Golden ratio discovered in a quantum world

[FBM]

I hope you don't mind if I probe this post for a bit. It's just that this topic interests me greatly, and I don't find many chances to discuss it.

Certainly not a substance, but possibly a set of constraints, deriving from mathematical logic.

If those constraints are derived from mathematical logic, would mathematical logic, then, be ontologically prior to phenomena?

Such constraints may impose a limit on the potential structures of the material universe. The way in which physical laws are frequently found to closely mirror abstract mathematical relationships is suggestive of this, but certainly not proof...

As one of the quotes in my sig states, mathematics isn't a flawless or complete discipline. As such, it will naturally reach its limits of what it can describe. No doubt, scientists have done amazing things with it, and continue to do so, but it seems wise to be aware of its inherent limitations, too. Mathematics is a rational construct. A damned good one, no doubt, but nevertheless, it is a tool devised to describe the phenomenal world. Seems to me that the phenomenal world describes itself perfectly, and any rational construct used to describe it will always fall a tad short. Mathematics, I think, is subject to the same limitations as any other language.

Wittgenstein's Tractatus, according to the author, was specifically designed to describe this limit:
"Whereof one cannot speak, thereof one must be silent."

[JimC]

NotFBM wrote:

If those constraints are derived from mathematical logic, would mathematical logic, then, be ontologically prior to phenomena?

I have read several times similar musings by a variety of mathematicians and physicists, but only as speculations...

As one of the quotes in my sig states, mathematics isn't a flawless or complete discipline. As such, it will naturally reach its limits of what it can describe. No doubt, scientists have done amazing things with it, and continue to do so, but it seems wise to be aware of its inherent limitations, too. Mathematics is a rational construct. A damned good one, no doubt, but nevertheless, it is a tool devised to describe the phenomenal world. Seems to me that the phenomenal world describes itself perfectly, and any rational construct used to describe it will always fall a tad short. Mathematics, I think, is subject to the same limitations as any other language.

Wittgenstein's Tractatus, according to the author, was specifically designed to describe this limit:
"Whereof one cannot speak, thereof one must be silent."

The mathematical structures so far described have been certainly incomplete.

Possibly, any system of mathematics that could be expressed in symbolic language created by human brains may be doomed to be incomplete...

Perhaps such systems are like the flickering shadows in Plato's cave...

In other words, our mathematics is certainly a rational construct, and a damn fine job we have done too, but it is at least conceivalble that an abstract dimension of pure mathematical structure exists (possibly in a somewhat different sense of the word when we say the Universe exists). Our mathematics is a shadowplay, a faint echo of a grand symphony...

I am not strongly attached to that view, but I have come across several versions of it, and find it interesting...

[FBM]

I have read several times similar musings by a variety of mathematicians and physicists, but only as speculations...

I wonder how much the expression "To a man with a hammer, everything looks like a nail." applies here? Not saying it does, just asking.

The mathematical structures so far described have been certainly incomplete.

Possibly, any system of mathematics that could be expressed in symbolic language created by human brains may be doomed to be incomplete...

Perhaps such systems are like the flickering shadows in Plato's cave...

Damn. You've zeroed in on my point with uncommon alacrity.

In other words, our mathematics is certainly a rational construct, and a damn fine job we have done too, but it is at least conceivalble that an abstract dimension of pure mathematical structure exists (possibly in a somewhat different sense of the word when we say the Universe exists). Our mathematics is a shadowplay, a faint echo of a grand symphony...

Damn well put.

This is a good point to question what sort of reality abstractions participate in. Concrete reality (a potential misnomer) is classically held as the 'real' reality, but it's hard to deny that abstractions are somehow 'real', but not in the same way that concrete realities are, surely. What sort of reality do abstractions participate in? That is, how 'real' are they?

I am not strongly attached to that view, but I have come across several versions of it, and find it interesting...[/quote]