
Where is π today? The nature of the mathematical universe - got-any-grapes
https://billwadge.wordpress.com/2019/04/30/where-is-π-today-the-nature-of-the-mathematical-universe/
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state_less
I suppose it works well because it’s designed that way. We abstract away the
non essential and do our math. The results measure out in the non-abstract
world well enough to be useful. So we keep on with it. This process is
recurring, so we do math on our math.

I think it’s fun to ask if this abstract world is real. I think it is. It’s a
wonderful place in the mind to visit if you’re inclined to wander around
without trying too hard to get anywhere. That’s my hobbyist point of view
anyway.

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saagarjha
> 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)

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ncmncm
Good one. A "whole number" of "turns". Exactly one of them.

"Bleen" is as good a name for it is "tau".

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smitty1e
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...](https://en.wikipedia.org/wiki/List_of_humorous_units_of_measurement#Smoot)

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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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RcouF1uZ4gsC
>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 with bounded linear
operators (or something homomorphic to it).

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hawkjo
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.

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kevin_thibedeau
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.

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elvecinodeabajo
π is not an invention, it's the relation between a circle's lenght and its
radius. Not hard to understand.

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n4r9
The obvious counter-argument is that circles are an invention.

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sorokod
By humans? Do circles not exist without humans to point them out?

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n4r9
Not according to the author:

> According to intuitionism, mathematical objects are products of our mind,
> like characters in a novel. I agree, as far as it goes...

> Fictionalism holds that the mathematical universe is a collective fiction,
> like Star Trek or Game of Thrones.

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sorokod
Well, different characters behave differently in different novels. How is this
like an idea of a circle?

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n4r9
> the Cantor set or the Borel Hierarchy is like the USS Enterprise or the Iron
> Throne. In fact Star Trek fans talk of the Star Trek universe and GOT fans
> of Westeros and they talk like these places really exist.

You're right, it feels like quite a loose analogy, and only holds when
discussing a "canonical" fictional universe. Still, I'm sympathetic to the
idea that when we're talking about a circle we're talking about a shared
abstract understanding rather than something which objectively exists.

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elvecinodeabajo
The pupil in the eye. The sun through the clouds. The craters after an impact.
The waves when you drop a rock in water. The section of a bamboo stick... And
it gets more evident when you go to microscopic world. Some eggs are perfect
spheres, as small bubbles in water. I think circles are a real natural shape.
Not an invention. Nature brings us all kind of shapes, some of them are
discovered studying living creatures, like the scutoid.

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ncmncm
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 is canon even though it hasn’t been proven, because so
many proofs use it as an axiom.

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saagarjha
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.

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ncmncm
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](http://phys.lsu.edu/~fmoxley/bbm.pdf)

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Simon_says
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.

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ncmncm
Oops, wrong link.

[http://phys.lsu.edu/~fmoxley/r1.pdf](http://phys.lsu.edu/~fmoxley/r1.pdf)

