Ray Kremer wrote:I suppose math is a bit like time. Oh, we base the year, month, and day on the movement of our planet and moon, but hours, minutes, and seconds are arbitrary divisions. Leave Earth and even the day and year are arbitrary. Arbitrary time measurements don't mean anything to anything except people. Yet time and the passage of time is inherent in all things, the very fabric of the universe.
So far, so good. Agreed.
Ray Kremer, then wrote:Nature doesn't care about math, even though it functions in accordance with a great many mathematical principles. Math is just inherent in the system without anything paying it any attention. Making math into a thing that is codified with rules and theorems and number trickses, that's something people do.
I don't think mathematicians think like that. Mathematics isn't (in our view) inherent in anything except the human mind. We "see" order in the universe, but it is an order imposed by how we think of it, not, precisely speaking, how it is
Math is "pure mind stuff" (I think I'm quoting a badly remembered source here).
I'm pretty sure that physicists feel the same way. Physical theories aren't inherent in nature, but explanations of nature imposed by the way we choose to think. Both mathematicians and physicists build models of things and we have a bias for simple models (Occam's Razor). So, we say the earth follows an elliptical path around the sun, but that is far from accurate. It is just an approximation. The reality is that there is lots of wobble.
So, I think you have the understanding of the relationship between math and the universe just backwards; not an uncommon view. It isn't that there is math in the universe. It is that, in math (and somewhat differently in physics) we build models that help us understand, in a simple way, the complexity of the universe. But the math is in us
I think I'm on pretty solid ground above, so I'm going to speculate a bit here. I've gotten some push-back on the following in the past, and physics is not my main study. But I'll make the bold claim that Atoms don't "exist". Neither do quarks and muons and all the rest. Those are just explanations, thought up by smart people to try to explain the complexity of the small. They are a mental model from which we can predict phenomena pretty accurately (not exactly). The reality is more complex than the model. Physicists, however, speak of quarks as if they "exist", but I think that really what they mean is that there are some phenomena that are "well explained" by the idea of quarks.
So, in this view (my story, and I'm stickin' to it), the universe isn't "built up" from small things like quarks. It just IS. We use quarks as a way to get a simple (hmmm) way to think about that complexity. Neither does it embody mathematical principles. People think those up themselves. But math is also used to build "sensible" models (i.e. predictive models) of how it all hangs together.
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-- Charlie Grumbles