Everything that exists can be described precisely by some physics or algorithm, down to the point where it’s actually meaningless to differentiate between the algorithm and the process itself.
Because that thesis has made better predictions than every rival theory which seemed at the time more reasonable (superstition, vitalism, Cartesian dualism, etc). The Pythagoreans, amidst all their lunacy, stated perhaps the world’s best-confirmed audacious hypothesis, that the world is a mathematical object.
Because that thesis has made better predictions than every rival theory which seemed at the time more reasonable (superstition, vitalism, Cartesian dualism, etc)
When it comes to the question of consciousness, I humbly submit that “i-don’t-know-ism” has made better predictions (i.e. none) than any rival theory.
The thesis doesn’t predict that every reduction is going to be easy. And “I don’t know” really masks a good bit of knowledge, unless you’re equally surprised by all new data. Physicalism directly predicts a good many of the things we consider too obvious to categorize as “mysterious” (e.g. that brain damage can cause personality change).
Sure! And I would take decent odds on physicalism...at 20:1 in my favor I wouldn’t have to think too hard; I’d be pretty sure to take the bet, because there is some pretty convincing evidence, like how brain damage works and how simple formulas about e.g. mechanics or radiation explain phenomena in what we might naively assume to be different realms, e.g. solar sails and roof albedo and warm light bulbs. If you can formulate a hypothesis with one set of data and test it using several other sets and get confirmation, it makes sense to guess that it works on all sets. And if you put a gun to my head and said “guess a theory of everything,” I’d guess physicalism...as I said earlier, “of course physicalism or whatever you want to call it is the most plausible known and articulated theory of everything.”
My only point is that we don’t yet have enough evidence to be sure of physicalism in its broadest senses so as to justify shutting down alternative avenues of exploration for standing questions such as the origin of the universe, the nature of consciousness, and the computability of matter.
The results of science are indeed quite impressive.
Suppose you wanted to compare the Pythagorean hypothesis “the world is a mathematical object” with the slightly broader hypothesis “the world consists largely of objects following mathematical laws.”
Are there scientific results that would be predicted by one hypothesis but not the other?
No– this is a variant of the “green/grue” problem. However, the Pythagorean hypothesis puts higher probability on the things we’ve actually observed, because it doesn’t waste any on claiming that this thing or that is non-mathematical.
By Bayes’ Law, this means it’s continually gaining support against the rival candidate.
Would you be so kind as to define “mathematical object”? Possibly I agree with you on everything but semantics, a field in which I am almost always happy to compromise.
Er, a set with a simple definition, like the Mandelbrot set or the set of solutions to the Schrödinger equation on a given manifold? Honestly, I’d be surprised if this is the point you’re stuck on.
What I suspect might help is the distinction here between epistemology and ontology: it’s a meaningful hypothesis that we live in such a mathematical object, even if there doesn’t exist a mind sufficient to exhaustively verify this, and yet our smaller minds can acquire enough evidence about the world’s structure to raise that hypothesis to near certainty (modulo some chance of being in a simulation that’s more complicated than the laws we seek, but whose creators want us not to notice the seams).
I think you’re right that what we disagree about is
the distinction here between epistemology and ontology.
The dichotomy you’ve provided seems to me to be an excellent definition of the difference between mathematical epistemological proof and empirical epistemological proof...it happens all the time that we may not be able to rigorously show N, but we nevertheless have extremely good reason to believe N with near-certainty, and even stronger reason to act as if we believed N.
If I hear you correctly, you think that we could plug in “the Universe is merely a mathematical object” for N.
I disagree. For me, the difference between epistemology and ontology is that there is a difference between what we can know and what exists. There might be things that exist about which we know nothing. There could even be things that exist about which we cannot know anything. One could reasonably call for scientists to ignore all such hypothetical objects, but, philosophically speaking, it doesn’t stop the objects from existing.
It boggles my mind to hear the claim that a mathematical object, as you have just defined it in your last comment, “exists in this second, ontological sense. The mandelbrot set expresses a relationship among points. If several small spheres exist and it turns out that the points approximate the relationship defined by the Mandlebrot set, then we might say that a Mandlebrot-ish shape of spheres exists. But the set itself doesn’t have any independent existence. This result doesn’t seem to me to depend on whether we use spheres or rays or standing waves—you still have to be vibrating something* if you want to talk about things that actually exist. I’m not the sort of nut that believes in good old-fashioned aether, but mathematical relationships alone won’t get you a flesh-and-blood universe where things actually exist...they’ll just get you a blueprint for one. Even if, epistemologically, we can know everything about the blueprint and model all of its parameters, it still won’t exist unless it’s made of something.
