ETA: I feel like I may have distracted from the thrust of the post. I think the main point was that there really really probably shouldn’t be more then two stuffs, which is legit.
Because Tegmark 4 isn’t mainstream enough yet to get it down to one.
If there is a way to reduce it to zero or not is one discovery I’m much looking forward to, but there probably isn’t. It certainly seems totally impossible, but that only really means “I can’t think of a way to do it”.
It does indeed seem possible that in the long run we’ll end up with one kind of stuff, either from the reduction of logic to physics, or the reduction of physics to math. It’s also worth noting that my present model does have magical-reality-fluid in it, and it’s conceivable that this will end up not being reduced. But the actual argument is something along the lines of, “We got it down to two crisp things, and all the proposals for three don’t have the crisp nature of the two.”
That seems to me more like an irreducible string of methods of interpretation. You have physics, whether you like it or not. If you want to understand the physics, you need math. And to use the math, you need logic. Physics itself does not require math or logic. We do, if we want to do anything useful with it. So it’s not so much “reducible” as it is “interpretable”—physics is such that turning it into a bunch of numbers and wacky symbols actually makes it more understandable. But to draw from your example, you can’t have a physical table with physically infinite apples sitting on it. Yet you can do math with infinities, but all the math in the world won’t put more apples on that table.
...and since when is two apples sitting next to each other a pile??
Just as mental gymnastics, what if instead we would be able to reduce physics and logic to magical reality fluid? :)
Anyway, for the “logic from physics” camp the work of Valentin Turchin seems interesting (above all “The cybernetic foundation of mathematics”). Also of notice the recent foundational program called “Univalent foundation”.
Well, since nobody have done that yet, we cannot be sure, but for example a reduction of logic to physics could look like this: “for a system built on top of this set of physics laws, this is the set of logical system available to it”, which would imply that all the axiomatic system we use are only those accessible via our laws of physics. For an extreme seminal example, Turing machine with infinite time have a very different notion of “effective procedure”.
or even build up a system on top of physical laws without using logic?
It’s clear that such a demonstration needs to use some kind of logic, but I think that doesn’t undermine the (possible) reduction: if you show that the (set of) logic available to a system depends on the physical laws, you have shown that our own logic is determined by our own laws. This would entail that (possibly) different laws would have granted us different logics.
I’m fascinated for example by the fact that the concept of “second order arithmetical truth” (SOAT) is inacessible by effective finite computation, but there are space-times that allow for infinite computation (and so system inhabiting such a world could possibly grasp effectively SOATs).
That leaves information.
Large ensembles contain very little overall information because it takes little information to specify them, eg: “every real number”. However, they can still seem complicated from the inside. An ultimate ensemble plausibly contains no information because there is no need to pinpoint it in EverythingPossibleSpace.
However, it is not clear that level IV is general enough, since the existence of non mathematical thingies is not obvioulsy impossible.
EY’s made a kind of argument that you should have two kinds of stuff (although I still think the logical pinpointing stuff is a bit weak), but he seems to be proceeding as if he’d shown that that was exhaustive. For all the arguments he’s given so far, this third post could have been entitled “Experiences: the Third Kind of Stuff”, and it would be consistent with what he’s already said.
So yeah, we need an argument for; “You’re only supposed to have two kinds of stuff.”
So yeah, we need an argument for; “You’re only supposed to have two kinds of stuff.”
I think the whole point of “the great reductionist project” is that we don’t really have a sufficiency theorem, so we should treat “no more than two” as an empirical hypothesis and proceed to discover its truth by the methods of science.
He may be overreacting against a strain in philosophy that seeks to reduce everything to experience. Similar to the way behaviorism was an overreaction against Freud.
this third post could have been entitled “Experiences: the Third Kind of Stuff”
Not third, first. There are only two kinds of stuff, experiences and models. Separating physical models from logical is rather artificial, both are used to explain experiences.
We only access models via experiences. If you aren’t willing to reduce models to experiences, why are you willing to reduce the physical world of apples and automobiles to experiences? You’re already asserting a kind of positivistic dualism; I see no reason not to posit a third domain, the physical, to correspond to our concrete experiences, just as you’ve posited a ‘model domain’ (cf. Frege’s third realm) to correspond to our abstract experiences.
Agreed. The number two is ridiculous and can’t exist. Once you allow stuff to have a physical kind and a logical kind, what’s to stop you from adding other kinds like degree-of-realness and Buddha-nature?
OTOH, logical abstractions steadfastly refuse to be reduced to physics. There may be hope for the other way around, a solution to “Why does stuff exist?” that makes the universe somehow necessary. (Egan’s “conscious minds find themselves” is cute but implies either chaotic observations or something to get the minds started.) But we can’t be very optimistic.
