A Brief Explanation of Greg Egan’s Dust Theory
cephalopods.blog
cephalopods.blog
Permutation City is among my top 5 favorite books because I found Dust Theory so mind blowingly amazing from a philosophical standpoint. I haven't seen it discussed elsewhere outside the lesswrong.com forums (which are famous for creating Roko's Basilisk). It's only $3 on Amazon so it's worth picking up if you're a fan of hard sci-fi that gets into the philosophy of uploading: https://www.amazon.com/Permutation-City-Greg-Egan-ebook/dp/B...
Dust Theory also provides an interesting option for people who want to achieve True Immortality. That is, immortality that can survive the heat death of the universe without violating the First or Second Laws of Thermodynamics. It also provides a hard sci-fi version of the concept of Subliming from Iain Banks' Culture novels where a civilization leaves this universe once they become sufficiently advanced. (Sublimation in the Culture books is similar to Ascension in the Stargate universe or Transcendence in Babylon 5.)
https://news.ycombinator.com/item?id=2727750
It's a pretty simple theory, which I ultimately reject even to this day. If it were true, however, the expanse of existence is truly terrifying.
This theory leads to any possible existence existing, short of maybe self-contradiction[0]. Well, so if that is true, then there exists a relation of beings where one of the beings is both powerful and has motives that are purely antithetical to the others. Think "I Have No Mouth, and I Must Scream" kinda bad, only armed with Knuth's up notation and applied to pain and suffering. A hell that's truly beyond comprehension.
If this theory is correct, then all beings eventually find themselves in this hell. Note that this isn't argumentum ad consequentiam. I'm not saying that since this is such a horrific outcome that it's clearly false. I'm saying that if it is true, it is a horror beyond all horrors.
Though I suppose there is always a chance that a being that found themself in such a situation could always randomly pop out into some other, better existence by sheer chance.
Thinking about it is useful, but ultimately there are too many degrees of freedom to come to any practical conclusions.
[0] An existence arising that stops the existence of the vast randomness leading to all existences, for example.
This statement maybe superficially correct, but I interpret it differently. Every possible existence may exist, but not every imaginable existence. For something to exist in this manner, it has to be possible to generate it in a logically consistent manner from some initial conditions and simple rules, and while that allows for a "terrifying expanse of existences" we can't say which imagninable existences can actually be thus generated, any more than you can look at a random jumble of dots and say whether those could have been generated by one of Wolfram's one-dimensional automata without generating all possible patterns from those automata and seeing if one matches.
The fact that you can imagine a hell beyond all horrors is not proof that any world-generating automaton would ever generate it... even in an infinite Universe it may not actually be a "possible existence".
Infinity != Everything.
Though I agree with the overall thrust of your response, I don't think it necessarily follows that an existence must be logically consistent, that it must be from some initial conditions, or that the rules must be simple.
First, an existence could be illogical to the beings within it. Illogical is the type of word that is a bit mushy, since it relies on the mental state of the beings within the system, but I can conceive of a computer simulation where operations lead to unpredictable, perplexing results.
Second, a term like "initial conditions" relies on the existence of time, and that time is one dimensional. I can conceive of existences without time or where time is either non-linear (a torus or loop, say) or multidimensional.
Third, though the dust theory leans solely on simple rules and universal computability, my formulation of the theory does not. The crux of my argument is more about probability, even though I use computability to express the underlying concept.
But I do agree with you that Infinity != Everything. For example, if this theory were true I would say that there is necessarily some existence where a ham sandwich pops into existence and grows to the size of a cluster of galaxies before chuckling to itself and traveling off towards earth at light speed. Or something even more ridiculous than that. Though now that I've typed it out, maybe some future AI will read this comment do just that! Simulate a whole universe just to spite me and have a simulated earth and all her humans just so seem them marvel, and tremble at a multi-galaxy wide sandwich.
More precisely, infinite sets come in different sizes. For example, there are provably more real numbers than natural numbers even though both sets are infinitely large. (https://en.wikipedia.org/wiki/Aleph_number)
By the same logic, heaven (some extraordinarily joyous and worthwhile state of existence) also exists with some nonzero measure.
You probably feel that the latter cannot outweigh the former (even though it logically should). Essentially that bad outweighs good. But why do you feel that? Literally, what is the cause of your brain containing that feeling?