That, at any rate, is my modestly informed opinion. If you can see any flaws in my analysis, I would be grateful to you for pointing them out.
It continually amazes me that people think “physical existence” is somehow less mysterious and more fundamental than the existence of a mathematical object!
Er, no, it’s not less mysterious—we understand mathematical objects better than we understand physical existence; mathematical objects can be treated with, well, math, and physical existence gets dealt with by jokes like philosophy.
I’m not sure what you mean by more fundamental, but physical existence does seem to be roughly as important as mathematical objects...at any rate, it matters a lot to me whether things exist in fact or merely in theory.
We’ve been given special evidence in our own case, but if we step away from that for a moment, what I mean should be clear. Let’s take a hypothetical Universe X, which is very different from ours.
Saying “Universe X is a simple mathematical object” is pretty well comprehensible.
Saying “Universe X exists in some special way, distinct from just being a mathematical object, and in fact it might not be describable as a simple mathematical object” is just plain mysterious. It’s up for debate whether it’s even a meaningful statement.
But, but, you don’t understand. Math isn’t reeeeeeeaaaaaaaaaaaaaal!
I have an idea. Maybe it’d be more convincing if you said “Universe X is a simple computation.” People feel like computations are more real, and who knows, maybe they’re right. Maybe reality is computation, just a subset of mathematics. It seems a lot easier for people to envision that, at any rate. Or take Eliezer who (I think?) seems to think (or at least seemed to think) that reality juice is magically related to acyclic causal graphs.
You’ll still probably get the same objections, though: “Computations aren’t reeeeeeeaaaaaaaal, they have to be computed on something! Where’s the something coming from?” But that seems a little bit more silly, because the Something that is computing can be infinitely far back in the chain of computation. All of a sudden it feels more arbitrary to be postulating a Something that is Real. And real metaphysicists know that things shouldn’t feel arbitrary.
I am? I only read the decision theory chapters of Good and Real, the day before he showed up at SIAI house for the decision theory workshop. I’ll definitely read the last chapter when I get back to California.
I think your intuition is relying a little too much on the absurdity heuristic (e.g., “It boggles my mind...”) and flat out assertion (e.g., “But the set itself doesn’t have any independent existence.”). Metaphysical intuition is really misleading. I think most people underestimate that, especially because the absurdity heuristic is strong and therefore it’s easy to reach a reductio ad absurdum that is nonetheless true. I’ll give an example.
Once upon a time I didn’t think copies ‘counted’ in a multiverse, either morally or for purposes of anthropic reasoning. 200 Jacks had the same weight as 1 Mary. The opposite was absurd, you see: You’re claiming that 3 copies of the exact same computation are worth more than 2 computations of 2 different people, leading separate and diverse lives? Absurd! My moral and metaphysical intuition balks at such an idea! I came up with, like, 3 reductio ad absurdums to prove my point. Eliezer, Wei Dai, Steven Kaas, Nick Bostrom, what did they know? And there was some pride, too, because they way I was thinking about it meant I could easily deal with indexical uncertainty, and the others seemed clueless. … Well, turns out those reductios weren’t absurd: I just hadn’t learned to think like reality. I had to update, because that’s where the decision theory led, and it’s hard to argue with mathematics. And it came to my attention that thinking doubled computations had the same measure had a lot of problems as well. Since then, I’ve been a lot more careful about asserting my intuition when it disagrees with people who seem to have thought about it a lot more than I have.
In the case of the Mathematical Universe Hypothesis or permutations thereof (Eliezer seems to think the mysterious ‘reality fluid’ or ‘measure’ has a lot to do with directed acyclic graphs, for instance), there’s a lot of mental firepower aimed against you. Why do you believe what you believe? If it turns out the reason is metaphysical intuition, be on guard. Acknowledge your intuition, but don’t believe everything you think.
Look, of course physicalism or whatever you want to call it is the most plausible known and articulated theory of everything.
But why would you assign physicalism nontrivial probability as against (a) theories that are as yet unknown or unarticulated, or (b) the possibility that the Universe does not behave neatly in accordance with a single coherent, comprehensible theory?
Isn’t the concept-space of “single coherent Theory of Everything” vastly smaller than the total concept-space of concepts that could describe our reality?
The thesis at hand predicts that we should find complex things to be intricate arrangements of simple things, acting according to mathematically simple rules. We have discovered this to be true to a staggering degree, and to the immense surprise of the intellectual tradition of Planet Earth. (I mean, when even Nietzsche acknowledges this— I’ll reply later with the quote— that’s saying something!)
