Re: Possible Worlds, Logic, and MWI
Continuing with my last post... On Fri, Jan 10, 2003 at 08:54:38PM -0800, Tim May wrote: > Why would there be any reason to try to maximize the utility of this > "big picture"? > > For those of us who don't even strive for "the greatest good for the > greatest number" in a single-branch universe, why would striving for > more good (whatever "good" is) in 10^300+ branches be interesting or > important? Consider a thought experiment where you've been uploaded into a multi-tasking computer and there are 100 copies of you running in parallel in separate virtual environments. Would you prefer that all 100 copies of you experience the exact same things, or that they experience different things? I think running the same computation 100 times is pointless, so I'd prefer the latter. This seems to be essentially analogous to prefering variety across branches in MWI. Even if you disagree personally with these choices, do you have any reason to think that they are irrational, rather than just different? If they're not irrational, then decision theory has to be able to handle them, and that has interesting consequences. > In any case, if MWI is correct, then there is every type of universe > imaginable, consistent only with the laws of physics and math, and > every decision for the good or the bad or whatever has been made > countless times in countless ways. By any calculus of the multiverse, > the sheaf of universes in which Tim May or Hal Finney even exist is of > measure approaching zero. > > Meanwhile, I'm _here_. I'm not sure what your point is here. You may be saying that the multiverse is so big, and the part of it that we can affect is so small, that if you try to optimize the "big picture" the difference you can make is almost undetectable on a human scale. If so, I agree -- it's a very alien way of thinking, but that doesn't mean it's wrong.
Re: Possible Worlds, Logic, and MWI
On Fri, Jan 10, 2003 at 08:54:38PM -0800, Tim May wrote: > But in this, the only universe I will ever, ever have contact with, I > optimize as best I can. And I assume all the myriad mes are doing the > same in their universes, forever disconnected from mine. You're taking the question too personally. The issue here is whether rationality only involves local optimization within the branch that one is in without regard to other branches, or whether one can also take into account what one believes to be happening in other branches. You yourself may be a local optimizer, but the larger question is whether rationality allows global optimization or not. Notice that the latter is more general than the former, because all local optimizers can be modeled as global optimizers with a special form of utility function. My point is that since there doesn't seem to be a reason to disallow global optimization, it shouldn't be ruled out. I'm interested in a decision theory that allows global optimization and want to know its practical and philosophical consequences. On the question of QS, I think all QS'ers can also be modeled as global optimizers with a special form of utility function. From this perspective, the disagreement between QS'ers and local optimizers like Tim can be seen as a difference of opinion on what kind of utility function one should have. (Personally I'm not convinced by either side and I'm not sure how to answer the question myself.) Do you find this perspective useful?
R: Possible Worlds, Logic, and MWI
Tim May: > (Again, I currently have no pet theory of what Reality is. But I'm > happy to be building a base of tools to be able to more intelligently > comment later. Having a pet theory is not so important.) The best definition, imo, is: "Reality is that which, when you stop believing in it, does not go away." - Phillip K Dick, in an essay (1978) titled "How to Build a Universe that Doesn't Fall Apart Two Days Later." A Canadian coed asked him (1972) to define reality for a philosophy class she was taking. Leibniz also wrote: "although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough if, using reason well, we were never deceived by it." > * Borges. I mentioned him because of his seminal "Garden of Forking > Paths" story. He was not the first to write about alternate > histories...I'm not sure who wrote the first recognizable story in this > genre. Probably as old a concept as any. Somebody thinks that J.L. Borges was an Everettista :-) http://www.lehman.cuny.edu/ciberletras/v1n1/crit_06.htm http://www-personal.umich.edu/~rojoa/ The Aquinas and Wyclif (and also Ockam!) wrote about the possibility of many universes, created by God. Sometimes I feel there is something good with MWI and there is something wrong with orthodox QM Consider a diaphragm, with two slits, slit 1 and slit 2. Each of these slits can be opened, or closed, by a shutter connected with a separate counter. A weak alpha-particle emitter is placed between the two counters. Imagine that, in the beginning of the gedanken experiment, both slits are closed. If an alpha-particle strikes one of the counters, the slit connected with this