Max Tegmark: The Mathematical Universe
This arXiv paper should be of interest here. - Forwarded message from "Yonatan Fishman, Ph.D." <[EMAIL PROTECTED]> - Thought this would be of interest: The Mathematical Universe Authors: Max Tegmark (Submitted on 5 Apr 2007) Abstract: I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. http://arxiv.org/abs/0704.0646 Yon - End forwarded message - -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 13 Sep., 00:48, Russell Standish wrote: > It would be possible to construct an ensemble of purely finite strings > (all strings of length googol bits, say). This wouldn't satisfy the > zero information principle, or your no-justification, as you still > have the finite string size to justify (why googol and not googol+1, > for instance). I suspect the observable results would be > indistinguishable from the infinite string ensembles for large enough > string string size, however. We've a little misunderstanding in this point. I did never suggest strings of an overall fixed length, but only of a finite length that may vary from string to string without being limited. The idea behind this was that imaginable things should be describable completely (e.g. by a person telling me about them) and not only asymptotically (which---I thought---could be the case if the descriptions were infinite). On the other hand, I do see two arguments in favor of the infinite strings: 1. It may be that something can be described by a finite description in one "language", but must be described by an infinite description in another "language". A simple example is the number pi which can be defined by finite expressions (e.g. by writing down formally the Gregory-Leibniz series). But if we restrict ourselves to describe numbers by writing down their digits in the decimal numeral system, then the description of pi is infinite. This can be seen as a motivation to allow infinite strings. 2. The difference between finite and infinite strings is somehow similar to the difference between natural and real numbers (at least as far as their cardinalities are concerned) in mathematics. If, in a far future, we want to establish analytical methods to study the Everything ensemble (this of course is a very, very problematic task and cannot be our concern here) it may turn out useful to allow infinite strings as it turned out useful for ordinary mathematics to allow real numbers instead of natural or rational numbers. > Where differences lie is in the measure attached to these strings. I > take each string to be of equal weight to any other, so that there are > twice the measure of strings satisfying 01* as 011*. This leads > naturally to a universal prior. I'm still hesitant to accept the idea that the Everything ensemble by itself comes up with a measure. Although undoubtedly the measure is a fundamental ingredient of our theories, I think that it should only be introduced for practical reasons, i.e. whenever we are interested in probabilities. Then the measure is adapted to our state of ignorance. The standard case will be that one has no information whether to prefer a given description which leads to your measure of equal weight and the universal prior. This is very analogous to statistical physics where we usually assign equal measure to every microstate. I am not yet familiar with Schmidhuber's ideas but I am going to read up on this topic soon, in particular in the context of the White Rabbit paradox. Youness Ayaita --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On Wed, Sep 12, 2007 at 07:32:32AM -0700, Youness Ayaita wrote: > > The two concerns, how to give a precise notion of the Everything, and > how to deduce predictions from a chosen notion, lie at the very heart > of our common efforts. Though, I did not go into them for the simple > reason that I wanted to avoid discussions that are not directly linked > to the topic. > > When I first wanted to capture mathematically the Everything, I tried > several mathematicalist approaches. But later, I prefered the > Everything ensemble that is also known here as the Schmidhuber > ensemble. I assume that the no-justification naturally leads to this > ensemble. This comes from the development of the (degenerate) property > of existence which is then assigned to all imaginable things. I don't > think that a metaphysical discussion of the term "imaginable thing" is > necessary now, I'm satisfied with the idea that an imaginable thing > can be completely described by means of language. For further > research, it is then natural to identify imaginable things with their > descriptions and to choose a simple alphabet for expressing the > descriptions (e.g. strings of 0 and 1). In the past I assumed these > strings to be of finite length. I read that Russell Standish also > permits infinite strings. > These sorts of discussions "No-justification", "Zero-information principle", "All of mathematics" and Hal Ruhl's dualling All and Nothing (or should that be "duelling") are really just motivators for getting at the ensemble, which turns out remarkably to be the same in each case - the set of 2^\aleph_0 infinite strings or histories. Where differences lie is in the measure attached to these strings. I take each string to be of equal weight to any other, so that there are twice the measure of strings satisfying 01* as 011*. This leads naturally to a universal prior. Schmidhuber has a different measure, assuming that the strings are generated in real time from a machine with bounded resources. This is his "speed prior", and leads to a quite different measure on the strings. Neither Bruno's nor Max's theories give a measure, but remarkably the Occam's razor theorem and White Rabbit result is fairly insensitive to the measure chosen (so long as it's not too pathological!). On your comment on permitting infinite strings - the ensemble I describe in my book has only infinite strings, which belong to syntactic space. A finite string corresponds to a set of infinite strings all having the same finite prefix, and as such belongs to semantic space. It would be possible to construct an ensemble of purely finite strings (all strings of length googol bits, say). This wouldn't satisfy the zero information principle, or your no-justification, as you still have the finite string size to justify (why googol and not googol+1, for instance). I suspect the observable results would be indistinguishable from the infinite string ensembles for large enough string string size, however. -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