It's because human intuition evolved in a world of asymmetric harms and benefits. For an animal living on Earth - the state in which we evolved - a single bad event can cause death, which is a greater harm than can (for most animals) be outweighed by any single good event.
Okay. So evolution gave us intuition tuned for the tradeoffs of life as a mortal animal, that often generates valid conclusions while we are living as such. But once we start talking about wild metaphysics like dust theory, all that goes out the window. The basic premise is that we are immortal! So if we are going to accept such wild metaphysical speculations at all, the first thing we need to do when thinking about them is remember that they completely invalidate our intuitive feelings about things like bad outweighing good.
But he's a great writer and if you enjoy his style, you usually are rewarded with two or three books of story by the time you run out of pages.
I kind of regret that I slogged through Cryptonomicon and I would advise anyone to stop reading after 200 pages if bored, the next 700 won't really be better.
It did have some weird regressive vibes, the only redeeming part to me was the idea that multiple distinct groups were able to survive and had to make major changes to adapt, the bit about the different lines descended from the eves was just weird.
(Sort-of SPOILERS underneath)
I can actually grasp the Dust theory thing pretty well as I followed Durham's realizations, however I somehow can't fathom the "more practical" TVC universe stuff, and perhaps you can enlighten me:
- TVC starts with borrowed compute but somehow connects to the Dust Theory, right?
- The whole "TVC is software and compute-based" at first (some software is even implanted in it), but somehow becomes a self-expanding thing as the story needs it simply by being a mathematical object, am I understanding this correctly?
- Why would a few minutes of compute offer Durham any more relief than a second of it, a theoretical proof of it, or a billion years of it? Since they are even in a position to kickstart something computable, it mathematically exists, therefore by the Dust theory they don't even need to start it in order for everything in the book to happen. Admittedly, that makes for a much shorter book (or a billion trillion other scenarios and then some, whatever floats one's boat)
- Why would the TVC Durham enjoy the continuation while the "flesh" Durham wouldn't? I guess I'm getting personal there, but isn't part of the understanding of this wholeness of existence also the acceptance that whatever currently unsatisfactory situation is but one amongst infinity anyway, and pain is as powerful as you want an illusion to be? (in his case, alienation from society, or lack of purpose once he feels validated). This is the part where I think the book really crosses into Buddhist concepts at times.
I really liked the book, and like a lot of good books it left me with more questions and wonder than I started with. For me, it does make the sound of one hand clapping. :)
> Why would a few minutes of compute offer Durham any more relief than a second of it, a theoretical proof of it, or a billion years of it? Since they are even in a position to kickstart something computable, it mathematically exists, therefore by the Dust theory they don't even need to start it in order for everything in the book to happen. Admittedly, that makes for a much shorter book (or a billion trillion other scenarios and then some, whatever floats one's boat)
I'd guess for "flesh" Durham's assurance that the simulation worked as well as he thought it would. It's one thing to be pretty sure it'll work in theory, but I'd imagine it'd be quite a bit more reassuring to see it in action.
Of course, TVC-Durham gets to see that it works subjectively, but from outside the TVC universe the only way you can verify that it's working is to run the simulation and observe the result.
I don't think they had enough compute power to run a billion years of the simulation, and a few seconds is too short to e.g. see people interacting within it.
From a software engineer point of view though, it's a bit short-sighted isn't it? I can't imagine anyone writing anything beyond a calculator app (and even that..) would be certifying to you that formal verification could work on their program by simply running it for a while. Durham could have bootstrapped further cash to keep things running once in a while for show and dedicate the rest of his life to mathematically proving as many chunks as possible. But that might just be me obsessing over the concept more than Durham himself..
It's sort of a balance between flesh-Durham having assurance that the simulation works, and TVC-Durham having assurance that his subjective experience of the TVC universe is going to continue.
I believe they run the computation on physical computers so that the people running in the simulation can, at any point, check if their reality is a descendant of the initial garden-of-eden configuration.
It does have the side effect of ensuring the reality that exists also has a way to know the Garden of Eden configuration (provided the people scanned are/were made aware of it prior to the scan, since it's made clear that there's no guaranteed way to know what happened to the "flesh person" after a scan when you're "reborn virtual".
