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Hoping I’m not too late to head off the usual confusion: this is an interesting result in philosophy of physics, not in physics. We already know that classical

Hoping I’m not too late to head off the usual confusion: this is an interesting result in philosophy of physics, not in physics. We already know that classical mechanics is non-physical. This result (and others) show that it is not even internally consistent— that is, you shouldn’t need any empirical evidence to know that there’s something else going on. That’s interesting to philosophers and historians, but since you and I already know empirically that it’s non-physical, it shouldn’t come as much of a surprise. Anyway, if you enjoyed learning about the dome, you may also look up the lesser-known “space invaders”, in which arbitrary objects can appear at infinity, with infinite velocity, and then be brought to rest at any time T. But again, don’t look for reasons that doesn’t actually happen— it means the theory is wrong.

kergonath 3y ago
> We already know that classical mechanics is non-physical. This result (and others) show that it is not even internally consistent— that is, you shouldn’t need any empirical evidence to know that there’s something else going on. I don’t think this is a right approach. We already know that no theory is complete and perfect, so we can say the same thing about any theory. Even worse than that, we can make the philosophical point that any theory, being conceived within our limited brains, physically cannot be anything other than models and approximations. The logical conclusion of this argument is then that we should throw our hands in the air and stop discussing anything. It’s also wrong in this case specifically because there is absolutely no reason why this thought experiment cannot be proven or disproven within Newtonian mechanics.
- Cushman 3y ago
  > I don’t think this is a right approach. You’re welcome not to think so! I’m just pointing out the relevant context. This isn’t an argument in a vacuum, there’s an academic discipline that has thoroughly engaged with it. Part of that is a vast body of literature that in turns agrees and disagrees with your observations— to take a side, I’d start clicking links from “theory-ladenness”. But the dome is rather boring. P1, this math describes a deterministic system; P2, here is a non-deterministic result; QED, P1 is false. Since we know that P1 doesn’t describe the universe, it should be hard to have a strong opinion unless you’re invested in a philosophical position about pre-modern scientific practice. (I’m not invested, so I don’t have an opinion other than that it isn’t trivially refutable as stated.)
  - kergonath 3y ago
    > You’re welcome not to think so! I’m just pointing out the relevant context. It isn’t, though. The argument is not “lol Newtonian physics are dumb” and you’ll see nothing of the sort in the Norton argument. The argument is instead “Newtonian physics can be non-deterministic”, which is something we can demonstrate regardless of the validity range of Newtonian physics. > This isn’t an argument in a vacuum, there’s an academic discipline that has thoroughly engaged with it. Sure. How is that linked to your point? > But the dome is rather boring. P1, this math describes a deterministic system; P2, here is a non-deterministic result; QED, P1 is false. Indeed. > Since we know that P1 doesn’t describe the universe, it should be hard to have a strong opinion unless you’re invested in a philosophical position about pre-modern scientific practice. That’s a strange position to take from a philosophical point of view. Why things are wrong matters more than whether they are because, again, everything is wrong to some extent. So, of course in some abstract epistemological sense anything that can be formulated within Newtonian mechanics is wrong. But then nothing is right, so who cares? The initial question is much more interesting from a philosophical point of view: does the old Newtonian mechanics, which is still the closest to our daily experience, contains seeds of non-determinism? But then the logic is flawed: the issue is not that Newtonian mechanics are wrong, it is that, in your formalism, P2 does not follow from P1 and is actually wrong.
    - Cushman 3y ago