counter is opened, and the counters cease to operate, and a light-source is turned on, in front of the diaphragm, and this light-source illuminate a photographic plate placed behind the diaphragm. Following qm rules, we can write psi = 1/sqrt2 (psi_1 + psi_2) where psi_1 is the wavefunction describing the system when the slit 1 is open (psi_2 when the slit 2 is open). Thus, from the theory, we'll get the usual interference pattern, on the photographic plate behind the diaphragm. But if we keep our eyes opened, and we observe which slit is open (slit 1, or slit 2) then, in accordance with the complementarity principle and the projection postulate, a reduction takes place, and no interference pattern *should* appear on the plate. [L. Janossy, K. Nagy, Annalen der Physik, 17, 115-121, (1956)] s. - Gottfried Wilhelm Leibniz [The Monadology, 64-66]
Re: Possible Worlds, Logic, and MWI
Interleaving... POINT 1 For example, "truth" is defined in formal logic with respect to, again, formal models with an infinite number of formal symbols in them. It is not defined with respect to some vague "correspondence" with external reality. Actually, science is just about such correspondences with external reality. I haven't argued that logic alone is a substitute for science, measurement, experimentation, refutation, correction, adjustment, model-building All I was saying is that the semantics that define the meaning with respect to each other of symbols and symbol-relationships is formal and, within each given well-formed framework, inarguable. whereas the semantics of the mapping of formal models to their "supposed" subject is not, itself, formal (yet anyway), and hence is suspect as to whether we understand it or get it right all the time. With science, all we have is: "this formal symbol system (theory) A seems to correspond better to our current observations than any competing formal symbol system (theory) B (that we've conceived of so far), so we'll consider A (as a whole) to be TRUE i.e. "the best observation-corresponding theory" (for now.) This scientific process works pretty well but is somehow loosy-goosy and unsatisfying. Do theories which replace other older, now discredited theories, keep getting better and better? Probably yes. But what is the limit of that? Is there one? Or a limit in each domain about which we theorize? But hold on, most of the scientific revolutions tell us that we had a nice theory, but were theorizing about a badly-scoped, badly conceptualized idea of what the "domain" was. A better theory is usually a better set of formal, interacting concepts which map to a slightly (or greatly) differently defined and scoped external domain than the last theory mapped to. None of this is very straightforward at all. For example, would you go out on a limb and say that Einstein's theories are the "best" (and only "true") way of modelling the aspects of physics he was concerned with? If so, would you be equally confident that his theories cover "essentially all the important issues" in that domain? Or might someone else, someday, re-conceptualize a similar but not 100% overlapping domain, and create an even more explanatory theory of fundamental physics than he came up with? Can we ever say for sure, until that either happens or doesn't? You can interpret the history of science in two ways: either we were just really bad at it back then (in Newton's day) and wouldn't make those kind of mistakes in our theory formation today, or you can say, no we're about as good at it as always, maybe a little more refined in method but not much, and we'll continue to get fundamental scientific revolutions even in areas we see as sacrosanct theory today. And the new theory will not so much "disprove" the existing one (as Einstein didn't really "disprove" Newton) but rather will be just relegating the old theory to be an approximate description of a partially occluded view of reality. And then one day, will the same thing happen again to that new theory? Is there an endpoint? What would the definition of that endpoint be? (SILLY) POINT 2 As far as I know, there is no good formulation of a formal connection between a formal system and ""reality" <-unbalanced quotes, the secret cause of asymmetry in the universe. How's that for a "quining" paragraph? I don't understand your "secret cause of asymmetry in the universe" point. We understand some things about symmetry breaking in particle physics theories, via gauge theories and the like. If you want more than this, you'll have to expand on what you mean here. It is a Koan (kind of). A self-referential, absurd example of a notion that an imbalance in a formal symbol system (the words I'm using, and the quotes) could possibly be the cause of asymmetry in the physical universe. It is an attempt to highlight the problems we get into when we confuse the properties of a model with the properties of the thing we are TRYING to model with it. "Quining" is the use of self-reference in sentences, often to achieve paradox. It is a childish ploy. e.g. of a Quine: "Is not a sentence" is not a sentence.
