I previously tried cutting and pasting the text instead of giving a link no one apparently went to before replying because the formatting was off. So I will do that because it seems that would be prudent. I figured it out. (I'm not computer guru....)

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sci.logic Groups Alerts Create a group... Recently Visited Groups | Help | Sign in sci.logic Top of Form Bottom of Form Top of Form Bottom of Form Discussions + new post About this group Subscribe to this group This is a Usenet group - learn more Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Options Top of Form There are currently too many topics in this group that display first. To make this topic appear first, remove this option from another topic. There was an error processing your request. Please try again. Standard view View as tree Proportional text Fixed text Bottom of Form 6 messages - Collapse all The group you are posting to is a Usenet group. Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful Brian Tenneson View profile More options Mar 1, 11:47 am Newsgroups: sci.logic From: Brian Tenneson <[EMAIL PROTECTED]> Date: Sat, 1 Mar 2008 11:47:48 -0800 (PST) Local: Sat, Mar 1 2008 11:47 am Subject: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author [This post is in sci.logic because of the employment of model theory and discussion of abstract math structures by the author and for other reasons which may come up during the discussion.] Here is a link to the article: http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.0646v2.pdf 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, randomness and initial conditions to broader issues like consciousness, parallel universes and G"odel incompleteness. I hypothesize that only computable and decidable (in G"odel's sense) structures exist, which alleviates the cosmological measure problem and may help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems. Quote from Intro: The idea that our universe is in some sense mathematical goes back at least to the Pythagoreans, and has been extensively discussed in the literature (see, e.g., [2-25]). Galileo Galilei stated that the Universe is a grand book written in the language of mathematics, and Wigner reflected on the "unreasonable effectiveness of mathematics in the natural sciences" [3]. In this essay, I will push this idea to its extreme and argue that our universe is mathematics in a well-defined sense. [End Quote] The article linked to above is regarded by its author as a sequel to this: http://space.mit.edu/home/tegmark/toe.pdf Abstract: (sorry, some characters didn't enjoy being c&p'ed) We discuss some physical consequences of what might be called \the ultimate ensemble theory", where not only worlds corresponding to say di erent sets of initial data or di erent physical constants are considered equally real, but also worlds ruled by altogether di erent equations. The only postulate in this theory is that all structures that exist mathematically exist also physically, by which we mean that in those complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically \real" world. We nd that it is far from clear that this simple theory, which has no free parameters whatsoever, is observationally ruled out. The predictions of the theory take the form of probability distributions for the outcome of experiments, which makes it testable. In addition, it may be possible to rule it out by comparing its a priori predictions for the observable attributes of nature (the particle masses, the dimensionality of spacetime, etc.) with what is observed. Quote: In other words, some subset of all mathematical structures (see Figure 1 for examples) is endowed with an elusive quality that we call physical existence, or PE for brevity. Specifying this subset thus speci es a category 1 TOE. Since there are three disjoint possibilities (none, some or all mathematical structures have PE), we obtain the following classi cation scheme: 1. The physical world is completely mathematical. (a) Everything that exists mathematically exists physically. (b) Some things that exist mathematically exist physically, others do not. (c) Nothing that exists mathematically exists physically. 2. The physical world is not completely mathematical. The beliefs of most physicists probably fall into categories 2 (for instance on religious grounds) and 1b. Category 2 TOEs are somewhat of a resignation in the sense of giving up physical predictive power, and will not be further discussed here. The obviously ruled out category 1c TOE was only included for completeness. TOEs in the popular category 1b are vulnerable to the criticism (made e.g. by Wheeler [6], Nozick [7] and Weinberg [8]) that they leave an important question unanswered: why is that particular subset endowed with PE, not another? ... In this paper, we propose that category 1a is the correct one. [End quote] I'm also interested in discussing what SAS'es might there be. Perhaps nail down axioms and/or defining traits of SAS'es. This next link might be a diversion, but it is a starting point for the discussion of formalizing awareness: http://cs.wwc.edu/~aabyan/Colloquia/Aware/aware2.html I suppose the direction I'd +like+ this discussion to go is investigation of this material as conjecture, what these conjectures would entail (physically, mathematically, and philosophically), etc., + +rather than debate as to the validity of these conjectures.