If anyone is interested, I think some of the ideas at my website, www.geocities.com/roger846, apply to the current discussion. Briefly, the ideas entail: o Something exists because it is completely defined. That is, you know exactly what's contained in that thing. This applies to material things outside the mind as well as to ideas and concepts within the mind. For instance, a book exists because you know what's contained within it (cover, pages, etc.). The concept "love" exists in someone's mind because that person knows what kinds of things are contained within the concept. o The complete definition of something is the same thing as an edge or boundary. This edge or boundary gives the thing substance or what we call "existence". o What we have traditionally called "non-existence" or the lack of all matter, energy, volume, ideas/concepts, etc. is completely defined. That is, there's nothing missing and nothing somewhere else, and you know exactly what's there-nothing at all. Because it's completely defined, what we've traditionally thought of as "non-existence" can also be said to exist. In other words, when seen from a different perspective than usual, "non-existence" and "existence" are really just the same thing. Another way of coming to this conclusion is as follows: When thinking about the question "why is there something rather than nothing?", two choices are: A. "Something" has always been here. B. "Something" has not always been here. Even though choice A is possible, it doesn't provide any explanation so let's go with choice B and see where it leads. If "something" hasn't always been here, then "nothing" must have been here before it. If "nothing" were here, there would be no mechanism in "nothing" to change this "nothing" into "something". Yet, we accept that "something" is here now. So, the only possible choice is that "nothing" and "something" are one and the same thing. Thanks. Roger --- Youness Ayaita <[EMAIL PROTECTED]> wrote: > > No(-)Justification Justifies The Everything Ensemble > Youness Ayaita > > > > In this message, I present my "no-justification" of > the hypothesis > that everything exists. The no-justification argues > that no > justification at all is needed to accept the > hypothesis. This provides > a new and very satisfying approach to the Everything > ensemble. > > > > 1 Hitherto proposed justifications > > In this first section I give a brief overview of > some existing > justifications for the Everything ensemble. The > reader familiar with > the topic may skip this section. > > Several thinkers have come independently to the > hypothesis that---in > some sense or another---everything exists. The > justifications they > have found in favor of this hypothesis vary as do > their intellectual > backgrounds (philosophy, computer science, > mathematics or physics). > When I myself developed the hypothesis, I found > three > justifications which I call respectively the > 'metaphysical approach', > the 'generalized Copernican principle' and the > 'no-justification'. The > main justifications supported by contributors to the > everything-list > are the 'zero information principle' and > 'arithmetical realism' (also > called 'mathematical Platonism'). Another > justification is due to the > analytic philosopher David Lewis: > > "Why believe in a plurality of worlds?---Because the > hypothesis is > serviceable, and that is a reason to think it is > true." > > For most philosophers Lewis's justification was not > convincing. Much > more attractive to many thinkers is arithmetical > realism, assuming the > objective existence of all mathematical objects. The > zero information > principle bases upon the observation that the > Everything has no > information content. Russell Standish writes: > > "There is a mathematical equivalence between the > Everything, as > represented by this collection of all possible > descriptions and > Nothing, a state of no information." > > This justification is impressive since it shows that > Everything is--- > in some sense---not more than Nothing. It thus > provides a striking > argument against the critics' objection that > supporters of the > Everything ensemble postulate too much additional > ontology. > > As a last example, I mention the generalized > Copernican principle. The > idea is to give up the categorical difference > between our world and > all other possible worlds: Everything is equally > real. > > > > 2 Remarks on new fundamental theories > > Before starting to explain my no-justification of > the Everything > ensemble, I want to summarize some important > statements in advance > which concern all new fundamental theories. Taking > seriously the > approach given by the no-justification, it will turn > out that the term > "Everything exists" is logically meaningless. > Nonetheless I'll s
Re: Rép : Observer Moment = Sigma1-Sentences
