"If math would depend on humans, then universe would not obey it" I didn't say math depends on humans.
Just because humans invent mathTALK, does not prevent coincidental correct matches of reality with the patterns that the mathTALK describes.
Mathematicians are like people trying to figure out the rules of an unknown game.
The more correctly do they describe the rules (pattern conservations, symmetries) in the unknown game; the more matches the game will have with their description. Of course the game is there anyway. I do not deny that math makes use of a universal logic deriving from Existence; that is my point too.
I do not claim that somebody has to label the phenomena; only that the phenomena has to BE.
And BEING means existing, being distinct.
I never implied that Maxwell equations require humans; only that Maxwell equations spoken by humans is mathTALK that may happen to correctly match a pattern in the Universe that derives from Existence. Some alien may have a different set of equations from which Maxwell equations can be obtained. That's their way of using mathTALK to match patterns in reality.
But reality does what it does, whether or not humanmathTALK correctly depicts it.
The situation regarding "what is maths?" is addressed in detail by John Barrow. I found a long extract from his book "THe World within the World" in another book.
He shows that since there can be several different solutions to a physical problem, some can not apply to reality. An additional 'correspondence principle' is needed to judge realitymath applicability.
5 men shipwrecked on an island. 1 monkey. Lots of coconuts. They agree: split coconuts 5 ways equally, remainder for the monkey.
During the night; 1 man wakes up and decides to make the shareout. A coconut is left over, and given to the monkey. He then hides his 5th share and puts the other 4 shares back together as if nothing happened. Later at night a 2nd man wakes up, thinks nothing has happened, does the same thing. As do the 3rd, 4th, and 5th men. Always one was left and given to the monkey.
In the morning, no one admits their independent actions overnight; they all just split the coconuts 5 ways equally (not knowing of the shares stashed away by each during the night). And there's one left given to the monkey. Find the initial number of coconuts.
They say that there are an infinite number of solutions to this problem, but the minimum number of coconuts is 15621. But Paul Dirac gave another solution: 4 coconuts. Each man finds 4, the monkey gets 1 so that's now 5. He takes a fifth ( 1) and then there's 4 again!
So math (eg. also 'toy universes' and mathfantasyscenarios) does not necessarily correspond with reality. Although Julian Barbour rightly exposes the importance of not neglecting previously ignored solutions; the discrepancies between some math correct solutions, and actual reality, show that 'comparing and matching patterns' is more basic than math. Toy universes of mathplay might only be real as logical constructs.