Re: Possible Worlds, Logic, and MWI
On Saturday, January 11, 2003, at 01:39 AM, Eric Hawthorne wrote: This strict "anonymous symbols" interpretation is how one must treat formal logic and propositions expressed in formal logic too. Every time I read someone bemoaning how logic has difficulty with expressing "what is going to happen in future", I think, why would you expect a formal system of symbols to have anything to do with future time in reality? There are excellent reasons to expect a formal system of symbols to correctly predict future time in reality: the operation of machines, chips, programs. Of enormous complexity, iterating for trillions of steps in time, the outcomes are consistent and predictable. As for someone "bemoaning how logic...future," temporal logic is an active research area. Arthur Prior has written much about the logic of time. Modal logic is essentially about this kind of reasoning. Pace the point below about comets hitting planets, a formal symbol system is not going to predict something dependent on events we cannot see (yet) or model (yet). It would be unreasonable to expect a logic of time to somehow predict events from outside our "knowledge cone" (like a light cone, but for knowledge). As far as I know, there is no good formulation of a formal connection between a formal system and ""reality" <-unbalanced quotes, the secret cause of asymmetry in the universe. How's that for a "quining" paragraph? We analyze Reality in bits and pieces, in facets. We analyze planetary motions, and now we have logical symbol models which are enormously accurate and far-reaching in time. Granted, models of future planetary positions cannot predict events outside the model, such as collisions with comets not yet charted, and so on. But this is not a plausible goal of any model. I don't understand your "secret cause of asymmetry in the universe" point. We understand some things about symmetry breaking in particle physics theories, via gauge theories and the like. If you want more than this, you'll have to expand on what you mean here. Is there? For example, "truth" is defined in formal logic with respect to, again, formal models with an infinite number of formal symbols in them. It is not defined with respect to some vague "correspondence" with external reality. Actually, science is just about such correspondences with external reality. I haven't argued that logic alone is a substitute for science, measurement, experimentation, refutation, correction, adjustment, model-building. Someone was writing about "correspondence theory" with this goal in mind many years back, and that sounded interesting. I haven't read Tegemark et al. What do they say about the formalities of how mathematics extends to correspond to, or to be? external reality? To me, there is still a huge disconnect there. Again, I don't understand what you mean by "there is still a huge disconnect there." If you are refuting Tegmark, you should read his articles first. If you are saying that much still needs to be done, this is of course true, fortunately. --Tim May
Re: Possible Worlds, Logic, and MWI
Re: possible worlds in logic. Logic (and its possible worlds semantics) says nothing (precise) about external reality. Logic only says something about the relationship of symbols in a formal language. Remember that the reason non-sloppy mathematicians use non-meaningful variable-names (i.e. terms) is to avoid names that connote something in the world and would lead one astray in understanding the precise "formal" semantics of the mathematical formulae. e.g. of problematic meaningful variable names: one = 2. two = 2. four = 4. therefore, one + two = four. This strict "anonymous symbols" interpretation is how one must treat formal logic and propositions expressed in formal logic too. Every time I read someone bemoaning how logic has difficulty with expressing "what is going to happen in future", I think, why would you expect a formal system of symbols to have anything to do with future time in reality? As far as I know, there is no good formulation of a formal connection between a formal system and ""reality" <-unbalanced quotes, the secret cause of asymmetry in the universe. How's that for a "quining" paragraph? Is there? For example, "truth" is defined in formal logic with respect to, again, formal models with an infinite number of formal symbols in them. It is not defined with respect to some vague "correspondence" with external reality. Someone was writing about "correspondence theory" with this goal in mind many years back, and that sounded interesting. I haven't read Tegemark et al. What do they say about the formalities of how mathematics extends to correspond to, or to be? external reality? To me, there is still a huge disconnect there. E.g. again, Godel's incompleteness theorem is a theorem about the properties and limitations of formal symbolic systems. The original theorem says nothing whatsoever about reality itself, whatever that may "informally" be, nor about the limitations of human minds, unless we take minds to be theorem provers working on formal symbolic systems.