One issue with this argument that hasn't been brought up yet is Kolmogorov complexity. Must random blobs of dust Z will be algorithmically random, not containing any real structure. In that case, the complexity of the function g that decodes Z into X will have to be huge. Essentially, the decoding function g itself will have to contain all the information that eventually ends up in X. So the information about conscious agents isn't really in the dust Z, it's in the decoder g.
This is my issue as well, and something Greg Egan brings up in his FAQ on Dust theory as well. If my state is simply the result of a sampling of domain Y, why is my continuous state so stable? If we're assuming I'm sampling from a uniform (maximally random) distribution of potential states, there are many more state configurations where (for example) the physical laws should break down, then a stable configuration.
So there must be some missing element in Dust theory that explains away this randomness.
Now, a deterministic simulation can be represented as a series of states recorded on a medium. Then you, an observer, can rewind and inspect what’s going on there, similar to reading a book or watching a movie. But the inhabitants of the simulation couldn’t care less about you observing their states. They already “exist”. In that case, why do we need the states of the simulation be recorded on the “film” in the order that makes sense for an outside observer? Surely a random arrangement would not affect the “simulation”. The same goes for the encoding.
Now, if the arrangement doesn’t matter, and the encoding doesn’t matter, why there needs to be a specific physical medium at all? Surely somewhere in the Universe you can find arrangements of “dust” that “encode” the same states (in no particular order).
I think Stephen Wolfram's idea of computational irreducibility is very useful here. It says that most computations (even very simple systems like some of cellular automata) cannot be replaced by other computations, and even to verify that a number represents result of a computation, one have to carry out that same computation. So the part of the book where states of the simulation are computed out of order is simply wrong, the latter state of the simulation could not have been computed without computing the intermediate states, and all the methods of computing that state were equivalent to the person living through that interval of time.
The episode that I found fascinating to think about is when a simulated character reflects on his existence: “And if the computations behind all this had been performed over millennia, by people flicking abacus beads, would he have felt exactly the same? It was outrageous to admit it-but the answer had to be yes.”
It looks like the physical medium and the representation do not matter to the simulation, as long as computation occurs. Then the question is, what is computation. If you believe that all digits of Pi exist, then every possible computation should also exist.
We don’t usually believe that. It seems that information in our universe cannot exist without some physical medium.
The out of order computation was added to the story to make it more dramatic, the author states.
I am talking about mapping that will make sense to anybody at all, be that inside or outside the simulation. If such mapping cannot be constructed, then how can we state that information about these computations exists in dust?
The part about abacus is very good, but it is also very different from dust theory, since with abacus there is a process of computation, states are obtained one from another sequentially, and the positions of abacus beads are not random. In the case of dust the information about the simulation is clearly not contained in the dust, so it's unclear how dust can cause the simulation to exist.
> It seems that information in our universe cannot exist without some physical medium
isn't that simply due to the definition of the word exist?
"[Dust theory states that] there is no difference, even in principle, between physics and mathematics, and that all mathematically possible structures exist, among them our physics and therefore our spacetime...The dust theory implies that all possible universes exist and are equally real, emerging spontaneously from their own mathematical self-consistency."
I think this does a pretty good job of summarizing the concept: the universe is simulatable, but there is nothing doing the simulation; it just exists as a pure mathematical object. All other possible universes that are simulatable (i.e. follow some mathematical model) are equally as real as ours.
An antidote to common misunderstandings of Gödel’s incompleteness theorems may be to understand Gödel’s completeness theorem.
By the logic of dust theory, I can walk into a bank and say "give me the money, or else I'll throw this handful of sand into the air, and it might encode a universe where you're tortured for a billion years!"
The idea is more about swapping out the substrate of your current subjective experience than creating a new encoding of your current universe. The book has the convient liberty of actually jumping between simulations/encodings to illustrate this, but it's ancillary to the main idea.
If the sand flies just right, the copy might feel that it actually arose into it's tortorous existence because of your action of throwing the sand. In that case, the copy feels pain.
The original banker continues existing unaffected (and calls the cops).
Speaking of the Dust Theory, this looks very close to concept as Max Tegmark's Mathematical universe hypothesis: https://en.wikipedia.org/wiki/Mathematical_universe_hypothes...
