Re: naturally selected ethics, and liking chocolate
Eric Hawthorne writes: I think each form of emergent complex order which is capable of becoming intelligent and forming goals in general contexts problably would have by default an ethical principle promoting the continued existence of the most complex (high-level) emergent system in its vicinity of which it perceives itself to be a part, and which it perceives to be beneficial to its own survival. I can say this because forms of emergent complex order that included SAS's that didn't have this ethic would not survive long compared to other emergent complex orders whose SAS's did have this ethic. This is getting somewhat off-topic for this list, as it's not really multiverse related (except insofar as everything is multiverse related, since the multiverse includes everything). However you should be aware that evolutionary theory prefers to avoid this kind of reasoning. At one time it was widely assumed that such behaviors as altruism could be evolved and maintained for reasons similar to what you describe, that they benefit the group, and so groups whose members were altruistic would tend to survive better than groups whose members were selfish. Later analyses showed that this doesn't really work; that selfish behaviors have strong selective advantage compared to the relatively weak effects of group selection. It would be very difficult for an altruistic behavior to spread and persist within a group if it caused disadvantage to the individuals who possessed it. Instead, biologists eventually identified alternative explanations for altruistic behavior, in terms of kin selection and similar factors. Group selection is now discredited as an evolutionary force. See http://www.utm.edu/~rirwin/391LevSel.htm for some class lecture notes discussiong group selection. Hal Finney
Re: Is group selection discredited?
Unfortunately, disallowing notions of group selection also disallows notions of emergent higher-level-order systems. You must allow for selection effects at all significantly functioning layers/levels of the emergent system, to explain the emergence of these systems adequately. For example, ant colonies (as an emerged system) live for 15 years whereas the ants live for at most a year. Yet the colony (controlling for colony size) behaves diffently when it is a young colony (say its first five years) compared to when it is in its old age. (Essentially, the colony's behaviours become more conservative (less amenable to change of tactics.)) It would be very difficult to explain this solely from the perspective of the direct benefit to any individual ant's genes. For the benefit of ant-genes in general in the colony, yes. I think that it's just been too difficult to get adequate controlled studies to determine whether a group selection effect is happening. Because the individuals tend not to live at all if removed from their group. I think it is still an open debate. Group selection being discredited is just Dawkins and some like-minded people's favorite theory right now. Group selection is now discredited as an evolutionary force. See http://www.utm.edu/~rirwin/391LevSel.htm for some class lecture notes discussion group selection.
probabilities measures computable universes
I browsed through recent postings and hope this delayed but self-contained message can clarify a few things about probabilities and measures and predictability etc. What is the probability of an integer being, say, a square? This question does not make sense without a prior probability distribution on the integers. This prior cannot be uniform. Try to find one! Under _any_ distribution some integers must be more likely than others. Which prior is good? Is there a `best' or `universal' prior? Yes, there is. It assigns to each integer n as much probability as any other computable prior, save for a constant factor that does not depend on n. (A computable prior can be encoded as a program that takes n as input and outputs n's probability, e.g., a program that implements Bernoulli's formula, etc.) Given a set of priors, a universal prior is essentially a weighted sum of all priors in the set. For example, Solomonoff's famous weighted sum of all enumerable priors will assign at least as much probability to any square integer as any other computable prior, save for a constant machine-dependent factor that becomes less and less relevant as the integers get larger and larger. Now let us talk about all computable universe histories. Some are finite, some infinite. Each has at least one program that computes it. Again there is _no_ way of assigning equal probability to all of them! Many are tempted to assume a uniform distribution without thinking much about it, but there is _no_ such thing as a uniform distribution on all computable universes, or on all axiomatic mathematical structures, or on all logically possible worlds, etc! (Side note: There only is a uniform _measure_ on the finitely many possible history _beginnings_ of a given size, each standing for an uncountable _set_ of possible futures. Probabilities refer to single objects, measures to sets.) It turns out that we can easily build universal priors using Levin's important concept of self- delimiting programs. Such programs may occasionally execute the instruction request new input bit; the bit is chosen randomly and