tag:blogger.com,1999:blog-15005476.post3547463740367667598..comments2016-08-31T13:30:34.405-04:00Comments on Rationally Speaking: Mathematical Universe? I ain’t convincedAnonymousnoreply@blogger.comBlogger190125tag:blogger.com,1999:blog-15005476.post-3302806038479840082014-03-27T08:47:25.790-04:002014-03-27T08:47:25.790-04:00Hi Nick,
I would prefer to have this conversation...Hi Nick,<br /><br />I would prefer to have this conversation via another forum because I feel that Massimo has better things to do with his time than to have to approve moderation on comments between us that nobody else is likely to be reading, especially now that he has moved on from Rationally Speaking and onto Scientia Salon.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-68233901952723373362014-03-27T01:43:45.580-04:002014-03-27T01:43:45.580-04:00I suspect that Mathematical Platonism (MP), as a p...I suspect that Mathematical Platonism (MP), as a philosophical position about a “true” aspect of reality, is area that sits outside the empirical reach of science. It's adjacent. However at the same time I think that pairing Max Tegmark’s ideas with MP would be an unjustified conflation. <br /><br />I think the MP position, for example that “there exists” an infinite number of prime numbers regardless of whether we know about them or not, or that mathematical entities are not constituents of the spatio-temporal realm, is not the same as a position that abstract mathematical structures are a self-creating engine of creation. <br /><br />The first is passive (“prime numbers exist even if we don’t”), whereas the second is active (“the prime numbers got together one day somewhere outside of time and space and decided to create a Universe”). So I don’t see how Max Tegmark’s ideas are the same thing as MP – maybe they do start there but they quickly leave it in the dust. <br /><br />“Abstract Math as Creator” implies that mathematical machinery is operating in a manner whereby things including spacetime are created, whether or not this engine of creation is envisaged as occurring inside or outside of time and space. This is equivalent to the concept of God creating everything from outside time and space. A new label for an old idea? <br />Nick Kimhttp://www.blogger.com/profile/05733237253599715034noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-23477846912302823362014-03-26T16:10:52.092-04:002014-03-26T16:10:52.092-04:00Hi Nick,
Mathematical Platonism is quite a popula...Hi Nick,<br /><br />Mathematical Platonism is quite a popular view among philosophers and mathematicians, and perhaps physicists too. There are many who doubt it but it is far from a fringe view.<br /><br />Granted, I think it would have been good for Tegmark to make the dependency of the MUH on mathematical Platonism more clear. He seems to take Platonism as a given without giving much thought to defending it.<br /><br />That said, I do think mathematical Platonism is more defensible than the alternative. I have some thoughts on this on my blog also.<br /><br />http://disagreeableme.blogspot.co.uk/2013/10/mathematical-platonism-is-true-because.html<br /><br />This doesn't specifically address your argument, but if I could respond very quickly to your point I would say that it is a mistake to think of calculations or computations taking place to breath life into the universe. The mathematics defines (or is) the universe, there is no computational process which sustains it. Processes require time and there is no time outside the universe.<br /><br />If you would be interested in a more detailed discussion then you can reach me via my blog.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-91051754116227904812014-03-26T13:05:42.540-04:002014-03-26T13:05:42.540-04:00Thanks DM
Thank you for setting out your argument...Thanks DM<br /><br />Thank you for setting out your arguments there. From your blog post I see that the hypothesis rests on this statement as one of three "crucial premises":<br /><br />All mathematical objects exist abstractly and independently of minds <br /><br />...and what I'm saying is that there is no evidence that mathematics, or mathematical systems or patterns, can ever exist in the absence of a physical framework. There is simply no evidence for this, whether the math is being done in a brain, on paper, in a computer, or anywhere else. It would appear that the enactment of any mathematical operation presupposes the existence a medium in which the operation is carried out.<br /><br />I think it is the idea that abstract mathematics is inherently so pure and unsullied (so abstract) that it is able to exist independently (of anything) where this theory seems to have gone off the rails.<br /><br />To my mind all this does is replace the God concept with Abstract Mathematics. Is this really an improvement?<br /><br />- Nick<br /><br /><br />Nick Kimhttp://www.blogger.com/profile/05733237253599715034noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-84593886601757128052014-03-26T06:58:46.629-04:002014-03-26T06:58:46.629-04:00I think the conversation here is over, and this we...I think the conversation here is over, and this website is somewhat retired.