++ It seems to me that, at worst, these conjectures form an internally consistent theory, not unlike Cantor's theory of the infinite; whether or not these conjectures are correct in a physics sense as being an accurate characterization of "reality," I would like to view these conjectures/hypotheses as, in this discussion at sci.logic, at worst, an internally consistent framework, worthy enough of investigation because of the consistency, regardless of physical correctness. Obviously, if these conjectures/hypotheses are correct in a physics sense, then the investigation is even more justified when compared to mathematical and/or philosophical justification for the investigation. Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. Brian Tenneson View profile More options Mar 1, 12:30 pm Newsgroups: sci.logic From: Brian Tenneson <[EMAIL PROTECTED]> Date: Sat, 1 Mar 2008 12:30:05 -0800 (PST) Local: Sat, Mar 1 2008 12:30 pm Subject: Re: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author The last link provided is giving me intermittent failure, so here are two cached versions to try: 1st cached version of aware2.html: http://web.archive.org/web/20060827232622/http://www.cs.wwc.ed u/~aaby... 1st link to 2nd cached version of aware2.html: <a href="http://209.85.173.104/search?q=cache:dil-L-g7Mj0J:cs.wwc .edu/ ~aabyan/Colloquia/Aware/aware2.html +aware2+site:cs.wwc.edu&hl=en&ct=clnk&cd=1&gl=us">Google cached version</a> Hopefully this forum will allow the html above because the link might be too long with wrapping and c&p'ing considerations: 2nd link to 2nd cached version of aware2.html: http://209.85.173.104/search?q=cache:dil-L-g7Mj0J:cs.wwc.edu/~ aabyan/... Also, a new link in the direction of the non-computability of consciousness, which seems to be a strike against some of Tegmark's hypotheses (in particular, the computable universe hypothesis in section VII of the very first article linked to in the previous post, "assuming" that non-computability of consciousness implies the non- computability of the universe in that consciousness is "contained in" the universe), is here: Non-Computability of Consciousness http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.1617v1.pdf Abstract: With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to be no. A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer. Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element. The concept that this is solely a quantum effect and does not work for a classical case is also discussed. Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. Brian View profile More options Mar 3, 12:38 pm Newsgroups: sci.logic From: Brian <[EMAIL PROTECTED]> Date: Mon, 3 Mar 2008 12:38:29 -0800 (PST) Local: Mon, Mar 3 2008 12:38 pm Subject: Re: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author On Mar 1, 12:30 pm, Brian Tenneson <[EMAIL PROTECTED]> wrote: - Hide quoted text - - Show quoted text - > Also, a new link in the direction of the non-computability of > consciousness, which seems to be a strike against some of Tegmark's > hypotheses (in particular, the computable universe hypothesis in > section VII of the very first article linked to in the previous post, > "assuming" that non-computability of consciousness implies the non- > computability of the universe in that consciousness is "contained in" > the universe), is here: > Non-Computability of Consciousnesshttp://arxiv.org/PS_cache/arxiv/pdf/0705/0705.161 7v1.pdf > Abstract: > With the great success in simulating many intelligent behaviors using > computing devices, there has been an ongoing debate whether all > conscious > activities are computational processes. In this paper, the answer to > this > question is shown to be no. A certain phenomenon of consciousness is > demonstrated to be fully represented as a computational process using > a > quantum computer. Based on the computability criterion discussed with > Turing machines, the model constructed is shown to necessarily involve > a > non-computable element. The concept that this is solely a quantum > effect > and does not work for a classical case is also discussed. I recently came across an apparent rejoinder (intentional or not, I don't know) by Tegmark on the subject of the quantum nature of brain function. http://space.mit.edu/home/tegmark/brain.html Tegmark makes a case for brain function being modeled adequately with classical theoretical means (possibly such as Turing machines) and that brains do not function like quantum computers. (Essentially the main factor is that the brain is not nearly at absolute zero degrees, or otherwise in an environment in which superposition type effects that consciousness apparently mimics well enough to keep many on the fence, is more common than Earthly temperatures where our brains normally reside.) If Tegmark does prove his point, while others in his community remain skeptical that brain function is +not+ an example of a quantum computer, then the paper I cited about the non-computability of consciousness does not invalidate Tegmark's CUH, mentioned in section VII of the first link in the first post. The non-computability of consciousness would seem to