Monday, August 29, 2011

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 Universit√© 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.


(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.)


Guy Montag said...

Thanks for this and the link to the paper. I've been lurking on the everything list for several months now. needless to say Marchal's ideas are fascinating, regardless of how you feel about them. I for one am slowly coming to terms with his argument and am becoming increasingly sympathetic to them, although i do have several reservations.

Does the UDA really require empirical confirmation from modern cosmology? In the last step Marchal disposes of any concrete UD and only requires a platonic one. Elsewhere he says

"Once you explain why arithmetical machines are statistically right
to believe in physical laws without any real universe, such a real
universe is redundant.
By Arithmetical Realism and OCCAM razor, there is no need
to run the concrete UD, nor is there any need for a real concrete
(Or you can use the movie graph argument to show that a first
person is not able to distinguish real/virtual/and *Arithmetical*
nature of his own implementations, and this eliminates OCCAM.)"


In any case, it is causing me to challenge many of my assumptions about reality.

C. Seligo said...

Forestalling an objection by calling an argument a disgrace is so French. There are much clearer exponents of these ideas. David Deutsch, in The Fabric of Reality, does a pretty good job of explaining what it would mean to call the universe "computational" , without ever insisting that it is so (which is my sense of graceful thinking.) Sci Fi author Greg Egan's short stories and novels explore these questions, while retaining a sense of how human beings and error in the system can be very consequential. Read "The Kidnapping" or "Transition Dreams" or " The extra" to get an idea of how virtualized consciousness is problematic. There are so many unknowns, tenuous propositions, and we are generally very bad about thinking about large numbers, to say nothing of infinity. Any history of science will find great minds crashing at the cusp.

LizR said...

Thanks for that, but whatever happened to the movie graph argument? (which is where I fall over when I attempt to follow far.)

But, to deal with the last points, if you allow the UD to run in the physical universe, then there are an infinite number of copies of your consciousness created on it, which outnumber any "real" (physical) copies that may be around by, well, infinity to one. So the chances are quite good that you and I are "merely" being instantiated in the UD. Well, that's my understanding of it, at least.

But now Bruno works his magic and "explains" that you don't need a physical UD at all, because there is one already in existence in the natural numbers, along with every other software programme that has ever or could ever exist. This is a "Library of Babel" type thing - these things are also somewhere in the digits of pi, along with every movie ever made, every virtual reality possible, every experience anyone can have, and so on. (In some of them I'm Empress of the Universe, but I digress)

Hence the physical universe becomes unnecessary - we have no need of that hypothesis (although when we stub our toes on a rock we might entertain the notion for a while before remembering that actually we just bounced some electromagnetic fields off each other).

Now Bruno does some even more marvellous selight of hand and shows that not only is the universe unnecessary for consciousness, it can't even support consciousness - that is, there's a problem with the "physical supervenience" theory, the idea that consciousness "supervenes" on brain states. This is the movie graph argument, and is, I admit, where I get completely lost. It seems to be all smoke and mirrors - a joke that people who have read the MGA will, I hope, appreciate; but also true.

Nevertheless I have retired into monastic seclusion where apart from the odd roar in the night (Master Padmasambhava assures me this is just trolls flushing their toilets deep within the mountain) I shall, I hope, have time to meditate more fully on these matters. I must remember to drop by and post the answer before, insane for the light, I am the butterfly and I am gone.

Richard Ruquist said...

Here is a relevant Discussion from a yet to be published paper:

The above is a bare-bones description of how the Mathematical Universe Hypothesis (really a conjecture as hypotheses can be tested) can be made more concrete (in the context of a 26d-string-theory Metaverse cosmology) by replacing the usual postulate of a nebulous Platonic “information space” (where computations are made) by a Calabi-Yau subspace (a cubic lattice of compact manifolds) that computes everything in an effectively infinite 4D-Block Mindspace of the Metaverse. Besides recording everything that might happen everywhere in the common future of the Metaverse and all its universes, it also records everything that actually did happen in the sense of becoming physical in the past. This model of reality is an extension the accepted compactification of 10d-superstring theory into a 3D-cubic lattice of Calab-Yau compact manifolds that pervades the 3D space of each universe.
Without going into mathematical we described how the arithmetics of enumerable manifolds (each being distinct from all others) is fundamental to quantum mechanics, which in turn is fundamental to string cosmology. We proposed that from a human perspective, the computations of the manifold are instantaneous based on a holographic universe and by extension a holographic Metaverse as well as the likelihood that each universe manifold-subspace and the entire Metaverse manifold-subspace is quantum-entangled being a Bose-Einstein Condensate (BEC) at absolute zero. This is consistent with the contention of some experts in Computational Theory that the computations are outside of time, but more concrete. From the possibility of instant computations we suggest that Feynman’s Quantum Electrodynamics as well as Cramer’s Transactional Analysis may be realized without invoking particles coming back from the future which leads to the possibility of a single physical-world universe rather than the Many World (MWI) physical-multiverse. However, the MWI multiverse structure for sure exists in the Block Mindspace.
A perhaps more suspect concept novel to this paper is the idea of degrees of completeness based on the total (but limited) number of bits available for computation. This is connected to the idea suggested by Martin Rees that consciousness may result from computations requiring more bits than available in a holographic universe. That is that larger universes require a higher threshold of complexity for consciousness to be possible because the number of available bits is proportional to its surface area. Now some computationalists claim that the infinities of arithmetic computations result in both consciousness and matter. But this seems to invoke an infinite “information space”.
By introducing the concept of degrees of completeness based on the available number of bits, or equivalently the size of the computation machine (given by the surface area of the universe or Metaverse), we get a seemingly Mind-Body Dualism between matter and consciousness. The Metaverse is large enough to be effectively complete or sufficiently complete to create physical matter (ala Tegmark) but is effectively unconscious because of a very high threshold of complexity for consciousness (consistent with a static Block Space); whereas the bits available in any universe is too small to create matter, but small enough to allow for biological consciousness in cells according to Rees.