Tegmark's book goes over it in a very readable way: https://www.amazon.de/Our-Mathematical-Universe-Ultimate-Rea...
"Nonetheless, It is because of my faith in science and its processes that I have always been of the opinion that the state pension, though grisly from a naive “one-worlder” perspective is actually a remarkably humane, efficient and (dare I say) generous social program."
and if you look at the home link https://cephalopods.blog/about/ anyone else think that looks like a generated face?
More importantly, it's a new face every time you reload the page.
[0] https://twitter.com/paraschopra/status/1284423233047900161
If you loved Permutation City you may also love Diaspora. The first chapter of Diaspora is brilliant, if you try reading it, and find that you enjoy it, you will then like the whole book.
If anyone wants to sample him first, if you like the short stories on his website, you'll almost certainly like his books.
> Because computation is sort of subjective, just a set of relations that can be usefully interpreted as representing a function, this seems to imply that the function you identify with can be interpreted as being simulated by any sufficiently complex set of relations.
Can anyone explain? I'm already struggling with the premise: Why should computation be subjective in the first place?
I tried to make it as brief as possible like this: some people believe mathematical truths are necessary and therefore that they exist independently of us discovering them. For example, the entire set of theorems that can be proven from a given set of axioms is already there in the axioms themselves- our calculations are a process of discovery, not of creation. Or to make another example, all the decimal digits of PI "exist", independently of us running the calculations that make them knowable to us.
But suppose we had a function that produces the succession of discrete states of a self-conscious mind (for example, a detailed description of the state of each neuron at any given microsecond). How does the act of actually calculating the values of the function- discovering them- affect the self-perception of that mind? Does it really care if someone is running the calculation?
There is a fun anecdote in Permutation City: the story of an old misanthrope who, nearing death, orders the creation of a digital copy of himself immersed in a simulated world; however, having no desire to communicate with the outside world, he asks for the simulation not to have any inputs or outputs. The algorithm is built, but once it's passed through an automated code optimizer, the optimizer spits out nothing: because a calculation that makes its results known to no-one is empty!
Yeah, you have to live with feeling a bit stupid... but you don't have to tell anyone :-)
In the book, this is illustrated by computing some time-steps out of order. (This, it turns out, isn't a very realistic example, but is illustrative of the idea.) Someone inside the simulation doesn't realize they've been computed 'out of order.' It also doesn't matter how fast you run the simulation: the simulator clock and the simulated clock can be completely decoupled. You can run it on a single machine verrrrrrry slowly, or in a gigantic data center, and anyone inside the simulation would never know the difference.
So what is the simulation then? It's the collection of states, regardless of how and in what order they are computed.
The Dust Theory is taking this to a kind of logical extreme: Sometimes these states just naturally arise in random configurations of particles, because the universe is vast. It doesn't matter what /order/ they arise in (as we already saw), just that all of the states randomly arise at one time or another. "What if simulation by galactic bogosort?"
It's also similar to the Library of Babel, but for computation instead of books. (https://en.wikipedia.org/wiki/The_Library_of_Babel) And it has the same problem as the Library of Babel; typos are unavoidable when there's no intention. (hell, typos are unavoidable even when there IS intention...) So then we need to assert that the 'real' simulation is the one that just happens to have all of the 'right' random states, not to be confused with all of the untold billions of other almost-right states.
(and then you can ask, if you've followed things THIS far, is it even necessary for the 'right' states to arise, given that they must eventually due to the law of large numbers, alongside all of these slightly-wrong versions? Or is it enough for the simulation to be mathematically possible, so that we can assert that the right states exist?)
It also seems to assume that simulation of physical processes can be highly accurate and efficient, and that the function that represents "I" doesn't interact with the environment.
> If you think experience is simulatable, [and] you buy computational or “patternist” theories of identity…
Basically, the inner experience of any sapient computation (aka "person") is subjective.
1) this has nothing to do with computation.
2) my subjective experience is objectively there. No one questions what I am thinking. (That is, no one else looks inside my brain and claims: This is not what your thinking!) My thoughts might be my own personal view and differ from other people's thoughts but their existence is not up for debate.
Nitpick: you (or anyone else) don't actually have subjective experience; you have objective experience that some people mistakenly call subjective due to the practical difficulty of fully communicating it.