      Mmm, I promise I haven’t taken any position. Is that a position? In which case, mea culpa, I really don’t care if the dome holds. Even if I cared, I wouldn’t care, because space invaders already gets us all that plus sound effects. Not for nothing, even historians and philosophers of physics broadly don’t care if the dome holds. Some do, of course, but unless you're thinking of a specific paper it’ll probably be less frustrating for everyone to leave it there— with no hard feelings!
- drdeca 3y ago
  > We already know that no theory is complete and perfect, so we can say the same thing about any theory. If you mean this as an appeal to Gödel’s incompleteness results, the things those show can’t happen aren’t the same kinds of things that a “fully complete theory of physics” would have to satisfy. That’s not to say that I expect that we will ever (in this world) have a complete description of the physics of this world, But I’m quite confident that Gödel’s incompleteness theorems do not pose a fundamental barrier to the laws of physics of a world being perfectly known by entities in that world.
Cushman 3y ago
I’ll take my lumps for saying this: If you’ve downvoted me I’d love to know why! Did I sound preachy? I really don’t mean to! I’m not an educator, and it’s hard to communicate a discipline’s “common knowledge” without coming off a bit patronizing. It’s just, every time the dome comes up people want to talk about the physics of it— but the author isn’t a physicist, the journal isn’t for physicists, it’s not making any claims in physics… It’s a (famous) philosophy paper, specifically philosophy of science, specifically philosophy of physics. If you aren’t a philosopher, physics is annoyingly irrelevant here. There’s so much more to say— space invaders! It’s way weirder than this! The math still checks out! Philosophy is cool actually! Sorry to take up your time!
crazygringo 3y ago
> you may also look up the lesser-known “space invaders” Can you provide a pointer/link? I'm googling with various other keywords and can't find anything that isn't the video game.
- Cushman 3y ago
  Oh, of course! SEP’s summary is pretty readable. https://plato.stanford.edu/entries/determinism-causal/#ClaMec https://plato.stanford.edu/entries/determinism-causal/#ClaMe... Past that you’ll probably need to read the papers, it’s very niche. Sorry, I should have remembered that’s not actually an easy google :)
  - crazygringo 3y ago
    Thanks for that! What a fascinating set of problems. It is interesting that all of the ones listed in that section involve either infinities or infinitesimally small points -- except for Norton's dome. Which really makes it a great example for that reason.
    - Cushman 3y ago
      Yeah, exactly! You can see why the dome is the famous one, even though it’s the most recent. Previously there were models to finitize whatever term one was worried about specifically, but they all had an infinity somewhere. Even since Cantor, that makes philosophers antsy. The dome is analogous to a loophole-free Bell test— most people already accept the conclusion, so it’s not a surprising result, but having it in one simple argument closes the door to a lot of nitpicking.
Animats 3y ago
> this is an interesting result in philosophy of physics, not in physics. Yes. Although it has consequences. It's a demonstration that some physical variables have to be quantized or probabilistic to avoid divide by zero errors in reality. This becomes clear when you do idealized Newtonian physics with impulses. An impulse is an infinite force applied over zero time with finite energy transfer. That's not something that can exist in the physical universe. It's just asking for divide by zero problems. It's also why impulse-constraint physics engines for games have some rather strange semantics.
- Cushman 3y ago
  Indeed. Bittersweet consequences, I’ve always thought, since it implies we wasted centuries recording empirical data that didn’t add up, while pure logical coherence was pointing straight at quantization and a universal speed limit. Modern philosophers are (obviously?) most interested in how this historical fact should affect our handling of, say, our current best model for QG. That’s a fascinating thing for lay people to ponder, which is one reason I wish the context weren’t so opaque to HN. (I should caveat that I’m less familiar with the “history of philosophy of science” side of this— there may be a live debate as to whether this would obtain with the logic Newton himself had access to, for example.)