Your (b) makes no such specific predictions, and so the likelihood ratio should now be immensely in physicalism’s favor. Only a ridiculous prior could make it respectable at the moment.
As for (a), I’m talking about the general principle that the world is a mathematical object, not any particular claim of which object it is. (If I knew that, I’d go down and taunt the string theorists all evening.)
Our amazement.— It is a profound and fundamental good fortune that scientific discoveries stand up under examination and furnish the basis, again and again, for further discoveries. After all, this could be otherwise. Indeed, we are so convinced of the uncertainty and fantasies of our judgments and of the eternal change of all human laws and concepts that we are really amazed how well the results of science stand up.
Nietzsche, The Gay Science I.46
(NB: in this passage, “we” signifies modern atheists, not people in general.)
In long, because no matter how far off physics is from the ultimate algorithm, we can continue to narrow in on it indefinetly. Mathematically at least, even an infinite algorithm is possible. As a curious side note, I remember physcist Frank Tipler has a GUT of physics that is infinite. He claims this TOE has been known for a while, but avoided for obvious reasons. He then puts on a magic space cap and claims that this TOE proves Christianity is correct, but the TOE is interesting nonetheless (at least the idea of it—I am not a physicist).
I don’t know for certain that physics is computable, but from what I have read on that matter, all current indications are positive.
Successful at what, exactly? At modeling the behavior of the stuff that humans can easily observe using basic industrial technology over the span of 100 to 400 years? Why would you want to extrapolate from that to “everything that exists?”
In long, because no matter how far off physics is from the ultimate algorithm, we can continue to narrow in on it indefinetly.
Right, but what makes you think there is an “ultimate algorithm” to be found?
A single universal physics is adequate to explain all that we can observe, and a necessary derivation of that universal physics is a vast quantity of space and time which we can not directly observe but which we predict is also driven by the same universal physics. This is the “everything that exists”—whose existence is in some fact dependent on the universal physics itself.
Whether there is or is not an ultimate algorithm is not even the right question. It is true by default. We can continue to refine physics indefinetly. In other words, of course there is an ultimate algorithm, because we can invent it.
In fact, given any sequence of finite observations O, there is an infinite set of algorithms A that perfectly predict/compute the sequence O. Physics is concerned largely with finding the minimally complex algorithm that fully predicts O.
So yes, mathematically it is trivially true that there is an infinite set of ultimate algorithms.
Thank you for one (of several) intelligent responses.
a necessary derivation of that universal physics is a vast quantity of space and time which we can not directly observe
This isn’t quite right. The only thing that makes the derivation “necessary” is your adjective “universal.” We could just as easily say that there is a supergalactic physics that explains all we can observe, and that same physics could plausibly explain what is happening in the space and time that we cannot or have not observed. Note that the unobservable realms are not merely those outside our past light cone, but also those within the limits of the Heisenberg uncertainty principle, beneath the smallest structures that we can repeatedly observe, and, for all practical purposes, the space beyond the nearest nebula and/or the objects too dull for our Earth-bound telescopes to detect. It would be remarkably bad science to voluntarily choose to sample only one kilobyte from one address out of thousands of terabytes of data and assume that the kilobyte is representative. The fact that all known scientific resources are clustered in the same tiny portion of spacetime forces us to use such a sample, but it cannot and should not force us to assume that the sample is representative.
whose existence is in some fact dependent on the universal physics itself.
I don’t understand what you mean. Intelligent minds with an ability to manipulate matter or energy can ‘create’ patterns in that matter/energy by rearranging it according to the laws of physics. However, I cannot think of any sense in which physics itself could be said to create its own patterns. Physics is the pattern in which all known matter is currently arranged, but physics does not create the matter—it merely arranges it. Physics does not explain why there is something instead of nothing; it would be perfectly consistent with the laws of physics for there to be no electrons orbiting no protons over a volume of no space-time. How then can “everything that exists” be dependent on physics?
given any sequence of finite observations O, there is an infinite set of algorithms A that perfectly predict/compute the sequence O.
Right, but who says our observations are finite? What if important phenomenon, like, e.g., consciousness (cough) turn out to depend on infinitely small particles? What if the fate of the universe in a cosmological sense turns out to depend on what happens over infinitely long periods of time? There is no rule that I know of that says that the Universe is not allowed to clog its equations with infinities.
Physics is concerned largely with finding the minimally complex algorithm that fully predicts O.
