I find Max a fascinating person, a wonderful conference organizer, someone who’s always been extremely nice to me personally, and an absolute master at finding common ground with his intellectual opponents—I’m trying to learn from him, and hope someday to become 10^-122 as good. I can also say that [...] I personally find the “Mathematical Universe Hypothesis” to be devoid of content.
(emphasis mine)
Peter Woit of Not Even Wrong agrees, unsurprisingly. More interestingly, Max Tegmark replies.
The people coming up with either “unfalsifiability” or “devoid of content” criticisms of the Mathematical Universe Hypothesis need to think long(er) and hard(er) about Occam’s Razor. Occam’s Razor doesn’t lose its validity just because parts of the least complex model to explain the data also extend into unfalsifiable regions. People denying such would need to claim that a ship going over the horizon, never to return, stops existing. When “stops existing” would introduce additional complexity.
I prefer the way Gary Drescher phrases it in Good and Real: he redefines “exist” as a deictic so that only this universe “exists”, but also says there’s nothing that makes the existing universe special among all mathematically possible universe other than the fact that we’re in it.
there’s nothing that makes the existing universe special among all mathematically possible universe other than the fact that we’re in it.
N.B. This assertion seems pretty falsifiable. If the laws of physics turn out to be particularly simple then we’ll be forced to conclude that the universe is special.
the laws of physics did turn out to be particularly simple. In the 5 seconds you were waiting, did the air wafting around the room obey Navier-Stokes, or Navier-Stokes+a-dragon-randomly-appears? Both of those are fine, formalizable mathematical rules; one just happens to be much much simpler than the other.
And because the observed laws of physics are so particularly simple, they are dwarfed in number by mathematically possible more complex laws that we never observe. Choose between “Navier-Stokes” and “Navier-Stokes+dragon-after-half-a-second” and “Navier-Stokes+dragon-after-a-quarter-second” and so on; why do you expect to see the former rule rather than any of the infinite collection of latter rules? Without some kind of special privileged probability measure, we have no reason to expect to be in such a special universe, but here we are.
Laws of physics are not some deep mysterious algorithms built into the universe when it was created, they are human approximations of the infinite complexity we observe. As long as the universe is at least somewhat predictable and not completely random, it is possible to construct a series of increasingly accurate ways to predict its behavior. If the universe included predictable dragons after half a second, these approximations would, too. In fact, the Navier Stokes equations happen to describe so many dragons, there is still an open Millennium problem related to them. If the dragons appear unpredictably… well, then, it’s just like the universe we already live in, where the unpredictability is everywhere (if you doubt that, please tell me the results of tomorrow’s lottery).
So no, our universe is not particularly simple. It’s mostly, to quote a historian, “one damned thing after another”.
What would you say the complexity of our laws of physics is? Feel free to choose your own definition of complexity and give no better than a back-of-napkin estimate.
I suppose you can estimate the complexity of a particular approximate equation as the number of bit required to simulate it in a particular setup. I did something like that for the Schrodinger equation here a couple of years ago, frustrated by Eliezer’s empty theorizing, but I cannot find my comment anymore. Anyway, it was basically the length of the computer code which simulates the equation, so not that large, maybe tens or hundreds of kilobytes. You have to keep adding other codes to describe the necessary math and physics, and pretty soon you have to count a large chunk of the scientific and engineering software required to simulate the physical phenomena and engineering machinery, with a multitude of special cases for special dragons. And we still cannot simulate everything we see.
Perhaps “Navier-Stokes” and “complexity” and such are (ironically) overcomplicating things. Let’s try to simplify:
I just walked out of a room with blue walls.
Is there a mathematically consistent universe in which, when I walk back in, the walls will have spontaneously turned red? Yellow? Plaid? (hint: for a universe with a set of physical rules S, is there anything mathematically inconsistent about the set “S union that-room-spontaneously-turns-red-in-2-minutes”?)
If all mathematically consistent universes exist and there is no special probability distribution preferring some over others, what subjective probability should I assign to the expectation that I will see the same shade of blue walls?
In the real world, what subjective probability should I assign?
If the previous two answers are different (for example, if the first probability is epsilon and the second is one minus epsilon...), why is that so?
Whoa, hold your horses, that’s a lot of complexity right there. We don’t have a way of describing what “I” even means, let alone simulate it. “walking” is also pretty complicated, though we do have some robots capable of that. And so on.
Is there a mathematically consistent universe in which, when I walk back in
Please don’t mix math with visual effects. But if you insist, Hollywood can do the color changing trick for you.