kergonath 3y ago

> We already know that classical mechanics is non-physical. This result (and others) show that it is not even internally consistent— that is, you shouldn’t need any empirical evidence to know that there’s something else going on. I don’t think this is a right approach. We already know that no theory is complete and perfect, so we can say the same thing about any theory. Even worse than that, we can make the philosophical point that any theory, being conceived within our limited brains, physically cannot be anything other than models and approximations. The logical conclusion of this argument is then that we should throw our hands in the air and stop discussing anything. It’s also wrong in this case specifically because there is absolutely no reason why this thought experiment cannot be proven or disproven within Newtonian mechanics.

Cushman 3y ago
> I don’t think this is a right approach. You’re welcome not to think so! I’m just pointing out the relevant context. This isn’t an argument in a vacuum, there’s an academic discipline that has thoroughly engaged with it. Part of that is a vast body of literature that in turns agrees and disagrees with your observations— to take a side, I’d start clicking links from “theory-ladenness”. But the dome is rather boring. P1, this math describes a deterministic system; P2, here is a non-deterministic result; QED, P1 is false. Since we know that P1 doesn’t describe the universe, it should be hard to have a strong opinion unless you’re invested in a philosophical position about pre-modern scientific practice. (I’m not invested, so I don’t have an opinion other than that it isn’t trivially refutable as stated.)
- kergonath 3y ago
  > You’re welcome not to think so! I’m just pointing out the relevant context. It isn’t, though. The argument is not “lol Newtonian physics are dumb” and you’ll see nothing of the sort in the Norton argument. The argument is instead “Newtonian physics can be non-deterministic”, which is something we can demonstrate regardless of the validity range of Newtonian physics. > This isn’t an argument in a vacuum, there’s an academic discipline that has thoroughly engaged with it. Sure. How is that linked to your point? > But the dome is rather boring. P1, this math describes a deterministic system; P2, here is a non-deterministic result; QED, P1 is false. Indeed. > Since we know that P1 doesn’t describe the universe, it should be hard to have a strong opinion unless you’re invested in a philosophical position about pre-modern scientific practice. That’s a strange position to take from a philosophical point of view. Why things are wrong matters more than whether they are because, again, everything is wrong to some extent. So, of course in some abstract epistemological sense anything that can be formulated within Newtonian mechanics is wrong. But then nothing is right, so who cares? The initial question is much more interesting from a philosophical point of view: does the old Newtonian mechanics, which is still the closest to our daily experience, contains seeds of non-determinism? But then the logic is flawed: the issue is not that Newtonian mechanics are wrong, it is that, in your formalism, P2 does not follow from P1 and is actually wrong.
  - Cushman 3y ago
    Mmm, I promise I haven’t taken any position. Is that a position? In which case, mea culpa, I really don’t care if the dome holds. Even if I cared, I wouldn’t care, because space invaders already gets us all that plus sound effects. Not for nothing, even historians and philosophers of physics broadly don’t care if the dome holds. Some do, of course, but unless you're thinking of a specific paper it’ll probably be less frustrating for everyone to leave it there— with no hard feelings!
drdeca 3y ago
> We already know that no theory is complete and perfect, so we can say the same thing about any theory. If you mean this as an appeal to Gödel’s incompleteness results, the things those show can’t happen aren’t the same kinds of things that a “fully complete theory of physics” would have to satisfy. That’s not to say that I expect that we will ever (in this world) have a complete description of the physics of this world, But I’m quite confident that Gödel’s incompleteness theorems do not pose a fundamental barrier to the laws of physics of a world being perfectly known by entities in that world.

Cushman 3y ago

I’ll take my lumps for saying this: If you’ve downvoted me I’d love to know why! Did I sound preachy? I really don’t mean to! I’m not an educator, and it’s hard to communicate a discipline’s “common knowledge” without coming off a bit patronizing. It’s just, every time the dome comes up people want to talk about the physics of it— but the author isn’t a physicist, the journal isn’t for physicists, it’s not making any claims in physics… It’s a (famous) philosophy paper, specifically philosophy of science, specifically philosophy of physics. If you aren’t a philosopher, physics is annoyingly irrelevant here. There’s so much more to say— space invaders! It’s way weirder than this! The math still checks out! Philosophy is cool actually! Sorry to take up your time!

crazygringo 3y ago

> you may also look up the lesser-known “space invaders” Can you provide a pointer/link? I'm googling with various other keywords and can't find anything that isn't the video game.

Cushman 3y ago
Oh, of course! SEP’s summary is pretty readable. https://plato.stanford.edu/entries/determinism-causal/#ClaMec https://plato.stanford.edu/entries/determinism-causal/#ClaMe... Past that you’ll probably need to read the papers, it’s very niche. Sorry, I should have remembered that’s not actually an easy google :)
- crazygringo 3y ago
  Thanks for that! What a fascinating set of problems. It is interesting that all of the ones listed in that section involve either infinities or infinitesimally small points -- except for Norton's dome. Which really makes it a great example for that reason.
  - Cushman 3y ago
    Yeah, exactly! You can see why the dome is the famous one, even though it’s the most recent. Previously there were models to finitize whatever term one was worried about specifically, but they all had an infinity somewhere. Even since Cantor, that makes philosophers antsy. The dome is analogous to a loophole-free Bell test— most people already accept the conclusion, so it’s not a surprising result, but having it in one simple argument closes the door to a lot of nitpicking.

Animats 3y ago

> this is an interesting result in philosophy of physics, not in physics. Yes. Although it has consequences. It's a demonstration that some physical variables have to be quantized or probabilistic to avoid divide by zero errors in reality. This becomes clear when you do idealized Newtonian physics with impulses. An impulse is an infinite force applied over zero time with finite energy transfer. That's not something that can exist in the physical universe. It's just asking for divide by zero problems. It's also why impulse-constraint physics engines for games have some rather strange semantics.

Cushman 3y ago
Indeed. Bittersweet consequences, I’ve always thought, since it implies we wasted centuries recording empirical data that didn’t add up, while pure logical coherence was pointing straight at quantization and a universal speed limit. Modern philosophers are (obviously?) most interested in how this historical fact should affect our handling of, say, our current best model for QG. That’s a fascinating thing for lay people to ponder, which is one reason I wish the context weren’t so opaque to HN. (I should caveat that I’m less familiar with the “history of philosophy of science” side of this— there may be a live debate as to whether this would obtain with the logic Newton himself had access to, for example.)