Reality, causation, and the great programmer

James Higgo	Universes are related to other universes only by correlation, which is a subjective feature. You may see that your hand moves smoothly from one point to another. In fact, you have viewed a huge number of unrelated universes in such a way that they appear related. It so happens that there is a universe in which you hand is at point a, and another in which your hand is at point a+1, and those universes appear to be related. But they are not. In an infinite multiverse universes which appear to have any relation you like do in fact exist. We appear to exist in those sets of universes which can be strung together so that the laws of physics appear to emerge (weak anthropic principle, my dear friend).
Bruno Marchal	I totally agree with what you are saying here, with some nuances. Replace Universe with Computational (and consistent) histories, etc. I will not try to be more precise at this stage. Even in the restricted interpretation of MWI these nuances exist.
James Higgo	I'm thinking of Tegmark's and Schmidhuber's ideas that complexity is only apparent when you see a subset of the simple reality, like the Mandelbrot set. This ties in nicely with the Buddhist idea that it is only our ignorance that allows us to see the world at all. Once you see the whole - like the Mandelbrot equation - you no longer see the one little piece of the set that you once thought so interesting and complex. It seems that everything has no meaning unless you view it from the very narrow subjective perspective that we have. If you take the Arcimedian perspective, then you can say nothing but 'everything is'. Resolution of separate phenomena can only occur as we occlude our vision. Before you can talk about anything, you have to define our level of ignorance. Or perhaps defining our level of ignorance is the only way to define anything.
Bruno Marchal	This is a very nice idea. In fact theoretical computer science is partially based on this principle. There exists also a lot of illustration of that idea in mathematical logic. For example with Skolem paradox.
James Higgo	Note that, although I can't see why our consciousnesses are not 'immortal' under MWI, that doesn't mean that I think we exist as separate entities undergoing successive experiences in time. And it doesn't mean I think it's good or desirable to be immortal.
Bruno Marchal	I am glad you are aware of that. Sometime I hope comp is false. Immortality, once you understand where it comes from with comp and/or MWI, is not necessarily a good news. The old materialist notion of death (eternal peace, nothingness) looks like wishful thinking now. The fact that you don't necessarily think we exist as separate entities undergoing successive experiences in time can be made more precise: 1) from the 3d person point of view, we are not separate entities undergoing successive experiences in time. 2) ... but we (at least most of us) feel that we live as separate entities undergoing successive experiences in time : and that should be explained.
James Higgo	The great program (Juergen, please correct me) looks something like LET A=A+1 GOTO START. Any ideas on how a program runs when you don't have a flow of time, but a static block universe?
Bruno Marchal	... the same as newtonian time "occurs" in the static relativity space-time. From the 3-person Archimedian point of view there is no running program. Your remark about the "moving hand" applies here as well ... Your "LET A=A+1 GOTO START" is correct but rather trivial (and unpedagogical) as a UD. You could have chosen the empty program as well. I suggest you write a real UD :). That is : you choose a universal machine, and you write an explicit generator of all the possible execution of your universal machines. (= about 10 lines in PROLOG, 100 lines in LISP, 1000 lines in FORTRAN). If you are courageous, you can write a dovetailer on the solutions of the Dewitt-Wheeler equations ! Note that a UD is (recursively) equivalent to a program which almost compute OMEGA Chaitin number.
James Higgo	One point of disagreement with Juergen: you don't need infinite strings of great programmers. There need be no great programmer, just the program. And since there's no programmer to make it complicated, the program is as simple as it can be.
Bruno Marchal	I guess Schmidhuber shouldn’t anthropomorphise UD. The great programmer (Schmidhuber recognize that explicitely) is a program. Its execution generates all possible (with Church's Thesis) possible UDs. Once you admit a minimal amount of arithmetical platonism, you inherit all the UDs, independently of your using or not using them.
James Higgo	Many thanks for this detailed and wide-ranging post. I am flabbergasted that anyone could read my "Universes are related to other universes only by correlation, which is a subjective feature...." post and agree with it. I thought it was pretty radical. I think I'll pass on the program-writing. I can't see why you need anything more than "LET A=A+1 GOTO START" to generate the universe. But if I did take up programming again I'd be sure to have a look at PROLOG. I've only ever really used Z80A machine code, BASIC and FORTRAN.