Re: Possible Worlds, Logic, and MWI
On Friday, January 10, 2003, at 08:54 PM, Tim May wrote: Wei suggested that in the context of a many-worlds universe (not just the quantum MWI but even for a broader set of possibilities), you might not make this same decision. You know that when the coin flips, the universe is going to effectively branch and both possibilities are going to be actualized. Let us suppose that in addition to slightly preferring apples to oranges, you have a strong value preference for diversity. You like variety and you dislike having everything the same everywhere. In that case, you might rationally choose to receive an apple on heads but an orange on tails. While this slightly reduces your average pleasure level in terms of tasting the fruit, this could be more than compensated by your increased pleasure at knowing that you are enjoying diverse experiences in the two worlds. To add something to my last comment, there is a huge difference between these two situations: 1. Alice believes in the MWI, whether it is true or not. 2. The MWI is true, whether Alice believes in it or not. I fully accept that Situation 1, where Alice believes in the MWI, can and likely will alter her choices. She may alter her risk assessment model, she may change what she believes about religion, and so on. I think, Hal, that in your language above you are confusing the issue of Alice's faith in MWI with the actual reality or nonreality of MWI. Your comments about "You know that when the coin flips" and "knowing that you are enjoying diverse experiences in the two worlds" are not statements about what is actually happening but, importantly, about what Alice _believes_ will happen. This is paralleled in religion: "Alice knows that when she prays to Baal, he listens and smites her enemies. She knows that Baal has prepared a place for her in his party room in the afterlife. She knows that dying young for Baal will only take her to Baal that much sooner. She awakens every day with hope and expectation." No doubt that belief alters behavior. But it doesn't make either the existence of MWI or Baal any more real. (Understand of course that I am not putting belief in MWI on the same level as belief in YHWH or Allah or Baal or Yog-Sotteth. But we must be careful in using language like "You know that your choice does such and such.") --Tim May
Re: Possible Worlds, Logic, and MWI
On Friday, January 10, 2003, at 05:21 PM, Hal Finney wrote: Conventional decision theory is designed to handle exactly this sort of situation. According to those principles, you would act to maximize your expected utility. Since you get more utility from an apple than from an orange, and the coin flip has a 50-50 chance of coming up heads or tails, your expected utility is maximized by specifying that you will get an apple whether the coin falls heads or tails. This is very obvious even without being expressed in the mathematical form that decision theory uses. Wei suggested that in the context of a many-worlds universe (not just the quantum MWI but even for a broader set of possibilities), you might not make this same decision. You know that when the coin flips, the universe is going to effectively branch and both possibilities are going to be actualized. Let us suppose that in addition to slightly preferring apples to oranges, you have a strong value preference for diversity. You like variety and you dislike having everything the same everywhere. In that case, you might rationally choose to receive an apple on heads but an orange on tails. While this slightly reduces your average pleasure level in terms of tasting the fruit, this could be more than compensated by your increased pleasure at knowing that you are enjoying diverse experiences in the two worlds. Accepting that I believe in the MWI (_really_ believe, not just believe in the formalism), I already know that all possible decisions, all diverse forks, are already unfolding in the multitude of forking paths. Even if I "decide" not to alter my rational choice for the fruit, there are countless other mes making every other possible choice, including 10^50 or more mes who wire up the coin toss to explode an H-bomb "just to make things interesting in that sheaf of branches." (The awkward word "mes" is the plural of "me." ) But in this, the only universe I will ever, ever have contact with, I optimize as best I can. And I assume all the myriad mes are doing the same in their universes, forever disconnected from mine. Someone here on this list asked me in private mail if I didn't take some amount of comfort from the MWI, knowing that versions of me were surviving and thriving in other branches regardless of what happened to me in this branch. No, I told him, while there may "be" other such paths (and I can argue there already are, via modal logic, without any quantum mechanics involved), these other paths are unreachable to me and may as well not exist at all. Nor do I find despair in the notion that there may be (_are_, if MWI is right) other universes in which I am a mass murder, in which I killed myself 12 years ago, in which the Earth was hit by a comet two centuries ago, in which a plague will be released next year and will wipe out all humans. Until some