If all mathematically consistent universes exist
I don’t even know what this might mean. It does not use the term “exist” in any way I understand. Seems like some kind of trans-Platonism. And why insist on mathematical consistency? And how can something we can imagine be mathematically inconsistent, given that our brains are apparently equivalent to Turing machines?
Anyway, it’s pointless to discuss this further until we agree on some basics.
I think you’ve got it backwards; if you picked at random a universe among all mathematically possible ones with probabilities proportional to (number of sentient beings in it)*2^-(Kolmogorov complexity) (i.e. SIA+Solomonoff induction), you’d most likely get a universe barely as complex as needed for sentience. If on the other hand the laws of physics turned out to be much more complex than that...
People denying such would need to claim that a ship going over the horizon, never to return, stops existing. When “stops existing” would introduce additional complexity.
This does seem to be the fundamental point of disagreement regarding ontological philosophy. At least, it is when the ‘horizon’ in question is an event horizon. It’s the most obvious simple test case. When people disagree about even the most basic questions in a subject then attempts to argue about extremely complex subjects relying on the same principles is largely pointless. Yet people still try.
The parent is not a rationality quote and the rationality quotes thread is not an appropriate place to place dump book review excerpts unless they happen to also contain rationality insight. In fact, the bolded quote is distinctly anti-rational quote in as much as it is almost certainly false claim (literally ‘devoid of content’?) of the kind optimised for debate and persuasion, not rationality expressions.
This isn’t a criticism of Scott or a support of the particular work (I haven’t read it yet). Were Scott trying to express a soundbite on the subject that could be worth quoting here then I expect he could. But this was just him taking an exaggerated dig at something he disagrees with.
Perhaps try the “Open Thread” for such excerpts. It is interesting enough to go there if only because Tegmark actually bothered to reply, and did so patiently.
Although his replies aren’t that interesting from an MUH-watcher’s perspective. On Aaronson’s & Woit’s blogs the only specific physical evidence I see in Tegmark’s comments relates to his “Level I”, “Level II” and “Level III” multiverses, but the MUH corresponds to his “Level IV” multiverse.
Replies where? I don’t see it on the linked page. EDIT: Wait, it’s on the first linked page, rather than the second. Suggest rephrasing the comment to make that clear.
Scott Aaronson on Max Tegmark’s Mathematical Universe Hypothesis:
(emphasis mine)
Peter Woit of Not Even Wrong agrees, unsurprisingly. More interestingly, Max Tegmark replies.
The people coming up with either “unfalsifiability” or “devoid of content” criticisms of the Mathematical Universe Hypothesis need to think long(er) and hard(er) about Occam’s Razor. Occam’s Razor doesn’t lose its validity just because parts of the least complex model to explain the data also extend into unfalsifiable regions. People denying such would need to claim that a ship going over the horizon, never to return, stops existing. When “stops existing” would introduce additional complexity.
The reason for the MUH being devoid of content is that it redefines the term “exist” into a trivial tautology, as in “everything imaginable exists”.
I prefer the way Gary Drescher phrases it in Good and Real: he redefines “exist” as a deictic so that only this universe “exists”, but also says there’s nothing that makes the existing universe special among all mathematically possible universe other than the fact that we’re in it.
N.B. This assertion seems pretty falsifiable. If the laws of physics turn out to be particularly simple then we’ll be forced to conclude that the universe is special.
And, wait for it...
(no, seriously, wait 5 seconds for it)
the laws of physics did turn out to be particularly simple. In the 5 seconds you were waiting, did the air wafting around the room obey Navier-Stokes, or Navier-Stokes+a-dragon-randomly-appears? Both of those are fine, formalizable mathematical rules; one just happens to be much much simpler than the other.
And because the observed laws of physics are so particularly simple, they are dwarfed in number by mathematically possible more complex laws that we never observe. Choose between “Navier-Stokes” and “Navier-Stokes+dragon-after-half-a-second” and “Navier-Stokes+dragon-after-a-quarter-second” and so on; why do you expect to see the former rule rather than any of the infinite collection of latter rules? Without some kind of special privileged probability measure, we have no reason to expect to be in such a special universe, but here we are.
Laws of physics are not some deep mysterious algorithms built into the universe when it was created, they are human approximations of the infinite complexity we observe. As long as the universe is at least somewhat predictable and not completely random, it is possible to construct a series of increasingly accurate ways to predict its behavior. If the universe included predictable dragons after half a second, these approximations would, too. In fact, the Navier Stokes equations happen to describe so many dragons, there is still an open Millennium problem related to them. If the dragons appear unpredictably… well, then, it’s just like the universe we already live in, where the unpredictability is everywhere (if you doubt that, please tell me the results of tomorrow’s lottery).