A noble goal, but who says that sufficient simplicity to allow for computability is possible? Suppose our universe contains some true randomness beyond its initial seeding? Suppose that limits on our ability to gather information (particles that put effective distance between themselves and our present location at faster than the speed of light due to cosmic inflation; ineradicable error rates in technologically perfect computers) mean that while the universe is computable in principle, we cannot perfectly compute even a portion of our universe from the inside?
I don’t mean to suggest that it’s implausible that everything is governed by a universal physics. That’s a respectable hypothesis. I just get frustrated when people assert, without evidence that’s apparent to me, that physics will surely explain everything that we might wish to know. This is a remarkably bold claim for a discipline that predicts that most of what exists is “dark energy” but cannot say what dark energy is. Physicalism should be classed as a statement of faith, I think, and not as a justification for specific predictions about the hard problem of consciousness.
a necessary derivation of that universal physics is a vast quantity of space and time which we can not directly observe
This isn’t quite right. The only thing that makes the derivation “necessary” is your adjective “universal.” We could just as easily say that there is a supergalactic physics that explains all we can observe,
Physics is generally held to be universal, instead of just ‘supergalactic’. For one, there is the multiverse. But in general, the idea is, as I discuss later, to find the most parsimonious explanation for everything. This is the optimal strategy, and universality is a necessary consequence of this strategy. Any other physics or system which does not explain all observations is of course incomplete and inferior.
It would be remarkably bad science to voluntarily choose to sample only one kilobyte from one address out of thousands of terabytes of data and assume that the kilobyte is representative.
Not at all. You seem to be applying the analogy that at the cosmic scale the universe is some sort of probabilistic urn that generates galactic-sized space-time slices at random whim. It is not.
There are an infinite set of potential physics that have widely different properties in regions we can not observe. There are strong reasons why these are all necessarily inferior, by the principle of Ockham’s razor and the low-complexity bias in Solonomoff induction.
given any sequence of finite observations O, there is an infinite set of algorithms A that perfectly predict/compute the sequence O.
Right, but who says our observations are finite?
Elementary physics. There are a finite number of humans, the earth has finite mass, finite information storage potential, and we have finite knowledge.
What if important phenomenon, like, e.g., consciousness (cough) turn out to depend on infinitely small particles?
If you want to believe something like this is true before you begin, that consciousness is somehow different and special, then you are abandoning rationality from the start.
There are no privileged hypothesizes and no predefined targets in the quest for knowledge.
What if the fate of the universe in a cosmological sense turns out to depend on what happens over infinitely long periods of time? There is no rule that I know of that says that the Universe is not allowed to clog its equations with infinities.
Sure, infinities are possible, although they generally are viewed to signal a problem in physics when they come up in one’s math.
But that’s all besides the point: our observations are obviously finite. And furthermore, infinities are not at all an obstacle towards a universal physics.
Physics is concerned largely with finding the minimally complex algorithm that fully predicts O.
A noble goal, but who says that sufficient simplicity to allow for computability is possible?
There is no such complexity limit whatsoever to computability—it is not as if a phenomena has to be sufficiently ‘simple’ for it to be computable in theory (although practical computability is a more complex issue).
Suppose our universe contains some true randomness beyond its initial seeding?
True randomness comes up immediately in quantum mechanics. This isn’t an obstacle to computability, whether theoretical or practical. People unfamiliar with computing often have the notion that it must be deterministic. This is not so. Computation can be nondeterministic and randomness is an optimal strategy in many algorithms.
Beyond that, the randomness in quantum mechanics is typically squashed by the central limit theorem; a vast quantity of non-deterministic quantum events become increasingly deterministic at the macro scale.
while the universe is computable in principle, we cannot perfectly compute even a portion of our universe from the inside?
This is true—we can’t perfectly compute very much of our universe from within it, but perfect computation is highly overrated, and regardless this has little bearing on whatever original track we once were on.
I don’t mean to suggest that it’s implausible that everything is governed by a universal physics
It is trivially true, tautological—it is implied by the very meaning of universal physics.
It sounds to me that you have a mystery (consciousness) that you would like to protect.
I just get frustrated when people assert, without evidence that’s apparent to me, that physics will surely explain everything that we might wish to know.
This also is trivially true, and is the main point I have been attempting to communicate. Anything that you could possibly want to know can be explained by some model. This fact doesn’t require much evidence at all.
If there is some new series of observations that physical science can truly not explain, then it is physical science which changes until it does explain them.
I’ve lost interest in the conversation, partly because of your minor ad hominem attack (“sounds to me like you have a mystery that you would like to protect”), but mostly because I see your arguments as dependent on assumptions that I do not share: you see it as “obvious” that physics is universal and that theories favored by Solonomoff simplicity are automatically and lexically superior to all other theories, and I do not.
