Permutation City

The Dust Theory: Frequently Asked Questions


Spoiler Warning

This “Frequently Asked Questions” page contains spoilers for my novel Permutation City, and probably won’t make a lot of sense to anyone who hasn’t read the book. If you haven’t read it, and have any intention of doing so, you will probably enjoy it more if you delay reading this FAQ until you have read the book itself.


Why an FAQ?

Since Permutation City was published in 1994, many readers have raised the same issues with me, again and again. Although I have replied to these questions before — in discussion group posts, interviews, and individual email responses — I thought I’d finally put my thoughts on this all in one place. So, almost thirteen years later, here is a kind of self-interview on the most contentious aspects of the book.

Q1: In the novel, Paul Durham runs a Copy of himself out of temporal order, skipping its mental state forward in time by ten seconds and then computing the intervening states backwards. Surely leaping over ten seconds of time without computing the intervening states would be impossible?

A1: Yes, it would almost certainly be impossible to compute the state of a complex computer model of a human brain and body at time t=10 from its state at time t=0, without computing thousands of intermediate states. So why did I include these scenes? Because this seemed like the simplest way to dramatise the notion that the arrangement of the successive states of the Copy in time (or space) should not affect its subjective experience.

A version of these computations that would have been possible would be to declare that the ordinary way of representing each state of the Copy was “canonical”, and then to find the t=10 state from the t=0 state by computing all the intermediate states in some “non-canonical” form. To give a trivial example, instead of storing and manipulating all the relevant quantities as binary floating-point numbers, they could be encoded in a variety of different schemes. Moving beyond that, the way in which the representation of the data reflected the three-dimensional layout of the physical objects being modelled could be obfuscated in various ways.

Now, it can be argued that it “obviously” makes no difference to the Copy whether the representation of each of its states was the simplest, most transparent data structure possible, or whether the representation was so complex and obscure that an uninformed observer could never have made sense of it in a million years. Then again, if this is so obvious, there’s no need to do the experiments at all (see Q2 below). In the end, the reason I glossed over the difficulty of computing the jump in time was simply that the basic concept was already complicated enough, and I think too many readers would have given up on the whole idea if I’d added further complications at this point.

[After I posted this FAQ, Jack Boyce emailed me to point out an algorithm called Hashlife, which sometimes makes it possible to skip over very large numbers of time steps in the evolution of John Conway’s famous Game of Life cellular automaton. This is a very interesting algorithm, but I don’t think there’s much chance that the same thing could be done, efficiently, for something like a simulation of the human body. Life is known to be “Turing complete” (that is, you can mimic any computation at all with some configuration of Life) but that in itself is not enough to make skipping steps in a Copy possible, because Hashlife does not provide a uniform speedup, and those configurations of Life that perform complex computations are unlikely to get any benefit.]

Q2: Don’t the results of Durham’s experiments prove nothing, given that the end product — the Copy’s mental state after the experiment is over — in each case is a foregone conclusion, completely determined by its initial state in a manner that has nothing to do with the details of the way the computation was carried out?

A2: Yes, the experiments prove nothing, and Durham’s Copy does reflect on this fact. At the same time, Durham and the Copies can’t help feeling that it is worthwhile to actually experience the various scrambled computations. This is, arguably, irrational, but it doesn’t seem absurd to me that someone obsessed with these ideas would nonetheless try these experiments, just in case something happened that surprised them.

Q3: Given that some of the characters in the novel take the Dust Theory seriously, why should they care whether or not they achieve any of their specific goals? Surely the same total set of events must happen to versions of them, regardless?

A3: I believe human nature is such that people would still act as they did in the novel. Obviously some people, faced with this idea, would become passive. Some people wouldn’t. I chose the more interesting story.

Q4: Doesn’t the ending of the novel go against the Dust Theory?

