My topic - the Universal Dovetailer Argument

This month I'm breaking with tradition and actually posting early! This is for two reasons, 1) because I have some time on my hands being sick at home today and 2) because the topic may be more challenging than the average so I'm giving you all some time to get acquainted with the material before we discuss it. I'm going to try to be as concise as possible but a certain level of verbosity is unavoidable.

First of all, let me make my own position on this theory clear. I don't 'believe' it as such. In fact I actively disbelieve it, for reasons I won't go into here - I'll leave that for the day. Nevertheless it does open up some pretty fascinating philosophical vistas, and ties into a whole bunch of stuff including the dreaded Cryogenic Paradox, quantum theory, the objective existence of numbers, the modern multiverse cosmology, and more. As a backgrounder, I stumbled on this through a Google group called the Everything List, a discussion group bound together by the concept that 'everything exists', which I'd been referred to by someone who left a comment on my Cryogenic Paradox post.

But I promised concision, so onwards! The idea I want to present is called the Universal Dovetailer Argument (UDA), and was proposed by a French academic by the name of Bruno Marchal, who is a research fellow in AI at the Université Libre de Bruxelles. Here is Marchal's original paper on the subject (from which I attempt to distill this summary). Unfortunately Marchal's argumentation style is not exactly crystalline in its clarity for a non-mathematician, a problem exacerbated by his inconsistent conjugation of English verbs. Nevertheless, I think I've succeeded in deciphering 90% of the gist. I'll tell you the bit I don't follow (and have my doubts about) when I get there.

So, the UDA proposes itself as a refutation of materialism, and purports to "reduce physics to fundamental machine psychology", by which I think he means the mathematically defined laws by which computing devices (namely, us) compute their self-consistent states (I'll explain). It relies on the following assumptions:

• That a brain (and a consciousness) can be substituted by a 'Turing-machine' type computational device, i.e., we could theoretically have a brain transplant and not know the difference.
• The 'Church Thesis', which basically says that one type of computer can always perfectly emulate another (contradicting my suspicion that my old Commodore 64 would struggle with Photoshop CS5, but if you fed the data through in small enough blocks, and could maintain state with enough memory...). We're talking mathematical inputs and outputs here, not the time taken nor the form of presentation.
• Arithmetical Realism - namely the idea that mathematical relations and propositions "are true independently of me, you, humanity, the physical universe" etc.

These assumptions sum to what Marchal calls Classical Computationalism (or just "comp" for brevity's sake). I can personally accept the second of these assumptions, C64 notwithstanding. The first and last are a lot more debatable, but as I said, we're "running with it".

So here goes the argument in 8 steps:

1. "Comp" allows for teleportation, whereby a person is cut at one place and pasted at another. (I can't resist relating a joke at this point: Man standing in teleporter hears an announcement: "Your duplicate has been created at the destination, but due to a technical fault, there has been a delay in vaporization at this end. Please stand by...") Now the person at the end of the teleportation is a "consistent extension" of the one prior to teleportation, so Marchal assumes it is the same individual/consciousness. All we have done is add to the individual's belief set a new one relating to location. This is in fact irresistible unless we try to "stick" consciousness to the physical substrate of the "computation" that is the mind, but that violates assumptions 1 (and 2) above.
2. Now let us imagine this person keeps a diary which gets teleported along with him or her and records what happens. A third-person account of the teleportation will at this stage be completely consistent with the diary (first person) account. The pronouns will be different, but the proposition will be logically identical ("Pierz was teleported from Melbourne to Sydney" vs "I was teleported from Melb to Syd"). But imagine there is now inserted a time delay between "departure" and "arrival" in the teleportation process. If the teleportee is not allowed reference to any external cues to the passage of time (eg, a non-teleported calendar), the first person account will now differ from the third person account, as the diary will not register any delay - the gap is invisible/non-existent from the first person perspective.
3. Now imagine the person's data is transmitted to two destinations, say Adelaide as well as Sydney. From the first person perspective, what is the chance my diary will say I arrived in Sydney after the experiment is complete? It has to be 50%. Even though there is no uncertainty in the third-person account, there is an irreducible uncertainty in the first person account (I'm going to use the abbreviations 1-p and 3-p from now on for these perspectives because I'm lazy). From 3-p, there's a fully determined, objective situation; from 1-p, there's a 50% uncertainty. Objectively (3-p) the person is going to end up in both places. But there is no diary where someone is in both places at once, so you could say from the point of view of the traveller, the chance of being in one place or another post-teleport is 50% each way.
4. Now let us introduce a delay in one branch of the teleportation. The internet connection to Adelaide is down and they can't email all the attachments required for reconstitution for a couple of days, say. In this scenario, the probability of ending up in Sydney or Adelaide is still 50% - the delay is irrelevant because it does not affect the 1-p account.
5. Now imagine we don't vaporize the person in Melbourne, but simply email a copy to Sydney and duplicate them. What now is the probability of ending up in Melbourne or Sydney from 1-p? It is still 50%, since the "original" that stays at home can be considered as having been "teleported" to the same place with a zero delay.
6. Next we can postulate the possibility of "teleporting" a subject into a virtual reality rather than an actual one. All the preceding steps can be performed with the reconstitution being virtual rather than real, without any change in the 1-p account for as long as the simulation is maintained and given an accurate enough virtual Sydney.
7. Now we come to the so-called Universal Dovetailer (UD), and now we get contentious (if the above wasn't contentious enough).  The UD is basically an algorithm that executes all possible programs. It is called a dovetailer because, in order not to "crash" on infinitely executing programs (there is in theory no way to exclude such algorithms), it executes one instruction from each program in sequence then goes on to the next instruction in the next program, and so on, thus doing what a multitasking OS with a single core effectively does - simulating parallelism. Now suppose that the universe is large enough and robust enough to allow such a device to run forever. It follows that will generate all possible Turing machine states infinitely often, including all possible virtual reconstructions of yourself in all possible locally emulable environments. And since we have established (or assumed) that your mind/brain is emulable and any such emulation will in fact result in a 1-p indeterminacy as to where 'you' end up - this indeterminacy being the infinite union of all finite portions of the UD machine where you are emulated - we can see that 'you' exist within the UD as one trace through the all the existing computational states of this "machine". So physics, as the science which gives correct predictions about the probabilities of  entities being in particular states, can be reduced to "fundamental machine psychology", or "some measure of consistent states" from a first-person point of view. It becomes an "average of consistent histories". GEDDIT??
8. OK, but here's the obvious objection. What if the universe is not big enough to support the UD? Then our normal physical predictions would be safe from interference from all the virtual states of this machine. According to Marchal, "such a move can be considered ad hoc and disgraceful" (!), but he doesn't really explain the disgrace of this obvious objection. Instead he goes on to argue that we cannot associate inner experiences with physical processing (this was the point I raised earlier when introducing teleportation), but instead that inner states must correspond to a type or branch of computation in the platonic mathematical space of all computation (Arithmetical Realism). But I cannot frankly follow his reasoning why (it's on page 11 of the paper if you want to have a crack). He draws the conclusion that computation is not performed by a physical machine (which the universe may not be able to support), but that these computations exist in mathematical space, requiring no physical substrate. 

OK, so the logic of the last part gets kinda weird and flaky, but consider this: modern cosmology now suggests the existence of an infinite universe, or in fact an infinity of universes separated by space expanding faster than the speed of light and therefore unable to communicate in a classical sense, but presumably still quantum-entangled. If this picture is true, then the universe itself could be the UD, creating all possible Turing states, and if it is the case (solving the Cryogenic Paradox) that a sufficiently accurately emulated state in effect "blurs into" all other equal states (i.e., another way of saying there is only one observer), then something like the above becomes almost plausible. We have a version of Everett's many universes interpretation of QT, in which the wave function is the "presence" of all the other universes adjoining ours in information space or, to use Marchal's lingo, it is the 1-p indeterminacy of all consistent states in the infinite trace of the UD. You can at this point dispense with the awkward terminology of the "dovetailer" and simply consider  the universe as a generator of all possible configurations of information. If information rather than matter is primary, then something along the lines outlined above is not as preposterous as it at first sounds.

DISCUSS!

(I realize this was a mega-crash-course in a some kinda out-there ideas, so apologies for that. I do recommend having a go at the first 12 pages of Marchal's paper if anything is unclear.)