invalidate Tegmark's CUH (Computable Universe Hypothesis) in that the universe, by even a narrow definition of universe, must contain consciousness, and, I presume, non- computability of consciousness would imply the CUH is false. That is, unless consciousness can have non-computable aspects that when "glued" (ultraproduct or some other method of "gluing"???) together throughout the universe, somehow (I know this is vague) the non- computable aspects of various parts of the universe all balance out to a computable universe. Hmm...things to think about... Maybe the CUH is true and brains work like quantum computers, somehow...? Anyway, Tegmark would be lending credence to his point by invalidating the proof of non-computability of consciousness for that relies on the "presumption" that consciousness is inherently a quantum process; obviously if their critical "presumption" is wrong, then their conclusion (consciousness not being computable) isn't necessarily so. I think it is worth splitting hairs here about the difference between consciousness and brain function but as of yet am aware of very little of the +formal+ theory behind either of these notions, philosophically, psychologically, or cognitive-scientifically. I am compiling a list of other discussion points. First on this list of discussion points, I will make a connection to abstract fuzzy logic and the Level IV multiverse situation. If you haven't read these fascinating articles yet, Level IV's brief definition is: Other mathematical structures give different +fundamental+ equations of physics. In the MUH article (first link, first post), appendix A defines what Tegmark means by a mathematical structure. [Compilation Process] I'm thinking of whether or not the aggregate of all MS's can be "glued" together somehow (doubtfully by a simple union) in order to get the MS of all MS's. This brings me to the connection to abstract fuzzy logic and my personal quest to continue my education in the area of Fuzzy Logic. (Apparently, no one in the US works specifically in the area I want to work in but there are many in Europe at institutions that award Phds.) It also gratifies me, on a personal note, to think that my research, if carried out, might settle some question about whether or not the [Compilation Process] is at all possible in any "reasonable" sense whatsoever. It would be nice to know either way, rather than a "this smells like Russell's Paradox, so let's not try it" sort of deal. My research would focus on somewhat recent papers on fuzzy logic pertaining to involving FL at the axiomatic level to create generalizations and anti-generalizations of ZFC set theory, or other suitably modified set theory (eg, remove Foundation Axiom immediately for reasons that would be clear later). According to the conclusion of that paper, linked to below, an open problem is figuring out how other axioms could be, should be, shouldn't be, and can't be consistently added to the list of axioms they present in a FL-sense. [[1]] http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zSzzSzw ww.cs.c... In an effort to push question (2) in a particular direction, let me attempt to formulate my question/problem. Start with the bare-bones fuzzy set theory presented in [[1]]. Let the truth set be denoted D. Consider the following axioms: [[U.Strong]] there is a y such that for all x, the truth degree of the formula "x is in y" is the maximal (in the sense appropriate to the type of algebraic structure D has, such as an MV-algebra, but definitely not Boolean as we know Russell's Paradox +will+ rear its ugly head in the Boolean case) element in D. In other words, if the maximal element in D is equipped with the baggage "true", U.S. says there is a set y for which all sets x are elements of y. This is one reason to drop the Foundation Axiom immediately, as such a y is obviously not well-founded. This could be called a (strong) universal set, with appropriate adjectives that reference D and the syntactical entailment axioms used, the underlying language, etc... [[U.Weak]] there is a y such that for all x, the truth degree of the formula "x is in y" is a designated element of D. In words, I view the designated, anti-designated, and non-designated partitions of D as shades of gray of truth. Designated means more light than not, where light = truth in this analogy, anti-designated means more dark than not, and non-designated means more gray than not. So to say " 'x is in y' is a designated truth value" would mean something like, "it's essentially true that y is a universal set." One could say that y would be a weak universal set and it is doubtful that such a y need be unique, unlike a strong universal set is. That sets (pun intended) up the problem (below) that I hope to formalize into the beginnings of a PhD thesis in the area of FL someday. Let R be some type of unary predicate. Recall that D is the set of truth degrees, with some algebraic (eg, MV) structure associated with it. Consider the statement below: [[Statement]] A fuzzy set theory, starting with the one in [[1]], without Foundation, plus either the strong or weak universal set axiom, is consistent relative to ZFC (the best situation one can hope for) if and only if R(D). The question: Determine for what R is the above statement true, if any, or prove