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...