John H. Mazetier, Jr.	OK, lets go with MWI. As I have admitted, I can as yet claim too little knowledge about the full scope of the proposal. So, one response will likely be, go read the book, dummy! Until then, I still have a few questions. To avoid proposing a silly putty universe (or multiverse), where things are whatever you make them, can we be clear about what kind of regularities shall obtain? Lets start here: If I scan this at all, it is saying that structure/regularity is in the eye of the beholder ("relative to a subject"). In order support this, are you presuming the existence of some version of cosmic consciousness via MWI? Pace Berkelely's God always watching the tree in the quad?
James Higgo	No, the structure and regularity do not somehow come into existence by virtue of there being a beholder, as the good Bishop argued. The regularity is there all along. But it is like looking at a grid, e.g.: 000000000000000000000 000000000000000000000 000000000000000000000 000000000000000000000 000000000000000000000 000000000000000000000 … and saying "Gosh! I can see a diagonal line of four 0's." (highlighted below): 00000000000000000000 00000000000000000000 00000000000000000000 00000000000000000000 000000000000000000000 000000000000000000000 That diagonal line is there but someone must take the trouble to define a diagonal line, find it interesting, and comment on it. From a perspective outside the grid, that is a fatuous enterprise. Because MWI contains everything, all possible relationships exist, so to single out some for special comment is arbitrary from the Archimedian perspective. It can only be done by someone inside the grid, who will, by virtue of his limited field of vision, find some proximate things more interesting than others. In MWI you could perhaps view one grid as one universe, and imagine that each locus is mapped to another in a grid above it, which is what we would (from our subjective viewpoint) call one Planck-time later. In fact, in MWI, each locus is mapped to an arbitrary number of locuses one Planck-time away from it, so one grid maps on to infinitely many grids just one step (Planck time) away. If you choose to see a certain set of relationships as representing a time axis, and others as being space, you can view the whole from the outside in such a way that you can see ass sorts of weird and wonderful things, like you or I. This is similar, as Tegmark has pointed out, to zooming in on a fractal picture and saying 'wow! look what's in there!'
James Higgo	I have ccd Juergen Schmidhuber's recent post to Vic Stenger, who I have failed to move even slightly towards this view, which he regards as bordering on solipsism (Hi, Vic, hope Japan doesn't sink into the sea as our economic data indicate). One point of disagreement with Juergen: you don't need infinite strings of great programmers. There need be no great programmer, just the program. And since there's no programmer to make it complicated, the program is as simple as it can be.
Doug Jones	While it's true that you don't NEED infinite chains of Great Programmers, they happen anyway. Since all possible worlds exist, then all possible programmers exist, and all possible (finite) programs will eventually be written by them given sufficient time. And they don't necessarily have to be great programmers. Obviously, the vast majority of the infinite collection of programs that are written within these infinite worlds will be buggy, ill-behaved, or even ill advised, resulting in many worlds containing no self-aware-substructures at all, or perhaps even lawyers and politicians. But an infinite number of them will give rise to things like chocolate and love, and even more programmers capable of great programs. (Actually, I just thought of a Great Program, but alas the margins of this message are too small to contain it.) Of course, even the greatest of these great programs may not be fully appreciated by their authors, who generally only have time to observe a very small portion of their output bitstrings. How many times throughout the multiverse has a careless slip of the hand sent a blast of particularly strong caffeinated beverage (or a particularly hot cup of tea) cascading into the mechanism, prematurely terminating one of the greatest of all Great Programs? Fortunately for us, there are lots of worlds where the program doesn't get aborted. For any given Great Program, there ought to be a very large number of worlds wherein that particular program is written, and in some of them that program may have the opportunity to run long enough to give rise to beautifully complex worlds, which give rise to even more programmers writing more programs that define even more worlds, and on and on, until someone writes that original program again. And of course it doesn't stop there (and it definitely doesn't start there either). So for any given world, there are a large number of programmers in a large collection of worlds who can justifiably take credit for writing it, and also no credit at all, since there is also a large collection of worlds containing mindless automatons busily enumerating all possible programs. Seems to me there may be somewhere in all this a proof of the existence or non-existence of God, depending on which God Model one subscribes to (if any). Perhaps a proof of the existence of the immortal soul can be glimpsed. Of course, all this is impossible. But then, I long ago reconciled myself to the notion of living in a world of measure zero.
James Higgo	The 'great programmer' could have the intelligence and consciousness of an amoeba. And why bother talking about him if he's not needed - Ockam would not approve.