that for all R, the above statement is false. Obviously, I want, at worst, an existence proof on R, that there are some properties D could possess that enables a fuzzy universal set theory that is consistent relative to ZFC. Also, I strongly hope that the statement is not false for all R, that there aren't any exotic D's or structures they could be equipped with, to make a universal set theory as consistent as ZFC. Clearly, if D = {0,1} then the set of all R's for which [[Statement]] is true is empty (bad but expected and well known). In the binary logic case, Russell's Theorem proves that the set of all R's for which [[Statement]] is true is empty. No properties on D make the universal set a possibility in classical logic (except possibly the work of the sort Quinne did with the New Foundations although, in NF, Choice must be dropped, in some sense, which is highly disadvantageous to anyone who enjoys using Zorn's Lemma). (I posed this to someone known in the area of FL and he encouraged me to come to Europe (as apparently no one does this type of work in FL in the U.S.) to formally work this into a PhD thesis.) Now, ultimately, the connection to the CUH is that if there is an ultimate set of +some kind+, like a strong universal set, then perhaps that could provide a link to the MS of all MS's, ie, the mathematical structure of all mathematical structures, without leading to deals like, "this smells like Russell's dirty laundry, so let's not go there." <punchline tag> Either that or provide an interesting, to say the least, MS (a fuzzy and strong universal set theory) to investigate in the context of the MUH, as this strong universal fuzzy set may, in fact, be a candidate for what the universe literally is in a physical sense, assuming the MUH, of course. </punchline tag> If I could make all of that work, I would be a very happy man. Even if I could be proved wrong, at least then I can rest on this issue in particular. Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. Brian View profile More options Mar 4, 10:21 am Newsgroups: sci.logic From: Brian <[EMAIL PROTECTED]> Date: Tue, 4 Mar 2008 10:21:00 -0800 (PST) Subject: Re: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author On Mar 3, 12:38 pm, Brian <[EMAIL PROTECTED]> wrote: - Hide quoted text - - Show quoted text - > On Mar 1, 12:30 pm, Brian Tenneson <[EMAIL PROTECTED]> wrote: > > Also, a new link in the direction of the non-computability of > > consciousness, which seems to be a strike against some of Tegmark's > > hypotheses (in particular, the computable universe hypothesis in > > section VII of the very first article linked to in the previous post, > > "assuming" that non-computability of consciousness implies the non- > > computability of the universe in that consciousness is "contained in" > > the universe), is here: > > Non-Computability of Consciousnesshttp://arxiv.org/PS_cache/arxiv/pdf/0705/0705.161 7v1.pdf > > Abstract: > > With the great success in simulating many intelligent behaviors using > > computing devices, there has been an ongoing debate whether all > > conscious > > activities are computational processes. In this paper, the answer to > > this > > question is shown to be no. A certain phenomenon of consciousness is > > demonstrated to be fully represented as a computational process using > > a > > quantum computer. Based on the computability criterion discussed with > > Turing machines, the model constructed is shown to necessarily involve > > a > > non-computable element. The concept that this is solely a quantum > > effect > > and does not work for a classical case is also discussed. > I recently came across an apparent rejoinder (intentional or not, I > don't know) by Tegmark on the subject of the quantum nature of brain > function.http://space.mit.edu/home/tegmark/brain.html > Tegmark makes a case for brain function being modeled adequately with > classical theoretical means (possibly such as Turing machines) and > that brains do not function like quantum computers. (Essentially the > main factor is that the brain is not nearly at absolute zero degrees, > or otherwise in an environment in which superposition type effects > that consciousness apparently mimics well enough to keep many on the > fence, is more common than Earthly temperatures where our brains > normally reside.) > If Tegmark does prove his point, while others in his community remain > skeptical that brain function is +not+ an example of a quantum > computer, then the paper I cited about the non-computability of > consciousness does not invalidate Tegmark's CUH, mentioned in section > VII of the first link in the first post. The non-computability of > consciousness would seem to invalidate Tegmark's CUH (Computable > Universe Hypothesis) in that the universe, by even a narrow definition > of universe, must contain consciousness, and, I presume, non- > computability of consciousness would imply the CUH is false. That is, > unless consciousness can have non-computable aspects that when > "glued" (ultraproduct or some other method of "gluing"???) together > throughout the universe, somehow (I know this is vague) the non- > computable aspects of various parts of the universe all balance out to > a computable universe. Hmm...things to think about... Maybe the CUH > is true and brains work