The line of reasoning is purely speculative.

Since we are the only species who have Mathematics, I will continue insisting Maths is invented, till we can compare notes with other life forms.

We’re the only species with which our species communicates maths. But we observe other species expressing mathematical properties we communicate. Does (for example) a snail “know” or “understand” the “golden ratio”? Who knows! But a snail’s shell expresses it. That’s partly something we can observe (so it can be designated “invented”), but partly something that appears so much it’s either a biological commonality, subject to some unknown universal constant, or an expression that many forms of life find a way to express.

the rate of occurrence of the golden ratio in nature is really overstated. snail shells follow approximate logarithmic spirals, and while you can certainly finds ones which approximate the golden spiral, it's not the mode or even the mean afaict. the reasons for this aren't really unknown; these patterns occur in very simple growth models.

even if the golden ratio were as prevalent as it popularly thought, it still wouldn't really situate math (the map) in a causal role; rather it would suggest a common physical factor which the math models.

in general, it arguably doesn't seem terribly surprising that lots of things in the world have share simple patterns, even without causal connections, simply by virtue of that there are far fewer simple patterns to go around than complicated ones, sort of a generalized 'law of small numbers'

> wouldn't really situate math (the map) in a causal role

I know I can improve my communication skills, but it’s extremely frustrating to have such a hard time expressing a thought without having drastically different intentions bolted onto it. Maybe you’re right that it’s not terribly surprising. But I didn’t even kind of suggest that “math” has a “causal role”. I made another comment higher up relating how the way I think is another set of approximations and abstractions of reality. My point was far from saying that there’s some “truth” in math, quite the opposite.

thats a fair frustration. i hadn't seen your comment in the other thread. in retrospect i was making an undue generalization based on "golden ratio" + "unknown universal constant". there's a lot of naively-platonist woo around this particular juxtaposition. apologies if that's not where you were going.

Thank you. This sincerely makes me feel better. And not that it’s related but right after hoofing a bunch of crap up a hill in rain with bags falling apart and almost losing a bunch of household basics, it’s a pleasant thing to return to an exchange on here that’s considerate and not escalated.

Addressing your response, I’m sure there’s a bit of detectable woo even after clarification, but it’s just wonder. I don’t think there’s a magical energy core connecting all life. I just think that it’s a fascinating thing about physical reality that a mathematical constant as defined by humans is something that finds expression in a lot of seemingly unrelated places.

It’s entirely possible that the ratio is just common enough in growth patterns, or just a pattern than emerges when the right set of otherwise common constraints come together.

It’s just neat to me, that’s all.

Note how you are ascribing Mathematical meaning to a snail shell.

You are somehow insisting that the mathematical expression (1 + sqrt(5))/2 is in some ways similar to a snail shell.

Don’t you find it even a little strange that just about anyone not schooled in algebra/arithmetic would doubt your claim?

I’m confused. I’m not saying there’s “meaning” to it of any kind, only that the ratio is present and observable. I’m not “insisting” anything. Maybe you’re accustomed to every thought being a conflict, but if I wasn’t clear already I was expressing wonder around a fairly common phenomenon whose commonality isn’t well known or understood.

It's not at all a conflict.

I am simply pointing out that where both of us observe/experience the pattern, your mind ascribes to it significance by relating it to the Mathematical construct called "Golden ratio".

My mind doesn't make that relation. I call that pattern (and other patterns like it) a "snail shell pattern".

We index the experience differently.

From your perspective a Mathematical expression describes the pattern. From my perspective an English expression does.

It sounds like we understand it the same way, with different words.

You could say that. But then it begs the question "What does it mean to understand?"

Either way, we index the pattern in our respective minds.

You index (understand?) it as a "Golden ratio".

I index (understand?) it as a "snail shell".

Your understanding it Mathematically, I do not. Which is why I said that you assign Mathematical meaning to the pattern.

This is essentially what Linguistic relativism is all about: https://en.wikipedia.org/wiki/Linguistic_relativity

> You index (understand?) it as a "Golden ratio".

> I index (understand?) it as a "snail shell".

> Your understanding it Mathematically, I do not. Which is why I said that you assign Mathematical meaning to the pattern.

Huh? I spoke of snail shells. If your characterization were accurate we probably wouldn’t even know we’re talking about the same thing.

These were your words: "a snail’s shell expresses it (the golden ratio)"

You connected the dots between the two...

I think basic math is just a natural part of most languages, since it describes a useful aspect of reality. Similar to distance, space or existence. I'd hazard that most languages has ways of expressing those concepts as well.

The fun begins when it comes to the deeper extrapolations of what can be readily observed. It seems possible that an alien civilization could be much more knowledgeable than us, yet never formulated the equivalents of our QM equations.

There are very credible linguists who theorize that there’s a universal human grammar and language foundation. It’s not a stretch to think that if they’re right about humans, the theory may apply to other life with language which we haven’t encountered yet.

If that’s the case, the property you’re describing belongs to abstract thought and language generally, of which mathematics is a subset.

The idea of universal grammar is that it is the portion of human language that is hardcoded into the genetics of humans. We would not expect other species to have the same universal grammar that humans do.

The notion is that there’s a commonality, the presupposition is that it’s genetic. But without knowing the mechanics of those genetics I don’t think you could say one way or another whether the expectation would be limited to humans.

afaik there's not even a lot of cross-cultural evidence for this, let alone cross-species, let alone pan-universal. what is or isn't considered math, or more specifically what kinds of reasoning are considered convincing/sound/etc have evolved a lot over history, and is continuing to do so. lakatos' 'proofs and refutations' is a nice short introduction to some of the issues involved here. long story short, what it really means to say 'math is universal' is actually pretty hard to pin down precisely enough to make anything even resembling a testable assertion

I don't have strong feelings towards anything you've said (in fact, I read Lakatos' paper just last weekend). You could say that I agree in general.

Much of what you point out is also what Quine identified in his paper "The two Dogmas of Empiricism" which is trivially the question "Is logic/mathematics empirical?". In my world-view inductive types (computations) are empirical.

But since you seem to be optimising for "pinning things precisely", general consensus/agreement may not be of any empirical value ;)