anything interesting, correct, and non-trivial.

reality does not conform to our models

Though the foundational crisis may non be resolvable, the generally accepted formalism provides the necessary mathematical tools to do an extraordinarily good job of describing reality. If someone wants to propose a different formalism, it better provide a better or more useful description of reality. Saying that the current formalism does not perfectly describe reality so we should adopt a formalism that is less useful and more confusing, is pure nonsense.

To quote Hilbert (1927 The Foundations of Mathematics):

For this formula game is carried out according to certain definite rules, in which the technique of our thinking is expressed.

Laying out a formalism with overlapping but ill-defined versions of "spin" and "product," is not cleverness or some deep philosophical insight, it's an expression of sloppy thinking.

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