evidence of cross-path communication or travel or interaction is found, the MWI gives the expected result, that I am in this world and no others, for all intents and purposes. By the way, I don't dispute at all that having a belief in MWI might very well cause behavior changes, even the change you and Wei have given as an example. Besides this change, of picking a less desirable fruit in your example so as to "increase diversity," I can imagine that some people who strongly believe in MWI may take _fewer_ risks (to maximize the number of their surviving dopplegangers in other branches), may take _more_ risks, may do things of various kinds which they think will somehow influence or be influenced by the reality of MWI. But the same may be said of beliefs of all sorts, including beliefs in an afterlife (fewer risks, more risks, fatalism, etc.), beliefs in cryonics, beliefs in the I Ching or magic, and so on. Most religious people behave quite a bit differently than I do. The Muslims who believe their martyrdom will bring them infinite reward in an afterlife are but the most obvious examples of how belief alters behavior. A strong belief in the MWI, at a basic level, would probably be sufficiently strong to alter psychological states in various ways. The hard part is finding any real rational argument for what those alterations might be. As it now stands, I will not be standing in front of any machine guns to test the MWI, nor will I be choosing different stocks to invest in so as to support "multidiversity." For all intents and purposes, this is the world I am in. I'll be interested to see if any more compelling examples can be produced. A brief comment: So here is an example where belief in multiple worlds could lead a rational person to behave differently than belief in a single world. For this effect to occur, I think our preferences in the many-worlds case have to depend on relations between the worlds, rather than independently on conditions in each world. We're not just acting to maximize the expected outcome in each world aver
Re: Possible Worlds, Logic, and MWI
With regard to the question of the significance or impact of the MWI, this is where Wei Dai's emphasis on the importance of decision theory comes in. The question is, are there things we would rationally do differently if we knew that all possible worlds existed, things that would be irrational in a single universe? In a single-world model we have uncertainty about the world we live in, its past, present and future. This can be captured by a probability distribution over possible worlds. We then use that probability distribution to make our decisions. But in a many-worlds model, we also have a probability distribution over possible worlds, and we would also use that probability distribution to make decisions. Given this similarity, are there cases where we would rationally decide differently in the many-worlds universe than in the single-world universe? Wei explored some possibilities along these lines in his postings in mid 2002. One such situation could be demonstrated with a simple thought experiment. Suppose you are going to flip a coin, and you will be given a piece of fruit as a result, either an apple or an orange. Also suppose that beforehand you can decide which kind of fruit you will be given for each of the two possible coin flip outcomes: for example, you could receive an orange on heads and an apple on tails, or any of the other three possibilities. Let us also suppose that you like both fruits but slightly prefer apples to oranges. Conventional decision theory is designed to handle exactly this sort of situation. According to those principles, you would act to maximize your expected utility. Since you get more utility from an apple than from an orange, and the coin flip has a 50-50 chance of coming up heads or tails, your expected utility is maximized by specifying that you will get an apple whether the coin falls heads or tails. This is very obvious even without being expressed in the mathematical form that decision theory uses. Wei suggested that in the context of a many-worlds universe (not just the quantum MWI but even for a broader set of possibilities), you might not make this same decision. You know that when the coin flips, the universe is going to effectively branch and both possibilities are going to be actualized. Let us suppose that in addition to slightly preferring apples to oranges, you have a strong value preference for diversity. You like variety and you dislike having everything the same everywhere. In that case, you might rationally choose to receive an apple on heads but an orange on tails. While this slightly reduces your average pleasure level in terms of tasting the fruit, this could be more than compensated by your increased pleasure at knowing that you are enjoying diverse experiences in the two worlds. So here is an example where belief in multiple worlds could lead a rational person to behave differently than belief in a single world. For this effect to occur, I think our preferences in the many-worlds case have to depend on relations between the worlds, rather than independently on conditions in each world. We're not just acting to maximize the expected outcome in each world averaged across all of them, we're acting to maximize the utility of the "big picture", the entire set of worlds affected by our acts, considered as a whole. To the extent that a whole is more than the sum of its parts, actions in a multiverse model may justifiably be different than in a single universe. Hal Finney