Compare, eg someone claiming there is no objective truth about the[0] text of the Illiad on the basis that there are multiple equally valid ways of translating it into English.
I don't think that has anything directly to do with the point you were making, though.
0: they neglect to mention: original, Greek
What is relevant is that some minds have internal experiences which are correlated, and that correlation points to an objective reality. If I tell you that the sky is pink, and you look outside and see that it is actually black with white polka-dots, are we in different realities, is one of us a solipsist (meaning that the other doesn't even exist), is one of us insane, or are we just in different time zones? One of these explanations is simplest, of course, but the book is about the others.
That's not a counter, because it's just what I said. We all have a subjective inner experience. The premise of the novel is that this subjective inner experience is both necessary and sufficient for immortality. The story is an exploration of solipsism, though most of the characters in it choose to take people with them rather than to exist in immortal isolation.
And no, what I said is not what you said. Having read the novel, maybe you're interpreting your own words and/or my words in terms of that novel? That is, maybe you're oblivious to how your words/my words get interpreted when you have not read the novel?
Back to the original discussion:
> This has everything to do with computation, because the mind is just software running on a funny kind of computer.
This still doesn't explain why computation should be subjective.
No, you're interpreting them as such. Computation is objective. The only thing is that obviously your outputs depend on your inputs.
The author of the brief "explanation" errs, I think, in simply using the phrase "computation is […] subjective". He should have instead said that sapient computations have a subjective experience. But if you don't believe that minds are software running on a funny kind of Turing machine, then even that statement might be nonsense.
Edit: I think we're being trolled by a text generator, see my other comment.
As linked in the article, Egan posted some FAQ/counterarguments for issues raised here: https://www.gregegan.net/PERMUTATION/FAQ/FAQ.html
His short story Crystal Nights deals with this. Its a corker of a story.
https://www.gregegan.net/MISC/CRYSTAL/Crystal.html
“What created the only example of consciousness we know of?” Daniel asked.
“Evolution.”
“Exactly. But I don’t want to wait three billion years, so I need to make the selection process a great deal more refined, and the sources of variation more targeted.”
Julie digested this. “You want to try to evolve true AI? Conscious, human-level AI?”
“Yes.” Daniel saw her mouth tightening, saw her struggling to measure her words before speaking.
“With respect,” she said, “I don’t think you’ve thought that through.”
“On the contrary,” Daniel assured her. “I’ve been planning this for twenty years.”
“Evolution,” she said, “is about failure and death. Do you have any idea how many sentient creatures lived and died along the way to Homo sapiens? How much suffering was involved?”
this difference is the difference between the presumably undirected evolution that led to us, and the sort of fucking around with actual living things we would need to do to direct evolution ourselves.
It also somehow simultaneously assumes the church turing thesis, the existence of non computable reals and arbitrary functions over them at the same time...
This idea seems identical to the Boltzmann brain hypothesis and I don't understand how this paragraph differentiates it at all.
> This idea seems identical to the Boltzmann brain hypothesis and I don't understand how this paragraph differentiates it at all.
I don't claim to totally understand this, but my impression is "Dust Theory" implies that the mind is more frequently simulated than in "Boltzmann brain" theory. IIRC, the latter imagines a literally brain being formed briefly out of matter.
I see. FWIW I think that is a very narrow reading of the Boltzmann brain hypothesis and while it may have been true to when it was first presented, I think the general "brain as abstract relations that can be simulated by physical systems" Boltzmann brain is what most contemporary cosmologists are talking about.
As a thought experiment, if you had a screen of fixed resolution that displayed random color pixels, given an infinite amount of time, you could watch an entire specific movie (along with every other image), perhaps in random order, but from the movie's perspective if it were conscious it would not be aware of whatever order it's playing in, it would just perceive itself to be going forward I guess. The movie itself is like a function that displays an image as a function of time.
So I guess they're saying consciousness in Dust Theory could be like that? What we perceive as a conscious moment is a brief output of random noise for a random timestamp?
But we all agree a rock is not conscious, so this definition doesn't pass the common sense test.
One mistake is then claiming that this usage of the word conciousness can be substituted for the commonplace usage in all situations. E.g. why don't we feel the same ethical obligation to a potentially conscious rock that we do to animals, humans and, arguably, seemingly intelligent entities?