Doug Jones	Ah, getting rigorous, eh? That's okay, I don't mind. I have no problem with the notion of there being no "THE" great programmer. This is one of the points Jürgen makes in his paper, that there isn't just one; any of us can imagine numerous ways of enumerating all possible finite programs, and can also imagine a variety of abstract computational systems to "run" such programs on, so we can all be the same "great programmer", potentially at least. (One could argue that if we only imagine programs that we will never possess hardware capable of running, we shouldn't be labelled "programmers", but let's not get personal.) Of course, we don't really have to refer to such ideas as "great programmer", but nonetheless, if you accept Jürgen's starting assumptions and his arguments, his paper concludes that such programmers exist, so is it really necessary that we avoid talking about them? After all, the paper is about Life, the Universe, and EVERYTHING. We have all seen examples of papers (or letters or statements to the lay press or whatever) that refer to The Great Programmer or to God or some such concept, written by serious people who are perfectly aware that such concepts may be unnecessary to the essential ideas in the work, and who are quite possibly atheists anyway. There are lots of reasons why people do this. Probably some people do it because a work that refers to universes that don't require a God will immediately turn off certain readers who might have something to gain from reading such a work (a defensive strategy). Perhaps some people do it because they have deeply held beliefs of their own, and are as yet uncertain how these beliefs tie in with the results of their research. I think some people do it because anthropomorphizing can make a paper less abstract and impersonal, and more accessible to a wider audience. And for many, I think it's just an In Joke. (Why Jürgen did it, I cannot say, I don't know what he believes.) When I read such things, I take it as an In Joke, and enjoy the humor. I have no difficulty mentally stripping the anthropomorphization out, to get at the meat of the paper. Some people may not find such humor to their taste, and they are welcome to write with utter rigor (somebody's got to do it). But I think it's important that somebody writes with humor too. One thing I have noticed lately is that a number of rather high concepts are starting to get exposure in non-specialist publications (and on the Web.) More and more, the educated lay public is being exposed to things like Many-Worlds and Fisher information and all manner of bizarre quantum mechanical stuff. Some of these ideas don't fit well with many traditional beliefs, so there is a frightening aspect to all this. The fact that nobody can really prove much of anything ("these are all just 'theories'") is comforting to some, but the more serious people get about Theories of Everything and such, the more important it becomes that people hang on to their sense of humor. So Jürgen did provide a service by writing his paper that way, in some sense. But whether people anthropomorphize or not doesn't necessarily affect the underlying ideas in their work, and I don't mind either way. Personally, I enjoyed Jürgen's paper immensely. Whether it has anything to do with the world we actually live in, I cannot say, but to this casual observer it vaguely looks like it (or something like it) might be another elegant, simple, parsimonious piece of that big Puzzle we're all wondering about. As to whether Ockham would approve, I have no idea, I suspect he might be as confused as I am. James Higgo wrote: The great program (Juergen, please correct me) looks something like LET A=A+1 GOTO START. Any ideas on how a program runs when you don't have a flow of time, but a static block universe? Doug replies: If there is no flow of time, then there's no present tense, and phrases like "how a program runs" have no meaning to me... ;->
Gilles Henri	I have much more objections in fact to models like Schmidhuber's one: again what are these Turing machines, Big programmer and so on made of?
Juergen Schmidhuber	This does not seem essential and is therefore left unspecified. You can try to make one of the stuff you find in your own universe. Note that many of the Great Programmer's universes indeed feature another Great Programmer who programs another (possibly different) Big Computer to run all possible universes. Obviously there are infinite chains of Great Programmers.
Bruno Marchal	I agree. Ultimately this important point relies on Church's thesis. Below I will give a argument showing there is no stuff at all. Consciousness AND matter are definissable only from within an infinite set of computationnal histories.
Gilles Henri	Who is "interpreting" a string as a Universe?
Juergen Schmidhuber	This may be a somewhat misleading question. It seems based on the assumption that the interpreter is not himself part of a computable world representable by bitstrings. E.g., your internal state changes and email messages and worries about "interpretations" are just part of the computable evolution of a particular universe. It does not matter that we may produce computable outputs claiming otherwise ("it doesn't feel like it"), to be interpreted by other computable interpreters like ourselves. None of us needs to be aware of the bitstring representation.
Bruno Marchal	Indeed. That is equivalent to what I was trying to explain to Gilles and James in a previous post where I insist that only a person can be conscious. But of course (with comp) a person can be embedded in a string. The basic principle is indeed to embed the subject in the object. This idea begin perhaps with Galileo, but has been considerably extended by Everett. Here we generalize it by embedding the computer scientist in the set of all computations.
Gilles Henri	Is it true that in this model every "state" is finite, that is the set of all possible states of all possible universes is countable?
