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Where is π today? The nature of the mathematical universe

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Re: Where is π today? The nature of the mathematical universe

#11

Post by hawkjo »

RcouF1uZ4gsC wrote: post #5

>What does it mean to exist independent of time and space? Nothing, as far as I can see. I was once at a UVIC philosophy seminar where this came up. I asked if, in the time of the dinosaurs, bounded linear operators already existed. Yes, I was told. I have no idea what this meant. I think a more interesting question is if an intelligent species that lived a billion light years away from us would eventually come up wi…

This is of the same flavor as wondering if said species would invent money, a collective fiction of usefulness so obvious it has been created many times. Or perhaps it’s closer to wondering if they would develop futures on a stock market.

Re: Where is π today? The nature of the mathematical universe

#12

Post by Simon_says »

ncmncm wrote: post #10
saagarjha wrote: post #6

Earlier quoted context omitted.

AFAIK, Riemann's hypothesis is not quite canon but many mathematicians posit that it is likely to be true due to a variety of "evidence" they feel leans in that direction.

I have seen a paper that says it's undecidable, and then seems to choose a continuation in which it is. I am not equipped to evaluate it. http://phys.lsu.edu/~fmoxley/bbm.pdf

I'm also not equipped to understand that paper, but my find tool is equipped to say the words "decidable", "undecidable", and "decidability" are not present.

Re: Where is π today? The nature of the mathematical universe

#13

Post by adrianratnapala »

ncmncm wrote: post #8
ncmncm wrote: post #3

Well, this is correct as far as it goes. But it raises the question of what, in modern parlance, is “canon”. As far as I can tell, mathematics becomes canonical if enough mathematicians think it’s beautiful. There is plenty of seriously presented mathematics that never achieves canon status. The practical effect of being canon is that other mathematicians care to do proofs with it, or about it. Riemann’s hypothesis i…

I tried to think of any mathematics that used to be canon but isn't anymore. All that comes to mind is the Principia Mathematica, demolished by Gödel. Is there mathematics that has just become unfashionable, not because anybody found anything wrong with it, but just because it turned out not to lead anywhere interesting? It would be hard to claim that such mathematics existed coeval with (non-avian) dinosaurs.

Euclid's five axioms.

For one thing we learned to understand "axioms" as something less than self-evidently necessary truths. For another we learned that the original axioms didn't really prove what they were thought to prove -- at least up to modern notions of rigour.

We would now understand the original Euclidean proofs to have been "sneaking in" other, implicit, axioms disguised as obvious deductions, and so modern formulations of the geometry need more elaborate axioms.

Re: Where is π today? The nature of the mathematical universe

#14

Post by kevin_thibedeau »

hawkjo wrote: post #11
RcouF1uZ4gsC wrote: post #5

>What does it mean to exist independent of time and space? Nothing, as far as I can see. I was once at a UVIC philosophy seminar where this came up. I asked if, in the time of the dinosaurs, bounded linear operators already existed. Yes, I was told. I have no idea what this meant. I think a more interesting question is if an intelligent species that lived a billion light years away from us would eventually come up wi…

This is of the same flavor as wondering if said species would invent money, a collective fiction of usefulness so obvious it has been created many times. Or perhaps it’s closer to wondering if they would develop futures on a stock market.

Dinosaurs didn't have numbers as they hadn't been invented yet. Merely being surround by quantities of stuff doesn't make human abstractions spring into existence.

The natural world doesn't perform arithmetic beyond summation and subtraction or symbolic manipulation of anything. We may use invented symbols to model abstract concepts aspects of the natural world but that doesn't make such things exist outside of collective human knowledge.

Re: Where is π today? The nature of the mathematical universe

#15

Post by smitty1e »

ncmncm wrote: post #4
saagarjha wrote: post #2

> Mathematicians discovered a new [whole] number. It’s between six and seven and is called “bleen”. I believe the actual term is τ (FWIW: Verdana's Greek glyphs are absolutely atrocious)

Good one. A "whole number" of "turns". Exactly one of them. "Bleen" is as good a name for it is "tau".

When you can't fathom something between 6 and 7, it may be a smoot point.

https://en.wikipedia.org/wiki/List_of_humorous_units_of_meas...

Re: Where is π today? The nature of the mathematical universe

#17

Post by ncmncm »

Simon_says wrote: post #12
ncmncm wrote: post #10

Earlier quoted context omitted.

I have seen a paper that says it's undecidable, and then seems to choose a continuation in which it is. I am not equipped to evaluate it. http://phys.lsu.edu/~fmoxley/bbm.pdf

I'm also not equipped to understand that paper, but my find tool is equipped to say the words "decidable", "undecidable", and "decidability" are not present.

Oops, wrong link.

http://phys.lsu.edu/~fmoxley/r1.pdf

Re: Where is π today? The nature of the mathematical universe

#18

Post by ncmncm »

adrianratnapala wrote: post #13
ncmncm wrote: post #8

Earlier quoted context omitted.

I tried to think of any mathematics that used to be canon but isn't anymore. All that comes to mind is the Principia Mathematica, demolished by Gödel. Is there mathematics that has just become unfashionable, not because anybody found anything wrong with it, but just because it turned out not to lead anywhere interesting? It would be hard to claim that such mathematics existed coeval with (non-avian) dinosaurs.

Euclid's five axioms. For one thing we learned to understand "axioms" as something less than self-evidently necessary truths. For another we learned that the original axioms didn't really prove what they were thought to prove -- at least up to modern notions of rigour. We would now understand the original Euclidean proofs to have been "sneaking in" other, implicit, axioms disguised as obvious deductions, and so moder…

Did axiomatic geometry become umfashionable? Or did it just get prettied up?

Re: Where is π today? The nature of the mathematical universe

#20

Post by vertline3 »

So my understanding is he believes math is invented, and exists in a "neo-fictional" space where things can be both true and false. Because if it were pure fiction like Star Trek then Math's statements would be false.

To me this seems a bit off, but I'll assume that it's my understanding of what he is trying to say that is flawed.

Also, didn't we all use the unit circle in Calc?

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