Dear Bruno, Dear List, > You could be right. The point we are addressing is the question of > making our hypotheses clear enough so that we can refute them or make > sense of how we could have them refuted at least in principle. > >> I also keep away from ANY thought experiences, they are products of >> OUR state of the mind at the time they are 'invented'. > > All proof in math are particular case of thought experiments. In > philosophy-of-mind, theology, theoretical physics and math, the only > tools available are the thought experiments. The problem is: in math what follows from the axioms is true per definition (that is what following from the axioms mean). How would you be able to "refute" comp? There is no way to do that, one can only call the axioms into question (and that is what John is doing). >> because the Flat Earth did not prove true later, either. > We have no proof that the earth is round, only solid evidence that the > roundity of earth is a solid *local* truth. In which models would the Earth not be round? (I am speaking here of models which have the property "roundness" in them and which other objects similar to Earth are also round - I guess that is as close to what we can call as something being true.) In this sense I would call the Earth as being round true. > No serious scientist will ever try to convince others (except for the > mundane purpose of getting some funds). As I said a scientist, not only > does not want to convince others, he want others to show him wrong > instead. You confuse scientists, and mediatico-pseudo-scientists, which > can exist still today due to 1500 years of abandon of the fundamental > question to political pseudo-religious authorities. Of course they have > had no choice, because it is best to do pseudo-science than to burn > alive ... (I don't judge them here). I agree strongly with you Bruno that science is about doubt and modesty. But I do not think that a scientist has to be so agnostic as to never want to convince anybody else of some positions (which is what teaching essentially is); I am adopting a critical rationalist position here: a scientist can look at the models and assign different plausibilities to them; he can say that the evidence speaks more for A than for B. But he sometimes can also say that C is strictly ruled out (of course, this is often said too soon in practice, but if one is careful one can nevertheless say this, of inconsistent theories for instance). Cheers, Günther -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
flying pigs
Hello all, after a rather long hiatus I am back on the list; I have been grappling with the relationship of mathematical entities to the real world and feel like entering the fray again :-)) > From: Youness Ayaita > > 3 No-justification > > In this last paragraph it can be seen that the no-justification has a > lot in common with the zero information principle. I wrote that, if we > want to introduce the property of existence, than this property must > be degenerate (given by no entity or given by the ensemble of all > entities). In other words, there cannot be any information separating > some entities that exist from other entities that don't. > > OK. So where are the flying pigs? > > Brent Meeker I would like to second Brent's comment - where are the flying pigs? Regards, Günther --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Space-time is a liquid!
(From the swedish Allting List:) The discrete space-time is a liquid. This explains why the space is isomorph in all directions. The one that discovered that the space-time is a liquid, was Xiao-Gang Wen (Home Page: http://dao.mit.edu/~wen ). He has found that elementary particles are not the fundamental building blocks of matter. Instead, they emerge as defects or "whirlpools" in the deeper organized structure of space-time. The space-time is a string-net liquid, and the photons, the light, are waves in this liquid. And the charged electrons are the the ends of open-ended strings. Xiao-Gang Wen has written a lot of articles about this, and they can all be found from his home page. But most of the articles are *very* mathematical. But there is an easy-to-read article at https://dao.mit.edu/~wen/NSart-wen.html . And there is a rather-easy-to-read article in 12 pages at https://dao.mit.edu/~wen/pub/intr-frmb.pdf , that explains more about these very interesting theories. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
The two concerns, how to give a precise notion of the Everything, and how to deduce predictions from a chosen notion, lie at the very heart of our common efforts. Though, I did not go into them for the simple reason that I wanted to avoid discussions that are not directly linked to the topic. When I first wanted to capture mathematically the Everything, I tried several mathematicalist approaches. But later, I prefered the Everything ensemble that is also known here as the Schmidhuber ensemble. I assume that the no-justification naturally leads to this ensemble. This comes from the development of the (degenerate) property of existence which is then assigned to all imaginable things. I don't think that a metaphysical discussion of the term "imaginable thing" is necessary now, I'm satisfied with the idea that an imaginable thing can be completely described by means of language. For further research, it is then natural to identify imaginable things with their descriptions and to choose a simple alphabet for expressing the descriptions (e.g. strings of 0 and 1). In the past I assumed these strings to be of finite length. I read that Russell Standish also permits infinite strings. But first of all, I'm interested in your opinions concerning the no- justification. Thank you, Stathis Papaioannou, for letting me know of Kant's ideas in this context. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Rép : Observer Moment = Sigma1-Sentences
Le 12-sept.-07, à 00:41, John Mikes a écrit : > Bruno, you ARE a teacher (a good and passionate one) but your > imagination is insufficient. You cannot imagine how much I don't > know. pick up 'words' and 'phrases' and apply common sense to them > with a certain authoritative flair, so those who understand the topic > can think that I am talking sense. As I already confessed: I never > studied logics and cannot 'read' the signs (nor can I 'decipher' those > equational formats) you all apply in otherwise human sentences. They > look like math to me. They are math! It is the game I play. I like very much David Deutsch's idea that if we are scientist we are in principle willing to know that our theory is wrong, but to discover this we have to take them seriously enough. > And i still did not get an acceptable explanation why 'numbers' are > the basics of everything (and WHAT they may be). Nobody can KNOW that. The fact is that ONCE you take the comp hyp seriously enough into consideration, then you can, by work, be eventually