A4: It does go against the “pure” Dust Theory, in which any arrangement of the dust that contains observers would persist. Actually, it could be argued that absolutely any set of experiences should be possible according to the Dust Theory, including this one. But that wasn’t my intention here. Rather, I wrote the ending as a way of dramatising a dissatisfaction I had with the “pure” Dust Theory that I never could (and still haven’t) made precise (see Q5): the universe we live in is more coherent than the Dust Theory demands, so there must be something else going on. The “battle” between Elysium and the inhabitants of the Autoverse to assert themselves as the primary reality was meant as an (admittedly not very rigorous) attempt to show that there was some deeper principle at work that the Elysians were yet to understand.

Q5: How seriously do you take the Dust Theory yourself?

A5: Not very seriously, although I have yet to hear a convincing refutation of it on purely logical grounds. For example, some people have suggested that a sequence of states could only experience consciousness if there was a genuine causal relationship between them. The whole point of the Dust Theory, though, is that there is nothing more to causality than the correlations between states.

However, I think the universe we live in provides strong empirical evidence against the “pure” Dust Theory, because it is far too orderly and obeys far simpler and more homogeneous physical laws than it would need to, merely in order to contain observers with an enduring sense of their own existence. If every arrangement of the dust that contained such observers was realised, then there would be billions of times more arrangements in which the observers were surrounded by chaotic events, than arrangements in which there were uniform physical laws.

Q6: What do you regret most about Permutation City?

A6: Something quite separate from the issues with the Dust Theory mentioned above, although these are all valid points. What I regret most is my uncritical treatment of the idea of allowing intelligent life to evolve in the Autoverse. Sure, this is a common science-fictional idea, but when I thought about it properly (some years after the book was published), I realised that anyone who actually did this would have to be utterly morally bankrupt. To get from micro-organisms to intelligent life this way would involve an immense amount of suffering, with billions of sentient creatures living, struggling and dying along the way. Yes, this happened to our own ancestors, but that doesn’t give us the right to inflict the same kind of suffering on anyone else.

This is potentially an important issue in the real world. It might not be long before people are seriously trying to “evolve” artificial intelligence in their computers. Now, it’s one thing to use genetic algorithms to come up with various specialised programs that perform simple tasks, but to “breed”, assess, and kill millions of sentient programs would be an abomination. If the first AI was created that way, it would have every right to despise its creators.

Addendum, 19 December 2009

My thanks to the mathematician Yair Glasner, who emailed me to point out a problem with Paul Durham’s idea that he could prove himself sane by starting the TVC cellular automaton in a “Garden-of-Eden configuration”: a state of the cellular automaton that could not arise under its rules from any prior state.

Durham argued that if he found himself in a TVC automaton whose history he could trace back to a Garden-of-Eden configuration, then that would be the only possible history that could be “found in the dust” that accounted for his experience (as opposed to his experiments when he seemed to be a Copy, but after being shut down woke to find other explanations of what he’d been through).

The problem with Durham’s argument is the “Garden-of-Eden Theorem” of Moore and Myhill [2,3], which says that a cellular automaton admits Garden-of-Eden configurations if and only if some states have more than one possible history, which would potentially prevent Durham from tracing back any later state unequivocally to a Garden-of-Eden configuration. In other words, if the cellular automaton update rule R is such that there’s a state, G, that can’t be produced by any prior state (there’s no F such that R(F)=G), then Moore and Myhill’s theorem requires that there are states H1 and H2 such that R(H1)=R(H2), i.e. it’s impossible in general to know which state preceded a given one.

Further reading

[1] The famous roboticist Hans Moravec wrote a fascinating and thoughtful essay, Simulation, Consciousness, Existence, which deals with ideas that are essentially identical to the Dust Theory. [Thanks to Mariano Chouza for showing me this.]

[2] Edward F. Moore, “Machine models of self-reproduction”, in Essays on cellular automata, A. Burks (editor), University of Illinois Press, Urbana, 1970, pp. 17-33.

[3] Myhill, “The converse of Moore’s Garden-of-Eden theorem”, Proc. Amer. Math. Soc. 14 (1963), 685-686. [Thanks to Yair Glasner.]



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