Juergen Schmidhuber	Yes, definitely! Just like sqrt(2) is describable by a finite algorithm. Most real numbers, however, are not describable at all - >they convey infinite information. We cannot even talk about them. No room for them in any of the Great Programmer's universes!
Bruno Marchal	Although most real numbers are not describable at all, we can easily talk about the set of all real numbers. Now, the Great Programmer (my Universal Dovetailer UD) not only dovetails on all computations but dovetails on all computations with all real (complex, quaternionic, ...) oracles. It does so by generating all finite initial segments of all reals. At each state of the computation of the UD, there is indeed no place for a real number, BUT, I show below that from the first person perspective of an "observer", the set of all real number does play an important role. In fact our prediction will depend on the measure on all infinite computationnal histories. More below.
Gilles Henri	Does it mean for example that the possible values of physical constants are discrete?
Juergen Schmidhuber	Discrete or at least computable. In none of the Great Programmer's universes there is Super-Turing computability, although the concept has become fashionable in our particular computable universe, and lots of computable people make computable noises about it.
Bruno Marchal	I am not quite sure about this. Perhaps. I need to think about it. The reason why I doubt here is still the the same result I will try to explain shortly below. I show that computationnalism entails that our local expectations depend on the global set of infinite computations, and this will entail the "observation" of truly random sequence or noise. Well, this happens with QM, and physicist are used to that. The possibility remains that some "physical" constant could also be truly random. I do not find this plausible, but, from a logical point of view, it is not entirely ruled out by comp : it would mean that some special oracle would play a significant role. That would entail that our "apparent universe" is not computable ! If that is true, that would nevertheless remains unprovable ! (Such statement would be a kind of Godelian Sentence).
Gilles Henri	The simplest program just enumerates all integer numbers. If you can tell me which integer describes the existence of consciousness or to the existence of anything like an electron or whatever you want, I would be very grateful to you!
Juergen Schmidhuber	To comment on this in the spirit above, I took a paragraph from my little paper and replaced every occurrence of "life" by "consciousness": What is consciousness? The answer depends on the observer. For instance, certain substrings of E_k may be interpretable as the evolving consciousness of a living thing L_k in U_k. Different observers will have different views though. What's consciousness to one observer will be noise to another. In particular, if the observer is not like the Great Programmer but also inhabits U_k, then its own consciousness may be representable by a similar substring. Assuming that recognition implies relating observations to previous knowledge, both L_k's and the observer's consciousness will have to share mutual algorithmic information: there will be a comparatively short algorithm computing L_k's from the observer's consciousness, and vice versa.
Bruno Marchal	What do you mean by "an observer inhabits U_k" ? Of course, for a physicalist inclined philosopher, such an expression seem to have an obvious meaning. But I believe such an expression has no (non-ambiguous) meaning once we take seriously the comp hypothesis. An observer cannot so easily be said inhabiting a precise U_k. The observer cannot be localized in a unique computation. He can only be associate with an infinity of "sufficiently similar" computations (which all belong to UD* : the complete work of the UD). This entails a rather big localisation-indeterminism. More below.
Bruno Marchal	...I will be very short. Nevertheless, about Schmidhuber, although there is some superficial resemblance with my thesis, I realise Schmidhuber has an inconsistant understanding of the computationnalist hypothesis. More on this later....
Juergen Schmidhuber	Did I miss a follow-up message? I guess I haven't seen any subsequent explanation of Bruno's claim.