So no, our universe is not particularly simple. It’s mostly, to quote a historian, “one damned thing after another”.
What would you say the complexity of our laws of physics is? Feel free to choose your own definition of complexity and give no better than a back-of-napkin estimate.
I suppose you can estimate the complexity of a particular approximate equation as the number of bit required to simulate it in a particular setup. I did something like that for the Schrodinger equation here a couple of years ago, frustrated by Eliezer’s empty theorizing, but I cannot find my comment anymore. Anyway, it was basically the length of the computer code which simulates the equation, so not that large, maybe tens or hundreds of kilobytes. You have to keep adding other codes to describe the necessary math and physics, and pretty soon you have to count a large chunk of the scientific and engineering software required to simulate the physical phenomena and engineering machinery, with a multitude of special cases for special dragons. And we still cannot simulate everything we see.
Perhaps “Navier-Stokes” and “complexity” and such are (ironically) overcomplicating things. Let’s try to simplify:
I just walked out of a room with blue walls.
Is there a mathematically consistent universe in which, when I walk back in, the walls will have spontaneously turned red? Yellow? Plaid? (hint: for a universe with a set of physical rules S, is there anything mathematically inconsistent about the set “S union that-room-spontaneously-turns-red-in-2-minutes”?)
If all mathematically consistent universes exist and there is no special probability distribution preferring some over others, what subjective probability should I assign to the expectation that I will see the same shade of blue walls?
In the real world, what subjective probability should I assign?
If the previous two answers are different (for example, if the first probability is epsilon and the second is one minus epsilon...), why is that so?
Whoa, hold your horses, that’s a lot of complexity right there. We don’t have a way of describing what “I” even means, let alone simulate it. “walking” is also pretty complicated, though we do have some robots capable of that. And so on.
Please don’t mix math with visual effects. But if you insist, Hollywood can do the color changing trick for you.
I don’t even know what this might mean. It does not use the term “exist” in any way I understand. Seems like some kind of trans-Platonism. And why insist on mathematical consistency? And how can something we can imagine be mathematically inconsistent, given that our brains are apparently equivalent to Turing machines?
Anyway, it’s pointless to discuss this further until we agree on some basics.
If the universe is somwhat predictable and not completely random, it is not nfinitely complex.
I don’t see what you base this assertion on. Also, consider paying attention to your spellchecker.
The information-theoretic definition of entropy, Chaitin, etc.
I think you’ve got it backwards; if you picked at random a universe among all mathematically possible ones with probabilities proportional to (number of sentient beings in it)*2^-(Kolmogorov complexity) (i.e. SIA+Solomonoff induction), you’d most likely get a universe barely as complex as needed for sentience. If on the other hand the laws of physics turned out to be much more complex than that...
(Or at least that’s what I thought right after reading Good and Real. But it looks like the sum (number of sentient beings in it)*2^-(Kolmogorov complexity) might not even converge.)
This does seem to be the fundamental point of disagreement regarding ontological philosophy. At least, it is when the ‘horizon’ in question is an event horizon. It’s the most obvious simple test case. When people disagree about even the most basic questions in a subject then attempts to argue about extremely complex subjects relying on the same principles is largely pointless. Yet people still try.
The parent is not a rationality quote and the rationality quotes thread is not an appropriate place to place dump book review excerpts unless they happen to also contain rationality insight. In fact, the bolded quote is distinctly anti-rational quote in as much as it is almost certainly false claim (literally ‘devoid of content’?) of the kind optimised for debate and persuasion, not rationality expressions.
This isn’t a criticism of Scott or a support of the particular work (I haven’t read it yet). Were Scott trying to express a soundbite on the subject that could be worth quoting here then I expect he could. But this was just him taking an exaggerated dig at something he disagrees with.
Perhaps try the “Open Thread” for such excerpts. It is interesting enough to go there if only because Tegmark actually bothered to reply, and did so patiently.
Although his replies aren’t that interesting from an MUH-watcher’s perspective. On Aaronson’s & Woit’s blogs the only specific physical evidence I see in Tegmark’s comments relates to his “Level I”, “Level II” and “Level III” multiverses, but the MUH corresponds to his “Level IV” multiverse.
Replies where? I don’t see it on the linked page. EDIT: Wait, it’s on the first linked page, rather than the second. Suggest rephrasing the comment to make that clear.