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> except that space-time is itself a 4 dimensional hole, leading to more ambiguity. You keep repeating that spacetime were a hole. What makes you think that?

Maursault 4y ago
Holes are made of space by definition, therefore spacetime is a hole.
- nahstra 4y ago
  What definition? Definitely not true in math - if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 }) it has a hole as defined by homotopy in the middle and there is no 'space' there. If you fill it with space you get a disk (D^2 = { (x, y) : x^2 + y^2 <= 1 }) there is no longer a hole as defined by homotopy/is contractible.
  - Maursault 4y ago
    > What definition? The one that defines the noun, "hole," as a hollow place in a solid body or surface. > if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 }) Black holes are real, but your circle can only "exist" in mathematics.
    - codethief 4y ago
      > Black holes are real, but your circle can only "exist" in mathematics. You are aware that General Relativity is about the most mathematical (and mathematically rigorous and mathematically advanced) theory we have in physics? Several predictions were made purely based upon mathematical arguments, without much physical input. So your argument that math were a "different realm" with no connection to reality is full of, uhh, holes. In fact, I would argue mathematics is mainly a language that provides us with the precision that everyday language lacks, it's a tool that allows us to make precise arguments while ruling out logical fallacies. In the present case it allows us to say very precisely what we mean by a hole. This definition[0] has been employed in countless predictions in physics and its usefulness has been confirmed by experiment. Meanwhile, your definition is vague at best. [0]: Look up "simple-connectedness" or, more generally, "homotopy groups".
      - Maursault 4y ago
        > So your argument that math were a "different realm" with no connection to reality This straw man was not my argument. My argument is that circles only exist mathematically.
        codethief 4y ago
        For this argument to work you must implicitly assume that mathematics were a different realm, with no connection to reality. But it doesn't matter. The definition of a hole doesn't rest on the definition of a circle.
        Maursault 4y ago
        > For this argument to work you must implicitly assume that mathematics were a different realm, with no connection to reality. No I don't, and this is still a straw man.
- codethief 4y ago
  Even if I agreed with your definition of "hole" (which I don't, compare nahstra's comment), there are two flaws in your causal chain: 1) If a hole is made of space, it doesn't follow that space is a hole. 2) Space is not spacetime.
  - Maursault 4y ago
    > 1) If a hole is made of space, it doesn't follow that space is a hole. Yes, it absolutely does, so long as there is no category error, and there is none here. The Universe is just an inconceivably large, curved hole with a tiny little bit of stuff in it. > 2) Space is not spacetime. Einstein and I disagree with you. Prior to Einstein's work, space and time were independent dimensions. But over 100 years ago Einstein showed that relativity of motion mathematically combines space and time into one, spacetime. For all intents and purposes, anyone talking about space today under any circumstances is also talking about spacetime whether time is specifically mentioned or not it is always there along with space.

Maursault 4y ago

Holes are made of space by definition, therefore spacetime is a hole.

nahstra 4y ago
What definition? Definitely not true in math - if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 }) it has a hole as defined by homotopy in the middle and there is no 'space' there. If you fill it with space you get a disk (D^2 = { (x, y) : x^2 + y^2 <= 1 }) there is no longer a hole as defined by homotopy/is contractible.
- Maursault 4y ago
  > What definition? The one that defines the noun, "hole," as a hollow place in a solid body or surface. > if you take a circle (S^1 = { (x, y) : x^2 + y^2 == 1 }) Black holes are real, but your circle can only "exist" in mathematics.
  - codethief 4y ago
    > Black holes are real, but your circle can only "exist" in mathematics. You are aware that General Relativity is about the most mathematical (and mathematically rigorous and mathematically advanced) theory we have in physics? Several predictions were made purely based upon mathematical arguments, without much physical input. So your argument that math were a "different realm" with no connection to reality is full of, uhh, holes. In fact, I would argue mathematics is mainly a language that provides us with the precision that everyday language lacks, it's a tool that allows us to make precise arguments while ruling out logical fallacies. In the present case it allows us to say very precisely what we mean by a hole. This definition[0] has been employed in countless predictions in physics and its usefulness has been confirmed by experiment. Meanwhile, your definition is vague at best. [0]: Look up "simple-connectedness" or, more generally, "homotopy groups".
    - Maursault 4y ago
      > So your argument that math were a "different realm" with no connection to reality This straw man was not my argument. My argument is that circles only exist mathematically.
      - codethief 4y ago
        For this argument to work you must implicitly assume that mathematics were a different realm, with no connection to reality. But it doesn't matter. The definition of a hole doesn't rest on the definition of a circle.
        Maursault 4y ago
        > For this argument to work you must implicitly assume that mathematics were a different realm, with no connection to reality. No I don't, and this is still a straw man.
codethief 4y ago
Even if I agreed with your definition of "hole" (which I don't, compare nahstra's comment), there are two flaws in your causal chain: 1) If a hole is made of space, it doesn't follow that space is a hole. 2) Space is not spacetime.
- Maursault 4y ago
  > 1) If a hole is made of space, it doesn't follow that space is a hole. Yes, it absolutely does, so long as there is no category error, and there is none here. The Universe is just an inconceivably large, curved hole with a tiny little bit of stuff in it. > 2) Space is not spacetime. Einstein and I disagree with you. Prior to Einstein's work, space and time were independent dimensions. But over 100 years ago Einstein showed that relativity of motion mathematically combines space and time into one, spacetime. For all intents and purposes, anyone talking about space today under any circumstances is also talking about spacetime whether time is specifically mentioned or not it is always there along with space.