<br /><br />But I can invite you to read the following for a discussion of the motivation for the MUH.<br /><br />http://disagreeableme.blogspot.co.uk/2013/12/the-universe-is-made-of-mathematics.html<br /><br />Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-13173013011637417362014-03-26T04:02:00.818-04:002014-03-26T04:02:00.818-04:00...I’m writing this after the recent groundbreakin......I’m writing this after the recent groundbreaking discovery of the imprint of gravitational waves in the cosmic background radiation – another reminder that our space-time itself is a substrate. Okay spacetime itself might be made of mathematical operations, but why would those operations not be on some other, more fundamental, substrate?<br /><br />The jump from reality acts in a mathematical way to reality is math seems to me to be the same type of leap as moving from mind as embodied and realized in a brain, and a soul or spirit that is somehow independent of the brain. Again, it’s possible, but the evidence so far isn’t very good. Even if that were true, we could posit that the wavefunction of any disincarnate soul would probably need to exist within some other undiscovered substrate, rather than being substrate-free.<br /><br />I wonder whether Max Tegmark would mind admitting back a possibility that in our observable Universe, the likely Type I and II Multiverses, the postulated Type III Multiverse, and possible Type IV Multiverses, mathematical operations might always require substrata, and probably motive power, for their realization? Why not entertain the idea of math plus substrata, and see where that leads? <br /><br />An implication of this line of thought (positing math + substrate + energy which I think might equal computation) might be that the nature of the substrate determines which mathematical operations would be allowed, and which are forbidden (in a quantum mechanical sense). <br /><br />Existence of a single unified substrate could therefore rule out many types of Type III or Type IV Multiverses. Alternatively, substrata might vary between Universes, with the mathematical operations playing out in each being limited by constraints imposed by the substrate or substrata within each. This would also rule out many types of Type III or Type IV Multiverses, but we’d never know which ones.<br />Nick Kimhttp://www.blogger.com/profile/05733237253599715034noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-58155598644602089022014-03-26T03:49:37.301-04:002014-03-26T03:49:37.301-04:00I’m not sure why Max Tegmark felt it was necessary...I’m not sure why Max Tegmark felt it was necessary to jump from positing a reality either controlled in a computational sense by mathematics, or described by mathematics, to a reality which is mathematics. I’ve read his book now after enjoying the podcast. I’ve found many useful ideas and concepts explained in the book, such as the importance and predictive power of inflation and the implications of non-collapse of the wavefunction, and I really don’t have a problem with most of this material – it’s very good. <br /><br />However I am mystified about what evidence is driving the apparent position that reality is mathematics. It’s clear enough that the most basic properties of particles of strings can be described as being equivalent to a mathematical description, but can’t see why this would mean that these mathematical functions would not be being played out, or realised, in the form of operations applied to a substrate.<br /><br />For me, the nub of the problem is this: there is no evidence that mathematics can exist in the absence of a substrate.<br /><br />I’m a chemist. I know that physicists and mathematicians are used to distinguishing between abstract and applied mathematics, so at first this idea itself may sound surprising. But when you think about it, there can be no such thing as completely pure or abstract mathematics, because no mathematical operations can be enacted outside a physical framework, or at least there is no evidence that this could happen. <br /><br />Dubious? How do you calculate 2 x 2? <br /><br />It’s not abstract at all: you need a consciousness housed inside a brain to calculate 2 x 2. Energy is expended. <br /><br />There’s no evidence that 2 x 2 computations are being carried out in some non-physical non-reality which somehow gives rise to a physical reality, as a consequence of their being carried out nowhere and notime in particular. <br /><br />I’m not saying it might not be happening – I’m just saying that there is no evidence that mathematics independent of substrate could happen, and no examples exist that I know of, and I might not understand Max Tegmark’s arguments but I don’t think he provides any. A second related problem from the brain analogy is that realization of mathematical operations should also require energy, or motive power, whatever this means and wherever it comes from...<br />Nick Kimhttp://www.blogger.com/profile/05733237253599715034noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-71780529380083411562014-01-20T12:14:49.213-05:002014-01-20T12:14:49.213-05:00"There are other problems with MUH. For one, ..."There are other problems with MUH. For one, several critics of Tegmark’s ideas have pointed out that they run afoul of the seemingly omnipresent (and much misunderstood) Gödel’s incompleteness theorems."<br /><br />Are you saying there is conceptual evidence against MUH? Or are you only saying that it is premature to claim that MUH is at all probable rather than theoretically possible? littlespoon99http://feministx.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-60214163043438455592014-01-07T19:54:10.103-05:002014-01-07T19:54:10.103-05:00Hi Tomas,