That’s Tegmark’s Mathematical Universe Hypothesis, the best explanation I’ve seen of is Section 8.1 “Something for Nothing” in Good and Real by Gary Drescher.
I don’t get it. Okay, obviously our universe is a mathematical structure, that’s why physics works. “All math is real” is seductive, but “All computable math is real, but there are no oracles” is just weird; why would you expect that without experimental evidence of Church-Turing?
The idea that since there are twice as many infinite strings containing “1010” than “10100″, the former must exist twice as much as the latter nicely explains why our universe is so simple. But I’m not at all convinced that universes like ours with stable observers are simpler than pseudorandom generators that pop out Boltzmann brains.
That all math is “real” in some sense you observe directly any time you do any. The insight is not that math is MORE real than previously thought, but just that there isn’t some additional find of realness. Sort of, this is an oversimplification.
Combine this with the simulation hypothesis; a universe can only simulate less computationally expensive universes. (Of course this is handwavy and barely an argument, but it’s possible something stronger could be constructed along these lines. I do think that much more work needs to be done here.)
I’m pretty sure Eliezer’s approach is the opposite of Tegmark’s. For Tegmark, the math is real and our physical world emerges from it, or is an image of part of it. For Eliezer, our world, in all its thick, visceral, spatiotemporal glory, is the Real, and logical, mathematical, counterfactual, moral, mentalizing, essentializing, and otherwise abstract reasoning is a human invention that happens to be useful because its rules are precisely and consistently defined. There’s much less urgency to producing a reductive account of mathematical reasoning when you’ve never reified ‘number’ in the first place.
Of course, that’s not to deny that something like Tegmark’s view (perhaps a simpler version, Game-of-Life-style or restricted to a very small subset of possibility-space that happens to be causally structured) could be true. But if such a view ends up being true, it will provide a reduction of everything we know to something else; it won’t be likely to help at all in reducing high-level human concepts like number or qualia or possibility directly to Something Else. For ordinary reductive purposes, it’s physics or bust.
My best vulgarization, which I hope not to be a rationalization (read: Looking for more evidence that it is!), is that Physical kinds of stuff are about what is, while logical kinds of stuff are about “what they do”.
If you have one lone particle¹ in an empty universe, there’s only the one kind, the physical. The particle is there. Once you have two particles, the physical kind of stuff is about how they are, their description, while the logical stuff is about the axiom “these two particles interact”—and everything that derives from there, such as “how” they interact².
I do not see any room for more kinds of stuff that is necessary in order to fully and perfectly simulate all the states of the entire universe where these two particles exist. I also don’t see how adding more particles is going to change that in any manner. As per the evidence we have, it seems extremely likely that our own universe is a version of this universe with simply more particles in it.
So really, you can reduce it to “one”, if you’re willing to hyper-reduce the conceptual fundamental “is” to the simple logical “do”—if you posit that a single particle in a separate universe simply does not exist, because the only existence of a particle is its interaction, and therefore interactions are the only thing that do exist. Then the distinction between the physical and logical becomes merely one of levels of abstraction, AFAICT, and can theoretically be done away with. However, the physical-logical two-rule seems to be useful, and the above seems extremely easy to misinterpret or confuse with other things.
Defined as whatever is the most fundamentally reduced smallest possible unit of the universe, be that a point in a wave field equation, a quark, or anything else reality runs on.
I’ve read some theories (and thought some of my own) implying that there is no real “how” of interaction, and that all the interactions are simply the simplest, most primitive possible kind of logical interaction, the reveal-existence function or something similar, and that from this function derive as abstractions all the phenomena we observe as “forces” or “kinds of interactions” or “transmissions of information”. However, all such theories I’ve read are incomplete and also lack experimental verifiability. They do sound much simpler and more elegant, though.
How does EY know there are only two? Is it aprori knowledge? Is it empirical? Is it subject to falsification? How many failed reduictions-to-two-kinds-of-stuff do there have to be before TKoS is falsified?
Not to be obnoxious, but...
Why two?
ETA: I feel like I may have distracted from the thrust of the post. I think the main point was that there really really probably shouldn’t be more then two stuffs, which is legit.
Because Tegmark 4 isn’t mainstream enough yet to get it down to one.
If there is a way to reduce it to zero or not is one discovery I’m much looking forward to, but there probably isn’t. It certainly seems totally impossible, but that only really means “I can’t think of a way to do it”.