like quantum computers, somehow...? > Anyway, Tegmark would be lending credence to his point by invalidating > the proof of non-computability of consciousness for that relies on the > "presumption" that consciousness is inherently a quantum process; > obviously if their critical "presumption" is wrong, then their > conclusion (consciousness not being computable) isn't necessarily so. > I think it is worth splitting hairs here about the difference between > consciousness and brain function but as of yet am aware of very little > of the +formal+ theory behind either of these notions, > philosophically, psychologically, or cognitive-scientifically. > I am compiling a list of other discussion points. > First on this list of discussion points, I will make a connection to > abstract fuzzy logic and the Level IV multiverse situation. If you > haven't read these fascinating articles yet, Level IV's brief > definition is: > Other mathematical structures give different +fundamental+ equations > of physics. > In the MUH article (first link, first post), appendix A defines what > Tegmark means by a mathematical structure. > [Compilation Process] I'm thinking of whether or not the aggregate of > all MS's can be "glued" together somehow (doubtfully by a simple > union) in order to get the MS of all MS's. > This brings me to the connection to abstract fuzzy logic and my > personal quest to continue my education in the area of Fuzzy Logic. > (Apparently, no one in the US works specifically in the area I want to > work in but there are many in Europe at institutions that award > Phds.) It also gratifies me, on a personal note, to think that my > research, if carried out, might settle some question about whether or > not the [Compilation Process] is at all possible in any "reasonable" > sense whatsoever. It would be nice to know either way, rather than a > "this smells like Russell's Paradox, so let's not try it" sort of > deal. > My research would focus on somewhat recent papers on fuzzy logic > pertaining to involving FL at the axiomatic level to create > generalizations and anti-generalizations of ZFC set theory, or other > suitably modified set theory (eg, remove Foundation Axiom immediately > for reasons that would be clear later). > According to the conclusion of that paper, linked to below, an open > problem is figuring out how other axioms could be, should be, > shouldn't be, and can't be consistently added to the list of axioms > they present in a FL-sense. > [[1]]http://citeseer.ist.psu.edu/cache/papers/cs/22478/http:zS zzSzwww.cs.c... > In an effort to push question (2) in a particular direction, let me > attempt to formulate my question/problem. Start with the bare-bones > fuzzy set theory presented in [[1]]. Let the truth set be denoted D. > Consider the following axioms: > [[U.Strong]] there is a y such that for all x, the truth degree of > the formula "x is in y" is the maximal (in the sense appropriate to > the type of algebraic structure D has, such as an MV-algebra, but > definitely not Boolean as we know Russell's Paradox +will+ rear its > ugly head in the Boolean case) element in D. > In other words, if the maximal element in D is equipped with the > baggage "true", U.S. says there is a set y for which all sets x are > elements of y. This is one reason to drop the Foundation Axiom > immediately, as such a y is obviously not well-founded. This could be > called a (strong) universal set, with appropriate adjectives that > reference D and the syntactical entailment axioms used, the underlying > language, etc... > [[U.Weak]] there is a y such that for all x, the truth degree of the > formula "x is in y" is a designated element of D. > In words, I view the designated, anti-designated, and non-designated > partitions of D as shades of gray of truth. Designated means more > light than not, where light = truth in this analogy, anti-designated > means more dark than not, and non-designated means more gray than > not. So to say " 'x is in y' is a designated truth value" would mean > something like, "it's essentially true that y is a universal set." > One could say that y would be a weak universal set and it is doubtful > that such a y need be unique, unlike a strong universal set is. > That sets (pun intended) up the problem (below) that I hope to > formalize into the beginnings of a PhD thesis in the area of FL > someday. > Let R be some type of unary predicate. > Recall that D is the set of truth degrees, with some algebraic (eg, > MV) structure associated with it. > Consider the statement below: > [[Statement]] A fuzzy set theory, starting with the one in [[1]], > without Foundation, plus either the strong or weak universal set > axiom, is consistent relative to ZFC (the best situation one can hope > for) if and only if R(D). > The question: Determine for what R is the above statement true, if > any, or prove that for all R, the above statement is false. > Obviously, I want, at worst, an existence proof on R, that there are > some properties D could possess that enables a fuzzy universal set > theory that is consistent relative to ZFC. > Also, I strongly hope that the statement is not false for all R, that > there aren't any exotic D's or structures they could be equipped with, > to make a universal set theory as consistent as ZFC. Clearly, if