will remain fixed thereafter. Then the probability of some universe history is the probability of guessing a program for it. This probability is `universal' as it does not depend much on the computer (whose negligible influence can be buried in a constant universe-independent factor). Some programs halt or go in an infinite loop without ever requesting additional input bits. Universes with at least one such short self-delimiting program are more probable than others. To make predictions about some universe, say, ours, we need a prior as well. For instance, most people would predict that next Tuesday it won't rain on the moon, although there are computable universes where it does. The anthropic principle is an _insufficient_ prior that does not explain the absence of rain on the moon - it does assign cumulative probability 1.0 to the set of all universes where we exist, and 0.0 to all the other universes, but humans could still exist if it did rain on the moon occasionally. Still, many tend to consider the probability of such universes as small, which actually says something about their prior. We do not know yet the true prior from which our universe is sampled - Schroedinger's wave function may be an approximation thereof. But it turns out that if the true prior is computable at all, then we can in principle already predict near-optimally, using the universal prior instead: http://www.idsia.ch/~juergen/unilearn.html Many really smart physicists do not know this yet. Technical issues and limits of computable universes are discussed in papers available at: http://www.idsia.ch/~juergen/computeruniverse.html Even stronger predictions using a prior based on the fastest programs (not the shortest): http://www.idsia.ch/~juergen/speedprior.html -Juergen Schmidhuber
Re: probabilities measures computable universes
Are probabilities always and necessarily positive-definite? I'm asking this because there is a thread, started by Dirac and Feynman, saying the only difference between the classical and quantum cases is that in the former we assume the probabilities are positive-definite. Thus, speaking of MWI, we could also ask: what is the joint probability of finding ourselves in a universe alpha and of finding ourselves in a universe beta, which is 180 degrees out of phase with the first one (whatever that could mean)? s.
Re: Is the universe computable
Dear Stephen, At 12:39 21/01/04 -0500, Stephen Paul King wrote: Dear Bruno and Kory, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? [KH] The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that change. We have to address why it is that Time, even if it is ultimately an illusion, and the distingtion between past and future is so intimately intetwined in our world of experience. Good question. But you know I do address this question in my thesis (see url below). I cannot give you too much technical details, but here is a the main line. As you know, I showed that if we postulate the comp hyp then time, space, energy and, in fact, all physicalities---including the communicable (like 3-person results of experiments) as the uncommunicable one (like qualie or results of 1-person experiment) appears as modalities which are variant of the Godelian self-referential provability predicates. As you know Godel did succeed in defining formal provability in the language of a consistent machine and many years later Solovay succeeds in formalising all theorems of provability logic in a couple of modal logics G and G*. G formalizes the provable (by the machine) statements about its own provability ability; and G* extends G with all true statements about the machine's ability (including those the machine cannot prove). Now, independently, temporal logicians have defined some modal systems capable of formalizing temporal statements. Also, Brouwer developed a logic of the conscious subject, which has given rise to a whole constructive philosophy of mathematics, which has been formalize by a logic known as intuitionist logic, and later, like the temporal logic, the intuitionist logic has been captured formally by an modal extension of a classical modal logic. Actually it is Godel who has seen the first that Intuitionist logic can be formalised by the modal logic S4, and Grzegorczyk makes it more precise with the extended system S4Grz. And it happens that S4Grz is by itself a very nice logic of subjective, irreversible (anti-symmetric) time, and this gives a nice account too of the relationship Brouwer described between time and consciousness. Now, if you remember, I use the thaetetus trick of defining (machine) knowledge of p by provability of p and p. Independently Boolos, Goldblatt, but also Kusnetsov and Muravitski in Russia, showed that the formalization of that form of knowledge (i.e. provability of p and p) gives exactly the system of S4Grz. That's the way subjective time arises in the discourse of the self-referentially correct machine. Physical discourses come from the modal variant of provability given by provable p and consistent p (where consistent p = not provable p): this is justified by the thought experiment and this gives the arithmetical quantum logics which capture the probability one for the probability measure on the computational histories as seen by the average consistent machine. Physical time is then captured by provable p and consistant p