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I believe that in fact the numbers do exist as physical objects exist. Just in their own universe. How is it any different than believing that unicorns exist a

I believe that in fact the numbers do exist as physical objects exist. Just in their own universe. How is it any different than believing that unicorns exist as physical objects, just in their own universe? What we call "physical existence" could...just be "math all the way down". Or, math is also a number of simplified alternate views of reality of varying degrees of "applicability." (Where "applicability" has to do with predictive power over reality.)

kazinator 8y ago
> How is it any different than believing that unicorns exist as physical objects, just in their own universe? We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". (For starters, what is the definition of "unicorn"? If it's just a horse with a horn, then such a thing is plausible with genetic engineering in our universe.) As we endow the unicorn with additional properties, then it becomes less and less clear that there exists a universe where such a thing can exists other than as an imaginary being. If the concept of a unicorn could be axiomatized, then it could constitute a universe. > Or, math is also a number of simplified alternate views of reality. Well, that's the math that we do; not the math that we (possibly) are.
- stcredzero 8y ago
  We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". Indeed. The current better known attempts at a "unicorn universe" have problems with power scaling and the square-cube law. https://www.reddit.com/r/mylittlepony/comments/mrs81/according_to_my_dodgy_backofthecoaster_maths/ https://www.reddit.com/r/mylittlepony/comments/mrs81/accordi... Do you have a good definition of what constitutes a "well-developed" universe?
  - AgentME 8y ago
    >Do you have a good definition of what constitutes a "well-developed" universe? An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then everyone can calculate the 1000th item the same way. If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. There's no unambiguous rules for how the unicorn universe is calculated. Everyone has a different "unicorn universe" in their heads, and each of those universes operates on our own mind's whims rather than any rules we can describe to each other.
    - stcredzero 8y ago
      If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. Homo sapiens has this issue with this universe. Even if you subset that group to just scientists, there are still differences of opinion.
      - AgentME 8y ago
        Reality itself is well-defined in that it acts consistently with itself. We as humans don't have a well-defined embedding of this universe into itself. We would need to know the complete underlying rules of physics for that.
FabHK 8y ago
> How is it any different than believing that unicorns exist as physical objects, just in their own universe? Good question, but I think there might be a difference. Suppose, in a galaxy far, far away, there are aliens. They probably don't have the concept of unicorns. However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc. So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?
- kazinator 8y ago
  I would sadly have to say no. Because in some completely different universe unlike ours, the aliens have no concept of, say, "hemoglobin" because there isn't matter like ours: no atoms, no iron, no carbon. Unlike numbers, hemoglobin and unicorns contain a kind of arbitrary complexity. Yet one is definitely real. Some real entities are far removed from elementary math (even though they may ultimately rest upon it, many levels down). The question is: are unicorns bunk, or are they like hemoglobin.
  - FabHK 8y ago
    I'm not claiming that if something exists (haemoglobin), we must have a notion of it and true statements about it in every universe. Rather: if we have a notion of something and statements about it in every universe, then it must exist. However, come to think of it, that's bonkers. Still, it's remarkable that mathematics allows us to make reproducible true statements about fictional objects.
- stcredzero 8y ago
  However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc. We can only be confident of that if they're in this universe. Also, this is only a conjecture. It's just something some of us imagine would be true. You can't elevate such an idea to the level of empirical data. So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status? Unicorns. Kirin. Narwhals. Rhinos. So you have two independent origins in culture for such a creature, plus two appearances of something similar in nature. Does that confer it some sort of elevated ontological status?

kazinator 8y ago

> How is it any different than believing that unicorns exist as physical objects, just in their own universe? We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". (For starters, what is the definition of "unicorn"? If it's just a horse with a horn, then such a thing is plausible with genetic engineering in our universe.) As we endow the unicorn with additional properties, then it becomes less and less clear that there exists a universe where such a thing can exists other than as an imaginary being. If the concept of a unicorn could be axiomatized, then it could constitute a universe. > Or, math is also a number of simplified alternate views of reality. Well, that's the math that we do; not the math that we (possibly) are.

stcredzero 8y ago
We have very well-developed representations of the number universe that we can embed into our own universe. These things are governed by precise axioms. By contrast, we don't have such well-developed "unicorn universe". Indeed. The current better known attempts at a "unicorn universe" have problems with power scaling and the square-cube law. https://www.reddit.com/r/mylittlepony/comments/mrs81/according_to_my_dodgy_backofthecoaster_maths/ https://www.reddit.com/r/mylittlepony/comments/mrs81/accordi... Do you have a good definition of what constitutes a "well-developed" universe?
- AgentME 8y ago
  >Do you have a good definition of what constitutes a "well-developed" universe? An easy definition would be one where everyone agrees on the exact mechanics and sequence of states. The fibonacci sequence is well-developed: it has an exact definition that every competent simulator can simulate the same way. If I say my favorite number is the 1000th item in the sequence (starting with 0, 1, 1 as items #1, #2, #3), then everyone can calculate the 1000th item the same way. If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. There's no unambiguous rules for how the unicorn universe is calculated. Everyone has a different "unicorn universe" in their heads, and each of those universes operates on our own mind's whims rather than any rules we can describe to each other.
  - stcredzero 8y ago
    If we all try to talk about what happens in the "unicorn universe", everyone has their own different ideas about that. Homo sapiens has this issue with this universe. Even if you subset that group to just scientists, there are still differences of opinion.
    - AgentME 8y ago
      Reality itself is well-defined in that it acts consistently with itself. We as humans don't have a well-defined embedding of this universe into itself. We would need to know the complete underlying rules of physics for that.

FabHK 8y ago

> How is it any different than believing that unicorns exist as physical objects, just in their own universe? Good question, but I think there might be a difference. Suppose, in a galaxy far, far away, there are aliens. They probably don't have the concept of unicorns. However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc. So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status?

kazinator 8y ago
I would sadly have to say no. Because in some completely different universe unlike ours, the aliens have no concept of, say, "hemoglobin" because there isn't matter like ours: no atoms, no iron, no carbon. Unlike numbers, hemoglobin and unicorns contain a kind of arbitrary complexity. Yet one is definitely real. Some real entities are far removed from elementary math (even though they may ultimately rest upon it, many levels down). The question is: are unicorns bunk, or are they like hemoglobin.
- FabHK 8y ago
  I'm not claiming that if something exists (haemoglobin), we must have a notion of it and true statements about it in every universe. Rather: if we have a notion of something and statements about it in every universe, then it must exist. However, come to think of it, that's bonkers. Still, it's remarkable that mathematics allows us to make reproducible true statements about fictional objects.
stcredzero 8y ago
However, they probably have discovered numbers, pi, Pythagoras theorem, e^(i pi) + 1 = 0, etc. We can only be confident of that if they're in this universe. Also, this is only a conjecture. It's just something some of us imagine would be true. You can't elevate such an idea to the level of empirical data. So, does the fact that something is discovered (rather than invented), and can be discovered many times independently in identical fashion, confer it some sort of elevated ontological status? Unicorns. Kirin. Narwhals. Rhinos. So you have two independent origins in culture for such a creature, plus two appearances of something similar in nature. Does that confer it some sort of elevated ontological status?