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PaperclipPerfector  1yr ago (text post)   32274 thread views

Culture War Roundup for the week of July 17, 2023

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In that manner, it’s quite similar to maths, which also don’t materially exist but certainly can be studied.

Isn't math usually seen as objective - i.e. its truth or falseness is mind-independent? After all, we use it to come up with falsifiable theories of how the universe works. In fact, one line of argument for theism is that math is unreasonably useful here.

In fact, one line of argument for theism is that math is unreasonably useful here.

Um, what? It really is "heads I win, tails you lose" with theism, isn't it? I guarantee no ancient theologian was saying "I sure hope that all of Creation, including our own biology and brains, turns out to be describable by simple mathematical rules; that would REALLY cement my belief in God, unlike all this ineffability nonsense."

It's a hard problem from all possible directions, that people have been grappling with since before recorded history. There's going to be a pretty wide diversity of answers.

There's two catches with that. The first is that "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." (Albert Einstein)

Witness his special relativity, wherein 2 apples plus 2 apples might still be 4 apples but 2 m/s plus 2 m/s turns out to only be 3.9999 (and another dozen or so 9s, admittedly) m/s.

So we can come up with conceptual universes of axioms and prove all sorts of interesting things about them, but we can never be totally sure how completely any of them are really relevant to the actual universe we're in, rather than just amusing games. The fact that we've invented so many pure amusing games that turned out to be good descriptions of the building blocks of reality makes this a surprisingly tricky question.

The second is Gödel's Incompleteness Theorems. Any reasonable (able to handle basic arithmetic, not obviously inconsistent) system of foundational axioms for mathematics is inadequate to prove all statements which are true in that system, and is also unable to prove its own consistency. We can sometimes use a more complex system to prove the consistency of a less complex system, but then at that point it's turtles all the way down.

In fact, one line of argument for theism is that math is unreasonably useful here.

There are a lot of ways to interpret the unreasonable effectiveness of mathematics. To some extent the discovery of how much complexity can be derived from ridiculously simple rules hints at possible alternatives to theism, though I'm not exactly all on board the Tegmark train myself.

I've always been taken by Godel's theorem's as it really cuts us down to size. But if I'm understanding it properly, it doesn't preclude the idea of a proof itself from a series of other proofs, just we can't prove a system of them all lining up together on the same axiom base. But that's not quite the same as having an ambivalent confusion about everything in mathematics...?

These days I like Iain Mcgilchrist's left-brain, right-brain algorithmic vs gestalt brain thing. A lot of our thinking and limitations are because we mistake the left-brain view of the world for reality. The key scientific insights of the 20th century, Godel, quantum physics, relativity and, yes, postmodernism are all pointing us to somewhere else...

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Personally, I've seen too many cases where bizarre mathematical constructs we thought we just made up have been incredibly useful in describing natural phenomena (somehow complex numbers are useful in physics??) to say that's the case.

IIRC from my physics class in college a long time ago, this isn't even a "somehow." It's that complex numbers were formulated and used because they were useful in physics, specifically for modeling behaviors of real-world objects, not some obscure electromagnetism effects happening in a circuit or whatever. I wish I could remember the details and/or how apocryphal the story was, but it's certainly one of the less intuitive things that square-roots of negative numbers are so useful in real-world physics, looking at math from the outside.

This isn't true. They were originally developed to solve equations. The physics applications came much later

Nah; the whole reason imaginary numbers are called "imaginary" is that they were first used in formal, temporary, intermediate results in algorithms for calculating the "real" cubic/quartic polynomial roots that people care about. That was like 1600. I think Euler's formula a century later was when engineers and physicists first really started treating complex numbers as things of non-temporary interest, and quantum mechanics was when complex numbers started to feel more "real" than real ones.

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