It does indeed seem possible that in the long run we’ll end up with one kind of stuff, either from the reduction of logic to physics, or the reduction of physics to math. It’s also worth noting that my present model does have magical-reality-fluid in it, and it’s conceivable that this will end up not being reduced. But the actual argument is something along the lines of, “We got it down to two crisp things, and all the proposals for three don’t have the crisp nature of the two.”
That seems to me more like an irreducible string of methods of interpretation. You have physics, whether you like it or not. If you want to understand the physics, you need math. And to use the math, you need logic. Physics itself does not require math or logic. We do, if we want to do anything useful with it. So it’s not so much “reducible” as it is “interpretable”—physics is such that turning it into a bunch of numbers and wacky symbols actually makes it more understandable. But to draw from your example, you can’t have a physical table with physically infinite apples sitting on it. Yet you can do math with infinities, but all the math in the world won’t put more apples on that table.
...and since when is two apples sitting next to each other a pile??
I think you’re going to have better luck figuring out how to make the third thing crisp than reducing it to the first two.
Just as mental gymnastics, what if instead we would be able to reduce physics and logic to magical reality fluid? :)
Anyway, for the “logic from physics” camp the work of Valentin Turchin seems interesting (above all “The cybernetic foundation of mathematics”). Also of notice the recent foundational program called “Univalent foundation”.
I don’t think you can reduce logic to anything else, since you would need to use logic to perform the reduction.
Well, since nobody have done that yet, we cannot be sure, but for example a reduction of logic to physics could look like this: “for a system built on top of this set of physics laws, this is the set of logical system available to it”, which would imply that all the axiomatic system we use are only those accessible via our laws of physics. For an extreme seminal example, Turing machine with infinite time have a very different notion of “effective procedure”.
How would one show the above, or even build up a system on top of physical laws without using logic?
I have (at the moment) no idea.
It’s clear that such a demonstration needs to use some kind of logic, but I think that doesn’t undermine the (possible) reduction: if you show that the (set of) logic available to a system depends on the physical laws, you have shown that our own logic is determined by our own laws. This would entail that (possibly) different laws would have granted us different logics. I’m fascinated for example by the fact that the concept of “second order arithmetical truth” (SOAT) is inacessible by effective finite computation, but there are space-times that allow for infinite computation (and so system inhabiting such a world could possibly grasp effectively SOATs).
I only see one crisp thing and one thing borrowing some of the crispness of the first thing but mostly failing, in your model.
What would that mean? How do you reduce something to nothing? Or, well, everything to nothing?
Split the universe into energy and information.
Let positive and negative energy sum to nothing.
That leaves information. Large ensembles contain very little overall information because it takes little information to specify them, eg: “every real number”. However, they can still seem complicated from the inside. An ultimate ensemble plausibly contains no information because there is no need to pinpoint it in EverythingPossibleSpace.
However, it is not clear that level IV is general enough, since the existence of non mathematical thingies is not obvioulsy impossible.
That doesn’t mean you don’t talk about energy as a basic ontological kind. You still have to talk about it—to say that its value happens to be zero.
Whether it is actually zero, is an empirical matter. I haven’t heard of physical theories that claim this, so what do you mean exactly?
This.
EY’s made a kind of argument that you should have two kinds of stuff (although I still think the logical pinpointing stuff is a bit weak), but he seems to be proceeding as if he’d shown that that was exhaustive. For all the arguments he’s given so far, this third post could have been entitled “Experiences: the Third Kind of Stuff”, and it would be consistent with what he’s already said.
So yeah, we need an argument for; “You’re only supposed to have two kinds of stuff.”
I think the whole point of “the great reductionist project” is that we don’t really have a sufficiency theorem, so we should treat “no more than two” as an empirical hypothesis and proceed to discover its truth by the methods of science.
He may be overreacting against a strain in philosophy that seeks to reduce everything to experience. Similar to the way behaviorism was an overreaction against Freud.
Not third, first. There are only two kinds of stuff, experiences and models. Separating physical models from logical is rather artificial, both are used to explain experiences.
We only access models via experiences. If you aren’t willing to reduce models to experiences, why are you willing to reduce the physical world of apples and automobiles to experiences? You’re already asserting a kind of positivistic dualism; I see no reason not to posit a third domain, the physical, to correspond to our concrete experiences, just as you’ve posited a ‘model domain’ (cf. Frege’s third realm) to correspond to our abstract experiences.
Agreed. The number two is ridiculous and can’t exist. Once you allow stuff to have a physical kind and a logical kind, what’s to stop you from adding other kinds like degree-of-realness and Buddha-nature?