If you care to defend or explain these assumptions, I might regain interest, or I might not. Proceed at your own risk of wasting your time.
Sorry for the minor ad hominem, I jumped to the conclusion based on prior experience.
We can generate explanations for anything. Science has found that the universe appears to operate on a universal set of underlying principles—everything reduces to physics. We could have lived in a universe where this wasn’t so. But we don’t.
The computer I am working on right now is solid proof of physic’s success.
When you have two theories (algorithms) that both accurately prediction an observation sequence, you need some other criteria to guide you—and here ockham’s razor comes in to play.
There are always an infinite number of more complex theories that explain a series of observations, but only one that is minimally simple.
But again, I think the universality of physics stems just from the simple fact that there are an infinite number of algorithms (theories) that can explain any possible sequence of observations—so universality is always possible.
How do you know?
Because that thesis has made better predictions than every rival theory which seemed at the time more reasonable (superstition, vitalism, Cartesian dualism, etc). The Pythagoreans, amidst all their lunacy, stated perhaps the world’s best-confirmed audacious hypothesis, that the world is a mathematical object.
When it comes to the question of consciousness, I humbly submit that “i-don’t-know-ism” has made better predictions (i.e. none) than any rival theory.
The thesis doesn’t predict that every reduction is going to be easy. And “I don’t know” really masks a good bit of knowledge, unless you’re equally surprised by all new data. Physicalism directly predicts a good many of the things we consider too obvious to categorize as “mysterious” (e.g. that brain damage can cause personality change).
Sure! And I would take decent odds on physicalism...at 20:1 in my favor I wouldn’t have to think too hard; I’d be pretty sure to take the bet, because there is some pretty convincing evidence, like how brain damage works and how simple formulas about e.g. mechanics or radiation explain phenomena in what we might naively assume to be different realms, e.g. solar sails and roof albedo and warm light bulbs. If you can formulate a hypothesis with one set of data and test it using several other sets and get confirmation, it makes sense to guess that it works on all sets. And if you put a gun to my head and said “guess a theory of everything,” I’d guess physicalism...as I said earlier, “of course physicalism or whatever you want to call it is the most plausible known and articulated theory of everything.”
My only point is that we don’t yet have enough evidence to be sure of physicalism in its broadest senses so as to justify shutting down alternative avenues of exploration for standing questions such as the origin of the universe, the nature of consciousness, and the computability of matter.
The results of science are indeed quite impressive.
Suppose you wanted to compare the Pythagorean hypothesis “the world is a mathematical object” with the slightly broader hypothesis “the world consists largely of objects following mathematical laws.”
Are there scientific results that would be predicted by one hypothesis but not the other?
No– this is a variant of the “green/grue” problem. However, the Pythagorean hypothesis puts higher probability on the things we’ve actually observed, because it doesn’t waste any on claiming that this thing or that is non-mathematical.
By Bayes’ Law, this means it’s continually gaining support against the rival candidate.
Would you be so kind as to define “mathematical object”? Possibly I agree with you on everything but semantics, a field in which I am almost always happy to compromise.
Er, a set with a simple definition, like the Mandelbrot set or the set of solutions to the Schrödinger equation on a given manifold? Honestly, I’d be surprised if this is the point you’re stuck on.
What I suspect might help is the distinction here between epistemology and ontology: it’s a meaningful hypothesis that we live in such a mathematical object, even if there doesn’t exist a mind sufficient to exhaustively verify this, and yet our smaller minds can acquire enough evidence about the world’s structure to raise that hypothesis to near certainty (modulo some chance of being in a simulation that’s more complicated than the laws we seek, but whose creators want us not to notice the seams).
I think you’re right that what we disagree about is
The dichotomy you’ve provided seems to me to be an excellent definition of the difference between mathematical epistemological proof and empirical epistemological proof...it happens all the time that we may not be able to rigorously show N, but we nevertheless have extremely good reason to believe N with near-certainty, and even stronger reason to act as if we believed N.
If I hear you correctly, you think that we could plug in “the Universe is merely a mathematical object” for N.
I disagree. For me, the difference between epistemology and ontology is that there is a difference between what we can know and what exists. There might be things that exist about which we know nothing. There could even be things that exist about which we cannot know anything. One could reasonably call for scientists to ignore all such hypothetical objects, but, philosophically speaking, it doesn’t stop the objects from existing.
