Where is π today? The nature of the mathematical universe
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Where is π today? The nature of the mathematical universe
1–10 of 37 posts
Re: Where is π today? The nature of the mathematical universe
#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)
Re: Where is π today? The nature of the mathematical universe
#3Well, 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.
Re: Where is π today? The nature of the mathematical universe
#4> 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".
Re: Where is π today? The nature of the mathematical universe
#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 with bounded linear operators (or something homomorphic to it).
Re: Where is π today? The nature of the mathematical universe
#6Well, 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…
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.
Re: Where is π today? The nature of the mathematical universe
#7Well, 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…
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 think the point is that a conjecture or open question can be canon. Hilbert's problems are an example: https://en.wikipedia.org/wiki/Hilbert%27s_problems
The P=NP question would be an example of a canonical unsolved problem in CS.
Re: Where is π today? The nature of the mathematical universe
#8Well, 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.
Re: Where is π today? The nature of the mathematical universe
#9I 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.
Re: Where is π today? The nature of the mathematical universe
#10Well, 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…
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.