and p. Obviously people could think that for a consistent machine the three modal variants, i.e: provable p provable p and p provable p and consistent p and p are equivalent. Well, they are half right, in the sense that for G*, they are indeed equivalent (they all prove the same p), but G, that is the self-referential machine cannot prove those equivalences, and that's explain why, from the point of view of the machine, they give rise to so different logics. To translate the comp hyp into the language of the machine, it is necessary to restrict p to the \Sigma_1 arithmetical sentences (that is those who are accessible by the Universal Dovetailer, and that step is needed to make the physicalness described by a quantum logic). The constraints are provably (with the comp hyp) enough to defined all the probabilities on the computational histories, and that is why, if ever a quantum computer would not appear in those logics, then (assuming QM is true!) comp would definitely be refuted;
Re: naturally selected ethics
Later analyses showed that this doesn't really work; that selfish behaviors have strong selective advantage compared to the relatively weak effects of group selection. It would be very difficult for an altruistic behavior to spread and persist within a group if it caused disadvantage to the individuals who possessed it. Instead, biologists eventually identified alternative explanations for altruistic behavior, in terms of kin selection and similar factors. Group selection is now discredited as an evolutionary force. Agreed (both with your point and it's tenuous relevance to he list - unless it's all CAs and thus all intrinsically related..), but with a qualifier. Are species is generally just a few millennia (ranging from the present to 10 or 12 thousand years ago depending on what group or region you pick) away from a nomadic clan ecology. The probability of opportunities to act altruistically towards someone in such an ecology would be skewed towards that someone being a relation by blood or marriage. Fast forward to the present where, for a great swath of humanity, Darwinian natural selection has been turned on it's head. From a strict reproductive success measure, the meek (the poor anyway) have inherited the earth whereas from a resource control aspect the rich hold sway. Selection can be viewed as having all but been neutralized in the west on the former front in that potential reproductive success is only denied to the most severely developmentally disabled. But biologically we remain for all practical purposes identical to those clans people above and to the extent that we are hard wired (EO Wilson vs SJ Gould), we operate in response to the same nature as they. I think Desmond Morris is not far wrong when he muses that in the 1st and 2nd world (and rapidly the 3rd), our tribe now largely consists of the contents of our (email) address books. As a evolutionary biologist turned programmer, I have gradually shifted from the hard Wilson camp (Social Biology) towards the soft Gould(emergent Spandrels) by way of Wolfram: Natural selection tends to modify systems and structures at the margins whereas much of the complexity and organization of same is the direct result of self-organization only relatively constrained by selective pressures from sources on the same and other scales of hierarchal adaptation. Given all the above, then the admittedly rare but real phenomena of expensive (fitness lowering) altruism (as opposed to the cheap kind; aka: the rich never give more than they can afford) may not be surprising or unexpected.
Re: probabilities measures computable universes
Juergen Schmidhuber writes: What is the probability of an integer being, say, a square? This question does not make sense without a prior probability distribution on the integers. This prior cannot be uniform. Try to find one! Under _any_ distribution some integers must be more likely than others. Which prior is good? Is there a `best' or `universal' prior? Yes, there is. It assigns to each integer n as much probability as any other computable prior, save for a constant factor that does not depend on n. (A computable prior can be encoded as a program that takes n as input and outputs n's probability, e.g., a program that implements Bernoulli's formula, etc.) What is the probability that an integer is even? Suppose we use a distribution where integer n has probability 1/2^n. As is appropriate for a probability distribution, this has the property that it sums to 1 as n goes from 1 to infinity. The even integers would then have probability 1/2^2 + 1/2^4 + 1/2^6 ... which works out to 1/3. So under this distribution, the probability that an integer is even is 1/3, and odd is 2/3. Do you think it would come out differently with a universal distribution? The more conventional interpretation would use the probability computed over all numbers less than n, and take the limit as n approaches infinity. This would say that the probability of being even is 1/2. I think this is how such results are derived as the one mentioned earlier by Bruno, that the probability of two random integers being coprime is 6/pi^2. I'd imagine that this result would not hold using a universal distribution. Are these mathematical results fundamentally misguided, or is this an example where the UD is not the best tool for the job? Hal Finney
