4 ms·

I stopped believing in infinity. In the real, physical world. That makes much more sense to me and fits in much better with my understanding of the universe.

mr_mitm 4y ago
That's quite uncontroversial. But this is about math.
idiotsecant 4y ago
Well if we're going to start deciding what things to believe in based on whether they're comfortable or not I am going to stop believing in traffic and the texture of coconuts.
WastingMyTime89 4y ago
To be fair, mathematics are not really concerned with the real, physical world. What’s interesting is that we can built axiomatic rules allowing us to properly define infinite sets and these constructions display surprising properties. It’s all purely abstract but it’s a fun thought exercise if you enjoy that kind of things. Plus it has practical applications sometimes which is good I guess.
Der_Einzige 4y ago
Don't let the assholes here gaslight you into thinking that Finitism isn't a somewhat hetrodox but still respected field of math. A bunch of great mathematicians historically have felt this way, and a few great ones today still do. Even if you're willing to accept the idea of cardinalities of infinity (and I think you ought to), I find that the more broad acceptance of 1. The axiom of choice (vs the axiom of determinancy, it's opposite) and 2. The law of excluded middle to be highly suspicious. If you reject the axiom of choice, you're just in alternative but still correct math. If you reject the law of excluded middle, you've ended up with intuitionistic or "constructive" logic, where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality. Notably, in intuitonistic/constructive logic, infinity is rejected until it can be "constructed", which also means that Cantors diagonalisation argument is not so naively accepted. While that diagonalisation itself was constructive, Other related and stronger theories from Cantor are not.
- anthk 4y ago
  Ahem. Let me show you a simple example. Basic geometry. The diagonal of a right triangle. sqrt(2) Show me the end of a diagonal making the angle infinitely sharp no matter how much you "zoom" it. End of the bullshit.
  - Der_Einzige 4y ago
- swamp40 4y ago
  I don't mind infinity in mathematics, it seems quite useful. I just don't think infinity exists in the real world. To quote David Hilbert, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought... The role that remain for the infinite to play is solely that of an idea."
peppertree 4y ago
Do you believe in 0?
SoftTalker 4y ago
For me, I stopped thinking of "infinity" meaning "bigger number than you can imagine" to just simply meaning "unlimited" or "never ending." That way the term works equally well at different scales. There are infinitely many real numbers between 1 and 2. There are infinitely many natural numbers.
gspr 4y ago
How do you reconcile the fact that the best tool we have, by far, to describe the "real, physical world" depends on certain notions of infinity?
- deleted 4y ago
  [deleted]
- swamp40 4y ago
  > best tool we have Math? Which physical laws/equations need infinity? Or do they just need "as x approaches infinity"? But regardless, my only point was that in the real world everything is countable. The number of atoms in the sun, the distance to anywhere, the age of the universe, etc. Everything real is countable.
  - gspr 4y ago
    > Math? Which physical laws/equations need infinity? Pretty much all of them are phrased in the language of differential equations. Perhaps some can be salvaged through finitist approaches, but that seems far from certain or trivial.
mbrodersen 4y ago
I agree. The practical intuitive way to think about “infinity” I use is to simply use a variable N that can be arbitrarily large. And then reason about f(N). It stops you from asking nonsenses like “what is infinity divided by infinity?” since you have to explicitly use N when asking the question. As in “what is f(N)/g(M) for arbitrarily large numbers N and M?”. Which gives you a straightforward way to answer the question.

mr_mitm 4y ago

That's quite uncontroversial. But this is about math.

idiotsecant 4y ago

Well if we're going to start deciding what things to believe in based on whether they're comfortable or not I am going to stop believing in traffic and the texture of coconuts.

WastingMyTime89 4y ago

To be fair, mathematics are not really concerned with the real, physical world. What’s interesting is that we can built axiomatic rules allowing us to properly define infinite sets and these constructions display surprising properties. It’s all purely abstract but it’s a fun thought exercise if you enjoy that kind of things. Plus it has practical applications sometimes which is good I guess.

Der_Einzige 4y ago

Don't let the assholes here gaslight you into thinking that Finitism isn't a somewhat hetrodox but still respected field of math. A bunch of great mathematicians historically have felt this way, and a few great ones today still do. Even if you're willing to accept the idea of cardinalities of infinity (and I think you ought to), I find that the more broad acceptance of 1. The axiom of choice (vs the axiom of determinancy, it's opposite) and 2. The law of excluded middle to be highly suspicious. If you reject the axiom of choice, you're just in alternative but still correct math. If you reject the law of excluded middle, you've ended up with intuitionistic or "constructive" logic, where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and mathematics are not considered analytic activities wherein deep properties of objective reality are revealed and applied, but are instead considered the application of internally consistent methods used to realize more complex mental constructs, regardless of their possible independent existence in an objective reality. Notably, in intuitonistic/constructive logic, infinity is rejected until it can be "constructed", which also means that Cantors diagonalisation argument is not so naively accepted. While that diagonalisation itself was constructive, Other related and stronger theories from Cantor are not.

anthk 4y ago
Ahem. Let me show you a simple example. Basic geometry. The diagonal of a right triangle. sqrt(2) Show me the end of a diagonal making the angle infinitely sharp no matter how much you "zoom" it. End of the bullshit.
- Der_Einzige 4y ago
swamp40 4y ago
I don't mind infinity in mathematics, it seems quite useful. I just don't think infinity exists in the real world. To quote David Hilbert, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought... The role that remain for the infinite to play is solely that of an idea."

peppertree 4y ago

Do you believe in 0?

SoftTalker 4y ago

For me, I stopped thinking of "infinity" meaning "bigger number than you can imagine" to just simply meaning "unlimited" or "never ending." That way the term works equally well at different scales. There are infinitely many real numbers between 1 and 2. There are infinitely many natural numbers.

gspr 4y ago

How do you reconcile the fact that the best tool we have, by far, to describe the "real, physical world" depends on certain notions of infinity?

deleted 4y ago
[deleted]
swamp40 4y ago
> best tool we have Math? Which physical laws/equations need infinity? Or do they just need "as x approaches infinity"? But regardless, my only point was that in the real world everything is countable. The number of atoms in the sun, the distance to anywhere, the age of the universe, etc. Everything real is countable.
- gspr 4y ago
  > Math? Which physical laws/equations need infinity? Pretty much all of them are phrased in the language of differential equations. Perhaps some can be salvaged through finitist approaches, but that seems far from certain or trivial.

mbrodersen 4y ago

I agree. The practical intuitive way to think about “infinity” I use is to simply use a variable N that can be arbitrarily large. And then reason about f(N). It stops you from asking nonsenses like “what is infinity divided by infinity?” since you have to explicitly use N when asking the question. As in “what is f(N)/g(M) for arbitrarily large numbers N and M?”. Which gives you a straightforward way to answer the question.