D = > {0,1} then the set of all R's for which [[Statement]] is true is empty > (bad but expected and well known). In the binary logic case, > Russell's Theorem proves that the set of all R's for which > [[Statement]] is true is empty. No properties on D make the universal > set a possibility in classical logic (except possibly the work of the > sort Quinne did with the New Foundations although, in NF, Choice must > be dropped, in some sense, which is highly disadvantageous to anyone > who enjoys using Zorn's Lemma). > (I posed this to someone known in the area of FL and he encouraged me > to come to Europe (as apparently no one does this type of work in FL > in the U.S.) to formally work this into a PhD thesis.) > Now, ultimately, the connection to the CUH is that if there is an > ultimate set of +some kind+, like a strong universal set, then perhaps > that could provide a link to the MS of all MS's, ie, the mathematical > structure of all mathematical structures, without leading to deals > like, "this smells like Russell's dirty laundry, so let's not go > there." > <punchline tag> > Either that or provide an interesting, to say the least, MS (a fuzzy > and strong universal set theory) to investigate in the context of the > MUH, as this strong universal fuzzy set may, in fact, be a candidate > for what the universe literally is in a physical sense, assuming the > MUH, of course. > </punchline tag> > If I could make all of that work, I would be a very happy man. Even > if I ... read more " Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. Brian View profile More options Mar 4, 2:38 pm Newsgroups: sci.logic From: Brian <[EMAIL PROTECTED]> Date: Tue, 4 Mar 2008 14:38:26 -0800 (PST) Local: Tues, Mar 4 2008 2:38 pm Subject: Re: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author A paradox??? http://www.torrentreactor.net/torrents/1588942/Parallel-Worlds -Parall... There is one part when Tegmark is speaking, around the 27-30 minute mark or so, that they give a visual clue about parallel universes that was perhaps more interesting than the director realized, unless the director's assistant was Tegmark himself. When they showed two universes splitting, in one parallel, the Copenhagen interpretation is correct...and in the other, the Many Worlds interpretation is correct. There is a QM formula with [[[EXCEPT DURING OBSERVATION]]] in one half of the screen and in the other half of the screen, [[[EXCEPT DURING OBSERVATION]]] is + +crossed out++ by Tegmark. Interestingly, part of Tegmark's work says just that: not only do physical things split into parallels, but the laws of physics themselves are different in different universes. +++Therefore, The Copenhagen view is correct and the Many Worlds interpretation is correct.+++ But which is correct in THIS universe? Or, maybe, that is a loaded question. More details on why that might be a loaded question has to do with my crew's speculation about there not just being parallel universes but also "overlaying" (or overlapping) of parallels, where the aggregate of parallels (aka, the universe) are (is) very much like the water system on earth: separate at times and other times, quite combined and overlaid upon one another. Indeed, if one "frog" is floating on the river, the "bird" sees the "frog" actually pass from the North Pole somehow through down to the Nile, passing thousands of different waterways in between, and the "frog" just thinks he has been in one body of water all along, which couldn't have been more wrong, at least, as far as the "bird" sees things. Then again, is there a bird's "bird?" And a bird's bird's bird? And a bird's bird's bird's bird? And do frogs have pets? Do those pets have pets? Do those pets have pets that have pets? Sound familiar? To me it sounds like a self-similar fractal and the way the universe would look if you started at a string and zoomed out to view the universe from the boundary of the universe, which might not "exist", unless the boundary of the universe exists mathematically, of course! I suppose one might want to push the envelope of mathematics to determine what the boundary of the universe is, to mightily abuse language. Well, assuming the MUH, this overlaying of parallels +must+ be the case due to the hierarchical nature of mathematics. Set theory is on a +somewhat+ lower echelon in the hierarchy than Category Theory, which is, on a lower echelon than Logic which is, in turn, on a lower echelon than Fuzzy Logic, a generalization of Logic. Perhaps instead of the ultimate set, I need to search for the ultimate math, but I think Logic and Model Theory and/or Cat might be that, except Logic does have its limitations, in some sense. Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. Brian View profile More options Mar 4, 3:06 pm Newsgroups: sci.logic From: Brian <[EMAIL PROTECTED]> Date: Tue, 4 Mar 2008 15:06:35 -0800 (PST) Local: Tues, Mar 4 2008 3:06 pm Subject: Re: Any interest in discussing Tegmark's Mathematical Universe Hypothesis? Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author On Mar 4, 2:38 pm, Brian <[EMAIL PROTECTED]> wrote: - Hide quoted text - - Show quoted text - > A paradox??? > http://www.torrentreactor.net/torrents/1588942/Parallel-Worlds -Parall... > There is one part when Tegmark is speaking, around the 27-30 minute > mark or so, that they give a visual clue about parallel universes that > was perhaps more interesting than the director realized, unless the > director's assistant was Tegmark himself. > When they showed two universes splitting, in one parallel, the > Copenhagen interpretation is correct...and in the other, the Many > Worlds interpretation is correct. > There is a QM formula with [[[EXCEPT DURING OBSERVATION]]] in one half > of the screen > and > in the other half of the screen, [[[EXCEPT DURING OBSERVATION]]] is + > +crossed out++ by Tegmark. > Interestingly, part of Tegmark's work says just that: not only do > physical things split into parallels, but the laws of physics > themselves are different in different universes. > +++Therefore, The Copenhagen view is correct and the Many Worlds > interpretation is correct.+++ > But which is correct in THIS universe? > Or, maybe, that is a loaded question. More details on why that might > be a loaded question has to do with my crew's speculation about there > not just being parallel universes but also "overlaying" (or > overlapping) of parallels, where the aggregate of parallels (aka, the > universe) are (is) very much like the water system on earth: separate > at times and other times, quite combined and overlaid upon one > another. Indeed, if one "frog" is floating on the river, the "bird" > sees the "frog" actually pass from the North Pole somehow through down > to the Nile, passing thousands of different waterways in between, and > the "frog" just thinks he has been in one body of water all along, > which couldn't have been more wrong, at least, as far as the "bird" > sees things. > Then again, is there a bird's "bird?" > And a bird's bird's bird? > And a bird's bird's bird's bird? > And do frogs have pets? > Do those pets have pets? > Do those pets have pets that have pets? > Sound familiar? To me it sounds like a self-similar fractal and the > way the universe would look if you started at a string and zoomed out > to view the universe from the boundary of the universe, which might > not "exist", unless the boundary of the universe exists > mathematically, of course! I suppose one might want to push the > envelope of mathematics to determine what the boundary of the universe > is, to mightily abuse language. > Well, assuming the MUH, this overlaying of parallels +must+ be the > case due to the hierarchical nature of mathematics. Set theory is on > a +somewhat+ lower echelon in the hierarchy than Category Theory, > which is, on a lower echelon than Logic which is, in turn, on a lower > echelon than Fuzzy Logic, a generalization of Logic. Perhaps instead > of the ultimate set, I need to search for the ultimate math, but I > think Logic and Model Theory and/or Cat might be that, except Logic > does have its limitations, in some sense. The only problem is that Aristotle's mutual exclusivity might not actually be universal, to resolve this apparent paradox. But even within one parallel (mathematical structure?), ME (mutual exclusivity) might be true in one region of space (ie, the context between and containing mathematical structures), false in another, both true and false in still another part of that parallel, and absolutely all values of truth between true and false elsewhere in that parallel universe. It seems somewhat mind boggling when pondering that. In our "neck of the woods," I think ME is "almost" (sort of in a Lesbegue measure sense) true. In other words, locally to myself and probably you as well (whatever that might mean), the pseudo-well- formed-formula below has a ++designated++ truth value in some truth set D: ' for all wffs f, ( f & not(f) ||--> ^D) ' where ^D is the minimal element in D, or an arbitrarily chosen representative of the ones of equally least value, respective of the order on D. ^D is interpretable as the qualia FALSE. In fewer words (in English): "locally," D+( W(f)-->( f & not(f) ||--> ^D) ) where D+( ) means, "the truth degree of what follows is designated," and W( ) means, "what follows is a well formed formula," and ||--> means there is a fuzzy logical sort of valuation function being applied, and --> is the standard (in a fuzzy logical sense, of course, but the truth set of this symbol definitely need not also be D--too bad tex is not available to my knowledge here, that would make this notation less unappealing to the eye) conditional connective. (I think all of this is formalizable.) I think in our dreams (double entendre intended), ME is "almost" false, ie, D-( W(f)-->( f & not(f) ||--> ^D) ) where D-( ) means, "what follows has an anti-designated truth degree." Perhaps that could be related to the true difference between conscious and unconscious. Conscious could mean something like X( D+( W(f)-->( f & not(f) ||--> ^D) ) ) and unconscious could mean something like X( D-( W(f)-->( f & not(f) ||--> ^D) ) ) where X( ) means something like, "in the context of the the parallel network SAS labeled X is embedded or embeddable within, the following is true." Reply Reply to author Forward You must Sign in before you can post messages. To post a message you must first join this group. Please update your nickname on the subscription settings page before posting. You do not have the permission required to post. 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