convince that our own immateriality (which follows easily by comp) has to be "contagious" on our possible neighborhoods. > Those numbers applied in mathematical formal language are definitely > products of the human mind, yes sure. But we are not talking about those numbers humans (re)invented, but on those which have to exist independently of us once we accept some minimal amount of computer science, without which we could infer nothing fron comp (our, well mine, working hypothesis). > as David Bohm so clearly stated. No problem, Bohm is a serious guy, he makes clear he does not accept the comp hyp at the start. Bohm is serious, and as far as I can jujudge by my reding, he is 100% correct. But he denies comp. > I know: you represent the opposite way: not numbers from thinking, but > existence, ith all pertinent to it FROM numbers, which I reject just > as the 'personalized creator' in an any other form. You could be right. The point we are addressing is the question of making our hypotheses clear enough so that we can refute them or make sense of how we could have them refuted at least in principle. > I also keep away from ANY thought experiences, they are products of > OUR state of the mind at the time they are 'invented'. All proof in math are particular case of thought experiments. In philosophy-of-mind, theology, theoretical physics and math, the only tools available are the thought experiments. > In deducing some explanations from 'phenomena' we think we > experienced (depends upon the actual level of our observational and > explanatory cpacity) I always put an uncertainty in it, I totally agree with you here! > because the Flat Earth did not prove true later, either. We have no proof that the earth is round, only solid evidence that the roundity of earth is a solid *local* truth. > (Now geocentrism is true again, after Einstein, because it is quite > arbitrary that we can decide as a (relative) center for all others, no > matter how complicated the math would be...). > I am in subconscious trouble with the machine, which is differently > identified by Robert Rosen and I find a lot acceptable in his ideas. Imo, Rosen is wrong on Church thesis. But this could wait when I succeed to explain more about CT later ... > God and the angels are also hard: I do not go for assumption-based > consequences (not true: everything is such), in fairytales of > non-logical hearsay. Just keep track of the definitions. By angels and gods (note the plural) I mean things which are not turing-emulable, or if you prefer, any entities which are provably not machines. > I go with Colin's "mini solipsism" as I call it, the world is what we > make of it for ourselves. I am a realist. I guess there is something more than me. The rest, the, can be justified as first person points of view. > I use my own logic, it served me well for many decades, and my > 'narrative' about the world and its installation is such (and only > such) as it entertains me and my logic. Not the conventional sciences. What is conventional sciences. If by this you mean that sometimes the academy gives grades and honours wrongly, then you are right but this is really "human too much human" as Nietzche said once. We have no choice to learn with this facts. I prefer to talk about science, and describe some science has being wrong from time to time (like when Bohr dismissed Everett, just because what Everett said contradicted his (Bohr) wishfull thinking. Science = doubt and modesty. When scientist pretend to know the truth, they are mad, that's all. > After 5 decades of successful polymer chemistry (38 patents, 3 > continent consulting) I do not accept the existence of atoms and > molecules, Nor do I believe in the primary nature of those notion. Plotinus (+300) did already understand that such notions were
Re: No(-)Justification Justifies The Everything Ensemble
Le 12-sept.-07, à 13:08, Stathis Papaioannou a écrit : > > On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > OK. So where are the flying pigs? >>> >>> Elsewhere. Existence is not a property, but position is. >> >> Ok. Why are they there and not here? >> >> I'm sure that Stathis takes my point that saying everything-exists is >> not only "no-justification" it is also "no-information". By itself >> it is worthless for explaining anything. > > Yes, you have to show how the theory makes predictions about the real > world, otherwise it is impossible to know whether it is true or not > and the theory is worthless. I'm more or less ok with this, except that you can *never* know when a theory (about reality) is true (about reality). I have already criticize everything-like theories when they take a too big "everything" hyp. at the start, like pure mathematicalism à-la Tegmark. From that point of view Schmidhuber is a bit clearer on the type of everything notion available once you postulate the comp hyp. (Now Schmidhuber does not take the 1-3 pov distinction into account, so he missed apparently the role of the first person indeterminacy and its verifiable consequences, like the fact that the laws of physics have to emerge from the platonic existence of the many computations). It is really Church's thesis which provides the first coherent notion of "everything". That is why I'm motivated to tentattively explain what Church thesis is, and why it is a sort of completely unexpected miracle (to talk like Godel). Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No(-)Justification Justifies The Everything Ensemble
On 12/09/2007, Brent Meeker <[EMAIL PROTECTED]> wrote: > >> OK. So where are the flying pigs? > > > > Elsewhere. Existence is not a property, but position is. > > Ok. Why are they there and not here? > > I'm sure that Stathis takes my point that saying everything-exists is not > only "no-justification" it is also "no-information". By itself it is > worthless for explaining anything. Yes, you have to show how the theory makes predictions about the real world, otherwise it is impossible to know whether it is true or not and the theory is worthless. -- Stathis Papaioannou --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