It boggles my mind to hear the claim that a mathematical object, as you have just defined it in your last comment, “exists in this second, ontological sense. The mandelbrot set expresses a relationship among points. If several small spheres exist and it turns out that the points approximate the relationship defined by the Mandlebrot set, then we might say that a Mandlebrot-ish shape of spheres exists. But the set itself doesn’t have any independent existence. This result doesn’t seem to me to depend on whether we use spheres or rays or standing waves—you still have to be vibrating something* if you want to talk about things that actually exist. I’m not the sort of nut that believes in good old-fashioned aether, but mathematical relationships alone won’t get you a flesh-and-blood universe where things actually exist...they’ll just get you a blueprint for one. Even if, epistemologically, we can know everything about the blueprint and model all of its parameters, it still won’t exist unless it’s made of something.
That, at any rate, is my modestly informed opinion. If you can see any flaws in my analysis, I would be grateful to you for pointing them out.
It continually amazes me that people think “physical existence” is somehow less mysterious and more fundamental than the existence of a mathematical object!
Er, no, it’s not less mysterious—we understand mathematical objects better than we understand physical existence; mathematical objects can be treated with, well, math, and physical existence gets dealt with by jokes like philosophy.
I’m not sure what you mean by more fundamental, but physical existence does seem to be roughly as important as mathematical objects...at any rate, it matters a lot to me whether things exist in fact or merely in theory.
We’ve been given special evidence in our own case, but if we step away from that for a moment, what I mean should be clear. Let’s take a hypothetical Universe X, which is very different from ours.
Saying “Universe X is a simple mathematical object” is pretty well comprehensible.
Saying “Universe X exists in some special way, distinct from just being a mathematical object, and in fact it might not be describable as a simple mathematical object” is just plain mysterious. It’s up for debate whether it’s even a meaningful statement.
Apply that to discussion of our own universe.
But, but, you don’t understand. Math isn’t reeeeeeeaaaaaaaaaaaaaal!
I have an idea. Maybe it’d be more convincing if you said “Universe X is a simple computation.” People feel like computations are more real, and who knows, maybe they’re right. Maybe reality is computation, just a subset of mathematics. It seems a lot easier for people to envision that, at any rate. Or take Eliezer who (I think?) seems to think (or at least seemed to think) that reality juice is magically related to acyclic causal graphs.
You’ll still probably get the same objections, though: “Computations aren’t reeeeeeeaaaaaaaal, they have to be computed on something! Where’s the something coming from?” But that seems a little bit more silly, because the Something that is computing can be infinitely far back in the chain of computation. All of a sudden it feels more arbitrary to be postulating a Something that is Real. And real metaphysicists know that things shouldn’t feel arbitrary.
Now you’re just ripping off the last chapter of Drescher’s Good and Real. You know he comments here sometimes—he’d be so hurt at such plagiarism. :)
I am? I only read the decision theory chapters of Good and Real, the day before he showed up at SIAI house for the decision theory workshop. I’ll definitely read the last chapter when I get back to California.
I think your intuition is relying a little too much on the absurdity heuristic (e.g., “It boggles my mind...”) and flat out assertion (e.g., “But the set itself doesn’t have any independent existence.”). Metaphysical intuition is really misleading. I think most people underestimate that, especially because the absurdity heuristic is strong and therefore it’s easy to reach a reductio ad absurdum that is nonetheless true. I’ll give an example.
Once upon a time I didn’t think copies ‘counted’ in a multiverse, either morally or for purposes of anthropic reasoning. 200 Jacks had the same weight as 1 Mary. The opposite was absurd, you see: You’re claiming that 3 copies of the exact same computation are worth more than 2 computations of 2 different people, leading separate and diverse lives? Absurd! My moral and metaphysical intuition balks at such an idea! I came up with, like, 3 reductio ad absurdums to prove my point. Eliezer, Wei Dai, Steven Kaas, Nick Bostrom, what did they know? And there was some pride, too, because they way I was thinking about it meant I could easily deal with indexical uncertainty, and the others seemed clueless. … Well, turns out those reductios weren’t absurd: I just hadn’t learned to think like reality. I had to update, because that’s where the decision theory led, and it’s hard to argue with mathematics. And it came to my attention that thinking doubled computations had the same measure had a lot of problems as well. Since then, I’ve been a lot more careful about asserting my intuition when it disagrees with people who seem to have thought about it a lot more than I have.
In the case of the Mathematical Universe Hypothesis or permutations thereof (Eliezer seems to think the mysterious ‘reality fluid’ or ‘measure’ has a lot to do with directed acyclic graphs, for instance), there’s a lot of mental firepower aimed against you. Why do you believe what you believe? If it turns out the reason is metaphysical intuition, be on guard. Acknowledge your intuition, but don’t believe everything you think.