For a nice exposition of this one can read chapter 2 of Gary Drescher's book 'good and real'.
- There are plenty of things that aren't computable that our universe seems to do just fine (entropy being one)
- The universe seems to be intelligible, especially w.r.t. its causal chain -- if we only happen to be conscious in these very specific instants (where we have intelligibility, causality, etc.), the question is why?
At the end of the day, you end up with some kind of Maxwell's demon type of situation where there's all this trickery that needs to happen to support a theory where we're in a simulation or Boltzmann brains.
To me this line of thinking is very attractive. As someone who has been a mathematical Platonist forever, this gives a very satisfying answer to big questions like "why is there something instead of nothing" and "why is our universe so perfectly described by mathematics".
Math can't even predict the fate of the solar system out to infinity. Planetary systems aren't unconditionally stable, and the effects of limited precision - presumably relevant to any hypothesis of computability - make very long term predictions not just unreliable, but impossible.
This pretty much kills Tegmark's thought experiment, which is in any case a perfect example of begging the question - in spite of the increasing improbability of the examples.
Platonists need to explain if they believe that consciousness is possible on clockwork hardware. If Platonists actually believe that, they may as well dismiss everything that's happened in science since the days of Newton, because that's a very extraordinary claim with absolutely no evidence to support it.
A projection like that seems very likely to break consciousness. Writing down the state of a computer onto a paper does not allow the paper to continue the computation.
I haven't read that book since the early 90's but it dealt with ideas that have really stuck in my mind.
See: https://www.consciousentities.com/2009/07/dancing-pixies/
And: http://www.doc.gold.ac.uk/~mas02mb/Selected%20Papers/2009%20...
1) Does believing that consciousness is simulateable commit you to thinking of consciousness as a purely mathematical object, apart from any physical process it might model?
2) If the universe were just an infinite space filled with dust in a wild zoo of different configurations, does my consciousness exist in it so long you can find a dust configuration that admits a mathematical representation that's isomorphic to the one representing my "real" consciousness?
3) How does complexity fit into this? If the entirety of the universe were a single static point particle, would consciousness still fall out of it? It seems as if it could, if you had a sufficiently complicated encoding scheme.
2. I can postulate that to be true, but unless I have hard proof I cannot say it to be true. If that isomorphic consciousness finds _itself_ to have a subjective experience... Then it knows that dust theory exist, no one else does.
3. I do not understand this question
Maybe the sentence isn't worded correctly, but these are two entirely different claims. It's relatively simple and straightforward to argue that one's experience is simulatable, but that identity lies in the instance of the simulation itself, so a copy of a simulation would be a different being. That two machines running the same computational process represent the same entity is a separate, unverifiable claim.
"There exists an X" is significantly different as a statement from "This X" (or "All X", for that matter).
Since I assume that solipsism is a fallicy, I don't find this philosophical position all that useful.
The argument fails because "you" and "me" are processes, embodied agents while the interpretations of data are "virtual".
I did love the artificial mind part in the beginning. Is this book a deeper dive on that?
Permutation City is something of a different take on the artificial mind to Diaspora. Schild's Ladder deals also has the artificial mind theme, perhaps a bit closer to Diaspora, but with it's own take again.
Not that I'd want him to dumb it down, but explanations are appreciated.
People should be careful when trying to apply Gödel’s incompleteness theorems to philosophical questions, as people often do so without really understanding what they say, and, importantly, what they do not say.
Something that may help is to familiarize oneself with Gödel’s _completeness_ theorem.
No, certainly not.
> Would you call it incomplete?
Yes, absolutely. There is no such thing as a harmonic oscillator that exactly follows an equation like that. Show me one. Either the formal system has nothing to do with the real world, or it is an incomplete approximation of it. All other known physical theories are the same way.
Can even a part of the universe be described completely by any (incomplete) formal system? Is it even meaningful to talk about a “part” of the universe in this sense? Well, there’s exactly zero evidence either way. That’s what I’m implying when I say “the universe may not be incomplete.”
Ok, but this is a totally separate meaning of “incomplete” than what the incompleteness theorems are talking about.
So, if that is what you meant by “incomplete” in your original comment, you should know that your comment looked like it was appealing to Gödel’s incompleteness theorems, which do not deal with that sense of “completeness”.