OTOH, logical abstractions steadfastly refuse to be reduced to physics. There may be hope for the other way around, a solution to “Why does stuff exist?” that makes the universe somehow necessary. (Egan’s “conscious minds find themselves” is cute but implies either chaotic observations or something to get the minds started.) But we can’t be very optimistic.
That’s Tegmark’s Mathematical Universe Hypothesis, the best explanation I’ve seen of is Section 8.1 “Something for Nothing” in Good and Real by Gary Drescher.
For math as mere physics, see Egan’s Luminous.
This problem is already solved, the answer is here: http://arxiv.org/abs/0704.0646
I don’t get it. Okay, obviously our universe is a mathematical structure, that’s why physics works. “All math is real” is seductive, but “All computable math is real, but there are no oracles” is just weird; why would you expect that without experimental evidence of Church-Turing?
The idea that since there are twice as many infinite strings containing “1010” than “10100″, the former must exist twice as much as the latter nicely explains why our universe is so simple. But I’m not at all convinced that universes like ours with stable observers are simpler than pseudorandom generators that pop out Boltzmann brains.
That all math is “real” in some sense you observe directly any time you do any. The insight is not that math is MORE real than previously thought, but just that there isn’t some additional find of realness. Sort of, this is an oversimplification.
Also check out: http://lesswrong.com/lw/1zt/the_mathematical_universe_the_map_that_is_the/
That post is a confused jumble of multiple misinterpretations of the word “exist”.
If all levels of the Turing hierarchy are about as real, it’s extremely unlikely our universe is at level zero. Yet Church-Turing looks pretty solid.
Combine this with the simulation hypothesis; a universe can only simulate less computationally expensive universes. (Of course this is handwavy and barely an argument, but it’s possible something stronger could be constructed along these lines. I do think that much more work needs to be done here.)
I’m pretty sure Eliezer’s approach is the opposite of Tegmark’s. For Tegmark, the math is real and our physical world emerges from it, or is an image of part of it. For Eliezer, our world, in all its thick, visceral, spatiotemporal glory, is the Real, and logical, mathematical, counterfactual, moral, mentalizing, essentializing, and otherwise abstract reasoning is a human invention that happens to be useful because its rules are precisely and consistently defined. There’s much less urgency to producing a reductive account of mathematical reasoning when you’ve never reified ‘number’ in the first place.
Of course, that’s not to deny that something like Tegmark’s view (perhaps a simpler version, Game-of-Life-style or restricted to a very small subset of possibility-space that happens to be causally structured) could be true. But if such a view ends up being true, it will provide a reduction of everything we know to something else; it won’t be likely to help at all in reducing high-level human concepts like number or qualia or possibility directly to Something Else. For ordinary reductive purposes, it’s physics or bust.
Always two there are. No more. No less.
My best vulgarization, which I hope not to be a rationalization (read: Looking for more evidence that it is!), is that Physical kinds of stuff are about what is, while logical kinds of stuff are about “what they do”.
If you have one lone particle¹ in an empty universe, there’s only the one kind, the physical. The particle is there. Once you have two particles, the physical kind of stuff is about how they are, their description, while the logical stuff is about the axiom “these two particles interact”—and everything that derives from there, such as “how” they interact².
I do not see any room for more kinds of stuff that is necessary in order to fully and perfectly simulate all the states of the entire universe where these two particles exist. I also don’t see how adding more particles is going to change that in any manner. As per the evidence we have, it seems extremely likely that our own universe is a version of this universe with simply more particles in it.
So really, you can reduce it to “one”, if you’re willing to hyper-reduce the conceptual fundamental “is” to the simple logical “do”—if you posit that a single particle in a separate universe simply does not exist, because the only existence of a particle is its interaction, and therefore interactions are the only thing that do exist. Then the distinction between the physical and logical becomes merely one of levels of abstraction, AFAICT, and can theoretically be done away with. However, the physical-logical two-rule seems to be useful, and the above seems extremely easy to misinterpret or confuse with other things.
Defined as whatever is the most fundamentally reduced smallest possible unit of the universe, be that a point in a wave field equation, a quark, or anything else reality runs on.
I’ve read some theories (and thought some of my own) implying that there is no real “how” of interaction, and that all the interactions are simply the simplest, most primitive possible kind of logical interaction, the reveal-existence function or something similar, and that from this function derive as abstractions all the phenomena we observe as “forces” or “kinds of interactions” or “transmissions of information”. However, all such theories I’ve read are incomplete and also lack experimental verifiability. They do sound much simpler and more elegant, though.
How does EY know there are only two? Is it aprori knowledge? Is it empirical? Is it subject to falsification? How many failed reduictions-to-two-kinds-of-stuff do there have to be before TKoS is falsified?