Look, of course physicalism or whatever you want to call it is the most plausible known and articulated theory of everything.
But why would you assign physicalism nontrivial probability as against (a) theories that are as yet unknown or unarticulated, or (b) the possibility that the Universe does not behave neatly in accordance with a single coherent, comprehensible theory?
Isn’t the concept-space of “single coherent Theory of Everything” vastly smaller than the total concept-space of concepts that could describe our reality?
The thesis at hand predicts that we should find complex things to be intricate arrangements of simple things, acting according to mathematically simple rules. We have discovered this to be true to a staggering degree, and to the immense surprise of the intellectual tradition of Planet Earth. (I mean, when even Nietzsche acknowledges this— I’ll reply later with the quote— that’s saying something!)
Your (b) makes no such specific predictions, and so the likelihood ratio should now be immensely in physicalism’s favor. Only a ridiculous prior could make it respectable at the moment.
As for (a), I’m talking about the general principle that the world is a mathematical object, not any particular claim of which object it is. (If I knew that, I’d go down and taunt the string theorists all evening.)
Nietzsche, The Gay Science I.46
(NB: in this passage, “we” signifies modern atheists, not people in general.)
As opposed to what? Two or more incoherent theories? Isn’t that just a strange way to talk about an impossible reality?
In short, because physics is so successful.
In long, because no matter how far off physics is from the ultimate algorithm, we can continue to narrow in on it indefinetly. Mathematically at least, even an infinite algorithm is possible. As a curious side note, I remember physcist Frank Tipler has a GUT of physics that is infinite. He claims this TOE has been known for a while, but avoided for obvious reasons. He then puts on a magic space cap and claims that this TOE proves Christianity is correct, but the TOE is interesting nonetheless (at least the idea of it—I am not a physicist).
I don’t know for certain that physics is computable, but from what I have read on that matter, all current indications are positive.
Successful at what, exactly? At modeling the behavior of the stuff that humans can easily observe using basic industrial technology over the span of 100 to 400 years? Why would you want to extrapolate from that to “everything that exists?”
Right, but what makes you think there is an “ultimate algorithm” to be found?
A single universal physics is adequate to explain all that we can observe, and a necessary derivation of that universal physics is a vast quantity of space and time which we can not directly observe but which we predict is also driven by the same universal physics. This is the “everything that exists”—whose existence is in some fact dependent on the universal physics itself.
Whether there is or is not an ultimate algorithm is not even the right question. It is true by default. We can continue to refine physics indefinetly. In other words, of course there is an ultimate algorithm, because we can invent it.
In fact, given any sequence of finite observations O, there is an infinite set of algorithms A that perfectly predict/compute the sequence O. Physics is concerned largely with finding the minimally complex algorithm that fully predicts O.
So yes, mathematically it is trivially true that there is an infinite set of ultimate algorithms.
Thank you for one (of several) intelligent responses.
This isn’t quite right. The only thing that makes the derivation “necessary” is your adjective “universal.” We could just as easily say that there is a supergalactic physics that explains all we can observe, and that same physics could plausibly explain what is happening in the space and time that we cannot or have not observed. Note that the unobservable realms are not merely those outside our past light cone, but also those within the limits of the Heisenberg uncertainty principle, beneath the smallest structures that we can repeatedly observe, and, for all practical purposes, the space beyond the nearest nebula and/or the objects too dull for our Earth-bound telescopes to detect. It would be remarkably bad science to voluntarily choose to sample only one kilobyte from one address out of thousands of terabytes of data and assume that the kilobyte is representative. The fact that all known scientific resources are clustered in the same tiny portion of spacetime forces us to use such a sample, but it cannot and should not force us to assume that the sample is representative.
I don’t understand what you mean. Intelligent minds with an ability to manipulate matter or energy can ‘create’ patterns in that matter/energy by rearranging it according to the laws of physics. However, I cannot think of any sense in which physics itself could be said to create its own patterns. Physics is the pattern in which all known matter is currently arranged, but physics does not create the matter—it merely arranges it. Physics does not explain why there is something instead of nothing; it would be perfectly consistent with the laws of physics for there to be no electrons orbiting no protons over a volume of no space-time. How then can “everything that exists” be dependent on physics?
Right, but who says our observations are finite? What if important phenomenon, like, e.g., consciousness (cough) turn out to depend on infinitely small particles? What if the fate of the universe in a cosmological sense turns out to depend on what happens over infinitely long periods of time? There is no rule that I know of that says that the Universe is not allowed to clog its equations with infinities.
