2 ms·

> why we should believe in the existence of real numbers, even there is nothing in the whole universe that relates to most of them? Seems like you are defining

> why we should believe in the existence of real numbers, even there is nothing in the whole universe that relates to most of them? Seems like you are defining existence here. Supposed I asked you if 7-dimensional triangles (simplex) exists what would you say? What do the reals have to do with the physical universe?

still_grokking 4y ago
One can construct 7-dimensional triangles. So they surely exist (somehow). > What do the reals have to do with the physical universe? That's kind of a tangent, but the point is: There is absolutely nothing in the universe that relates to most reals! Most reals don't "exist" in any meaningful way. So why should we believe they "exist" at all? (Subsets exist for sure, but that's not the point). Triangles and dimensions exist. One can easily extend this kind of existence to more dimensions. So one can create 7-dimensional triangles. But in contrast one can't, by no means, construct most reals. So my question is: Why should I believe that something that can't be ever "observed" "exists". That's like someone trying to convince me to believe in God… The relation to the physical world is: If someone would say that "there is something" but it can't be even named (out of principle!), not to mention described meaningfully, most people would likely ignore such a purely made up "thing". Because it would have exactly zero influence on anything that may exist in fact. The whole idea that there is something like "smooth space" is absurd given how "the true reality" works. Quantum physics tells us that there is no smooth space, and smooth space is actually impossible. But mathematicians seem to still want to use a "leaky abstraction" that has absolutely nothing in common with reality. Like I said, that's like they would strongly believe in God. Or to phrase it differently: Something that can't be, just can't be. Nobody can construct most reals. That's by definition. So one would need very very strong arguments to still assume that they "exist" (somehow). But there is no such argument at all afaik. That's what I'm asking actually: Does anybody know any, even remotely, valid argument why we should believe in reals? I didn't find any while researching that. Mathematics started as a way to precisely describe "what can exist". But most reals can't be described in any way. So my conclusion would be that they're not part of any valid description of "what can exist". But as most mathematicians seem to believe in reals I wanted to know why it's like that. What do I miss? Where does this faith come form?
- nh23423fefe 4y ago
  Lots of things are unobservable though. Amplitudes of a wave function are unobservable. What does your idea of existence and relevance say about that? Why is constructibility of elements relevant for belief in a whole. You will never observe an amplitude, is the wave function then "non-real"? The inside of black hole is unobservable from beyond the event horizon. Does that mean the space isn't real? Why is this property of observability or constructibility of individual elements relevant for the existence of a set. Concretely. I believe in the reals because of taking analysis. I guess I don't understand the leverage of calling the reals a "leaky abstraction", it just reads like a skeptical argument taken too far. I hand you a box and say, "these are the reals, they behave this way". You respond, "I've looked in the box and almost all the elements have no recipe, this box doesn't exist." It seems like a non-sequitur to me.

still_grokking 4y ago

One can construct 7-dimensional triangles. So they surely exist (somehow). > What do the reals have to do with the physical universe? That's kind of a tangent, but the point is: There is absolutely nothing in the universe that relates to most reals! Most reals don't "exist" in any meaningful way. So why should we believe they "exist" at all? (Subsets exist for sure, but that's not the point). Triangles and dimensions exist. One can easily extend this kind of existence to more dimensions. So one can create 7-dimensional triangles. But in contrast one can't, by no means, construct most reals. So my question is: Why should I believe that something that can't be ever "observed" "exists". That's like someone trying to convince me to believe in God… The relation to the physical world is: If someone would say that "there is something" but it can't be even named (out of principle!), not to mention described meaningfully, most people would likely ignore such a purely made up "thing". Because it would have exactly zero influence on anything that may exist in fact. The whole idea that there is something like "smooth space" is absurd given how "the true reality" works. Quantum physics tells us that there is no smooth space, and smooth space is actually impossible. But mathematicians seem to still want to use a "leaky abstraction" that has absolutely nothing in common with reality. Like I said, that's like they would strongly believe in God. Or to phrase it differently: Something that can't be, just can't be. Nobody can construct most reals. That's by definition. So one would need very very strong arguments to still assume that they "exist" (somehow). But there is no such argument at all afaik. That's what I'm asking actually: Does anybody know any, even remotely, valid argument why we should believe in reals? I didn't find any while researching that. Mathematics started as a way to precisely describe "what can exist". But most reals can't be described in any way. So my conclusion would be that they're not part of any valid description of "what can exist". But as most mathematicians seem to believe in reals I wanted to know why it's like that. What do I miss? Where does this faith come form?

nh23423fefe 4y ago
Lots of things are unobservable though. Amplitudes of a wave function are unobservable. What does your idea of existence and relevance say about that? Why is constructibility of elements relevant for belief in a whole. You will never observe an amplitude, is the wave function then "non-real"? The inside of black hole is unobservable from beyond the event horizon. Does that mean the space isn't real? Why is this property of observability or constructibility of individual elements relevant for the existence of a set. Concretely. I believe in the reals because of taking analysis. I guess I don't understand the leverage of calling the reals a "leaky abstraction", it just reads like a skeptical argument taken too far. I hand you a box and say, "these are the reals, they behave this way". You respond, "I've looked in the box and almost all the elements have no recipe, this box doesn't exist." It seems like a non-sequitur to me.