Bruno Marchal	(1) First, when I say, Juergen, that you have an inconsistant understanding of comp, I say it with all my respect and even my friendship for someone who, like me, seem to believe that indeed comp could perhaps be the simplest explanation for "everything". Now, I do think that you (like Tegmark, but also Everett) are missing a key point. In particular, although I agree with almost your whole paper, I completely disagree with your philosophical conclusion. Like Hal Finney (see the very beginning of this discussion list), I belief you are "throwing the baby with the bathwater" when you told us that "... adopting the great Programmer's point of view, classic problems of philosophy go away". On the contrary, I believe that, with comp, we are just beginning to make it possible to build clearer formulations of these classic problems. For example, my thesis, http://iridia.ulb.ac.be/marchal/, consists in a reformulation of the classic Mind-Body problem in the frame of comp (along with some light on the qualitative aspects of the solution). (2) You did miss follow-up messages. In fact almost everybody in the list "miss" them. That is because some people send me private mail with more technical questions, and I have answer them privately (thinking it would have been indecent to explain my thesis in the discussion list). But now I guess it was key questions which bear on "your missing point". So I make my answer public. Bruno Marchal: UD, the Universal Dovetailer, is equivalent to your Great Programmer. UD is a finite program. UD* is the infinite extension of the UD. The question most people ask me was "Bruno, you say "you can only associate mind with the whole UD." - I'm not sure why." Here is a short answer. Take your time to read it, and please tell me if you disagree at some point. It is necessary to concentrate ourself on the following thought experiments (PE, PE1, PE2, PE3, PE4, PE-omega). The "practitionners" of computationnalism can use classical teletransport as a mean to move from one place A to another place B. This mean he is "read" at A, send (by wave radio, for example) at B, annihilated at A, and reconstituted at B. Let us call that experience : the primitive experience or simply the PE. Let us look first at two independent changes of the PE. PE1 : if, knowing it or without knowing it, the reconstitution is time-delayed at B, this doesn't change anything from his first-person point of view. In particular if he is certain to get B with PE, he must be certain to get B, in PE1. (The delay is supposed to be finite). PE2 : if he is told he will be reconstituted at B and B', his first-person future is undetermined. The domain of undeterminism is {B, B'}. Of course, from a third person point of view, everything is determined. Do you agree until here ? Now, consider the following experience PE3 which mixed PE1 and PE2. He is told that he will be reconstituted at B and at B' (like PE2), but a time-delay of reconstitution is introduced at B (like PE1). Now, if you agree with what I say about PE1 and PE2, you should agree with : IF he quantifies the indeterminism on {B, B'} in some way for PE2, THEN he must give the same quantification for the indeterminism on {B, B'} with PE3. For example, if he quantifies {B, B'} with a uniform probability distribution with PE2, he must quantify {B, B'} with a uniform probability distribution with PE3. To sum up, the delay doesn't change his expectation. This follows from comp (think on the first-person communication by the average robot instead of you, for example). The average robot = the normal (gaussian) robot when these duplication experiences are iterated. I guess you will also accept that nothing will change, in neither PE nor PE1 nor PE2, nor PE3, if at B (for exemple) he is reconstituted in a perfect virtual environment (which could exist by COMP). This is PE4. If you agree, you are ready for "PE-omega", which is just the infinite running of the UD. Suppose that you are in some state of mind s, captured at some digital level by a computationnal state S (which exist by COMP, and there is no restriction on the level other than permitting digitalisable capture). Now suppose the UD is running, and that it never ends (accidentally). Then you will be virtually reconstituted, in the state S, an infinite number of times in the all UD. From the conclusion of PE to to PE4, it follows that you must quantify the undeterminism (relatively to S) on the infinite set of reconstitutions, which is an infinite set which is include in the whole UD. This implies a very big form of indeterminism (the UD-indeterminism). Because your mind (consciousness) includes your immediate expectations, your effective mind is really defined by the whole UD, which has a (platonist) arithmetical reality. With Church's thesis, and the compiler theorem, the whole UD is embedded in Arithmetical Truth (or in the standart model of Peano Arithmetic as the logician like to put it). This (platonist) arithmetical reality should convince any "occamist" (like you or like James Higgo) that the "concrete running" of the UD is not necessary. (In my thesis I am much more cautious about that point). Of course the mind body problem is not solved here, as I said above, we 've got just a beginning of a formulation of the problem in the computationnalist framework. With comp the mind aspect is not so difficult. It admits even a positivist account as the study of the limit discourses of (self referentially sound) machines, but we 've got a real matter problem : we must explain our determinist belief from the a priori very big UD*-indeterminism. If I put it in some poetical way, we must extract our physical beliefs from all our possible (computationnal) dreams. Note also that a comp solution of the mind-body problem would provide a solution to the "other mind" problem (as philosopher of mind put it). This will provide a kind of computationnalist vaccine against solipsism. The high non triviality of computer science and of the logic of provability(°) suggest ways toward solutions as I illustrate in the chapter 5 of my thesis http://iridia.ulb.ac.be/marchal (°) A classical treatise on godelian provability logic is "THE LOGIC OF PROVABILITY" by Georges Boolos, 1993, Cambridge University Press. (It is a revised and considerably extended version of his classic book "THE UNPROVABILITY OF CONSISTENCY" 1979, Cambridge University Press). There is also a recreative introduction to this provability logic by Raymond Smullyan : FOREVER UNDECIDED. 1987, Knopf, New York. A graduate text is the book by Smorinsky 'Modal logic and Self-Reference", 1985, Springer-Verlag, New York.