Possible Worlds, Logic, and MWI
On Friday, January 10, 2003, at 12:34 PM, George Levy wrote: This is a reply to Eric Hawthorne and Tim May. (Tim comment: the quoted text below is partly a mix of my comments and partly George's.) Lastly, like most "many worlds" views, the same calculations apply whether one thinks in terms of "actual" other worlds or just as possible worlds in the standard probability way (having nothing to do with quantum mechanics per se). Good point. Or so I believe. I would be interested in any arguments that the quantum view of possible worlds gives any different measures of probability than non-quantum views give. (If there is no movement between such worlds, the quantum possible worlds are identical to the possible worlds of Aristotle, Leibniz, Borges, C.I. Lewis, David Lewis, Stalnaker, Kripke, and others.) Interesting. I don't know how to proceed in this area. I've been meaning to write something up on this for a long time, but have never gotten around to it. I'll try now. FIRST, let me say I am not denigrating the quantum mechanics issue of Many Worlds. I was first exposed to it maybe 30 years ago, not counting science fiction stories about parallel worlds, and even Larry Niven's seminal "All the Myriad Ways," which was quite clearly based on his MWI readings. Also, I am reading several recent books on QM and MWI, including Barrett's excellent "The Quantum Mechanics of Minds and Worlds," 1999, which surveys the leading theories of many worlds (the bare bones theory, DeWitt-Graham, Albert and Loewer's "many minds," Hartle and Gell-Mann's "consistent histories," and so on. Also, Isham's "Lectures on Quantum Theory," and I've just started in on Nielsen and Chuang's "bible of quantum computers" massive book, "Quantum Computation and Quantum Information," from whence I got the funny Hawking quote about him reaching for his gun when Schrodinger's cat gets mentioned. So I am deeply interested in this, more so for various reasons than I was 30 or 20 or 10 years ago. SECOND, my focus is much more on the tools than on any specific theory. I may be one of the few here who doesn't some wild theory of what the universe is! (I'm only partly kidding...we see a lot of people here starting out with "In my theory...universe is strand of beads...embedded...14-dimensional hypertorus...first person awarenesss...causality an illusion...M-branes are inverted..." sorts of theories. Some have compared our current situation to the various and many theories of the atom in the period prior to Bohr's epiphany. Except of course that various theories of the atom in the 1900-1915 period were testable within a few years, with most failing in one spectacular way or another. Today's theories may not be testable for 1000 years, for energy/length reasons. (One hopes some clever tests may be available sooner...) When I say tools I mean mostly mathematics tools. I'm a lot more interested, for instance, in deeply understanding Gleason's Theorem and the Kochen-Specker Theorem (which I do not yet understand at a deep level!) than I am in idly speculating about the significance of QM for consciousness or whatever. (No insult intended for those who work in this area...I just don't see any meaningful connections as yet.) And the mathematical tools of interest to me right now are these: lattices and order (posets, causal sets), the connections between logic and geometry (sheaves, locales, toposes), various forms of logic (especially modal logic and intuitionistic logic), issues of time (a la Prior, Goldblatt, causal sets again), and the deep and interesting links with quantum mechanics. I'm also reading the book on causal decision theory that Wei Dai recommended, the Joyce book. And some other tangentially related things. A lot of what I am spending time on is the basic topology and algebra I only got smatterings of when I was in school, along with some glimpses of algebraic topology and the like. I'm using category theory and topos theory not as end-alls and be-alls, but as the lens through which I tend to view these other areas. Frankly, I learn faster and more deeply when I have some such lens. If this lens turns out to be not so useful for what I hope to do, I'll find another one. But for now, it gives me joy. I wrote a fair amount here last summer about topos theory, intuitionistic logic, notions of time evolution, and the work of Baez, Smolin, Markopoulou, Crane, Rovelli, and about a half dozen others. This remains a core interest, with some interesting (but not worked out, IMO) connections with QM (cf. the papers of Isham and Butterfield, and I. Raptis, and even some Russians). Bruno is more advanced than I am on the logic, as I have only gotten really interested in it recently. (I studied some logic out of Stoll, Quine, etc., and one of my best profs was Ray Wilder, a leading metamathematician of the 1950s. But I always thought logic was "obvious, but grungy in the d