A noble goal, but who says that sufficient simplicity to allow for computability is possible? Suppose our universe contains some true randomness beyond its initial seeding? Suppose that limits on our ability to gather information (particles that put effective distance between themselves and our present location at faster than the speed of light due to cosmic inflation; ineradicable error rates in technologically perfect computers) mean that while the universe is computable in principle, we cannot perfectly compute even a portion of our universe from the inside?
I don’t mean to suggest that it’s implausible that everything is governed by a universal physics. That’s a respectable hypothesis. I just get frustrated when people assert, without evidence that’s apparent to me, that physics will surely explain everything that we might wish to know. This is a remarkably bold claim for a discipline that predicts that most of what exists is “dark energy” but cannot say what dark energy is. Physicalism should be classed as a statement of faith, I think, and not as a justification for specific predictions about the hard problem of consciousness.
Physics is generally held to be universal, instead of just ‘supergalactic’. For one, there is the multiverse. But in general, the idea is, as I discuss later, to find the most parsimonious explanation for everything. This is the optimal strategy, and universality is a necessary consequence of this strategy. Any other physics or system which does not explain all observations is of course incomplete and inferior.
Not at all. You seem to be applying the analogy that at the cosmic scale the universe is some sort of probabilistic urn that generates galactic-sized space-time slices at random whim. It is not.
There are an infinite set of potential physics that have widely different properties in regions we can not observe. There are strong reasons why these are all necessarily inferior, by the principle of Ockham’s razor and the low-complexity bias in Solonomoff induction.
Elementary physics. There are a finite number of humans, the earth has finite mass, finite information storage potential, and we have finite knowledge.
If you want to believe something like this is true before you begin, that consciousness is somehow different and special, then you are abandoning rationality from the start.
There are no privileged hypothesizes and no predefined targets in the quest for knowledge.
Sure, infinities are possible, although they generally are viewed to signal a problem in physics when they come up in one’s math.
But that’s all besides the point: our observations are obviously finite. And furthermore, infinities are not at all an obstacle towards a universal physics.
There is no such complexity limit whatsoever to computability—it is not as if a phenomena has to be sufficiently ‘simple’ for it to be computable in theory (although practical computability is a more complex issue).
True randomness comes up immediately in quantum mechanics. This isn’t an obstacle to computability, whether theoretical or practical. People unfamiliar with computing often have the notion that it must be deterministic. This is not so. Computation can be nondeterministic and randomness is an optimal strategy in many algorithms.
Beyond that, the randomness in quantum mechanics is typically squashed by the central limit theorem; a vast quantity of non-deterministic quantum events become increasingly deterministic at the macro scale.
This is true—we can’t perfectly compute very much of our universe from within it, but perfect computation is highly overrated, and regardless this has little bearing on whatever original track we once were on.
It is trivially true, tautological—it is implied by the very meaning of universal physics.
It sounds to me that you have a mystery (consciousness) that you would like to protect.
This also is trivially true, and is the main point I have been attempting to communicate. Anything that you could possibly want to know can be explained by some model. This fact doesn’t require much evidence at all.
If there is some new series of observations that physical science can truly not explain, then it is physical science which changes until it does explain them.
OK, thank you for talking with me.
I’ve lost interest in the conversation, partly because of your minor ad hominem attack (“sounds to me like you have a mystery that you would like to protect”), but mostly because I see your arguments as dependent on assumptions that I do not share: you see it as “obvious” that physics is universal and that theories favored by Solonomoff simplicity are automatically and lexically superior to all other theories, and I do not.
If you care to defend or explain these assumptions, I might regain interest, or I might not. Proceed at your own risk of wasting your time.
In any case, thank you for a stimulating debate.
Sorry for the minor ad hominem, I jumped to the conclusion based on prior experience.
We can generate explanations for anything. Science has found that the universe appears to operate on a universal set of underlying principles—everything reduces to physics. We could have lived in a universe where this wasn’t so. But we don’t.
The computer I am working on right now is solid proof of physic’s success.
When you have two theories (algorithms) that both accurately prediction an observation sequence, you need some other criteria to guide you—and here ockham’s razor comes in to play.
There are always an infinite number of more complex theories that explain a series of observations, but only one that is minimally simple.
But again, I think the universality of physics stems just from the simple fact that there are an infinite number of algorithms (theories) that can explain any possible sequence of observations—so universality is always possible.
“Why would you want to extrapolate from that to “everything that exists?”″
That’s all we’ve got?