I think it's not really correct to ...Hi Tomas,<br /><br />I think it's not really correct to call the Godel statement more than just mathematical. It really is mathematical, in syntax and in semantics and even in derivation. It is derived mathematically, just not within the mathematical operations allowed within a specific system. I really think it's a stretch to think it is metaphysically somehow more.<br /><br />Even without Godel sentences, there are plenty of perfectly ordinary mathematical conjectures which may well be true but have resisted attempts to prove them (The Goldbach Conjecture is my go-to example). Some of these likely are both true and impossible to prove.<br /><br />That does not, to my intuition, imply that they are in any way mysterious or transcendent. Your mileage may vary!Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-29837042695464941782014-01-07T18:56:02.009-05:002014-01-07T18:56:02.009-05:00Hi DM,
"I honestly don't see how you can...Hi DM,<br /><br />"I honestly don't see how you can get from the idea that there are true unprovable statements to an explanation of physicality and consciousness, unless by some form of very loose analogy."<br /><br />Yes, I don't know how to add much clarity to this idea, also due to the fact that I don't really understand the details of Godel's theorem. It just seems to me intuitively that if you can get an underivable object (a true unprovable statement) from a mathematical structure then perhaps this object might have a quality that seems more than just mathematical, simply because it cannot be derived from the mathematics.<br /><br />Consciousness seems to be a similar example of this phenomenon: it is believed to be resulting from a pattern of neuronal firings but is notoriously resistant to derivation from this pattern. You arrange neurons in a certain way, let them fire in some sequence or accord, and bang! - red color appears. In this case, the Godelian transition would be from a physical structure to a consciousness structure. <br />Tomas Paleshttp://www.blogger.com/profile/17752614252899277481noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-58600181596865145152014-01-07T18:24:46.585-05:002014-01-07T18:24:46.585-05:00To clarify my last sentence:
> I'm not sure...To clarify my last sentence:<br />> I'm not sure that is really of any great significance... <<br />... to any but mathematicians and philosophers of mathematics.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-15503024077524220882014-01-07T18:15:55.268-05:002014-01-07T18:15:55.268-05:00Hi Tomas,
Personally, I don't think there is ...Hi Tomas,<br /><br />Personally, I don't think there is anything inconceivable about how the physical world or consciousness could emerge from a mathematical structure, even without bearing Godel in mind.<br /><br />I would be very wary about invoking Godel as an explanation because there is a general tendency to explain consciousness by a vague appeal to whatever the mystery of the day might be. For example, there are many people who think consciousness must have something to do with quantum mechanics simply because both are weird and defy intuitive explanations.<br /><br />Your appeal to Godel seems to be of this nature to me. I honestly don't see how you can get from the idea that there are true unprovable statements to an explanation of physicality and consciousness, unless by some form of very loose analogy.<br /><br />I would resist your characterisation of true unprovable statements as axioms. I think an axiom is a fundamental statement of a mathematical system that is chosen somewhat independently of other axioms, whereas the true unprovable Godel statements are actually derived (indirectly) from the other axioms.<br /><br />(Although, admittedly I have said in comments elsewhere that we can adopt these Godel statements as axioms for new systems).<br /><br />I'm not sure it's fair to say that the original system is bigger than it seemed, as the full scope of the derivable statements of any system is generally unknown. We start with axioms and then the mathematicians see what they can make of them. Godel only shows that what is true is a larger set than what is provable. I'm not sure that is really of any great significance.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-71981197097928694682014-01-07T17:43:57.112-05:002014-01-07T17:43:57.112-05:00I like Tegmark's simple idea that reality is a...I like Tegmark's simple idea that reality is a mathematical structure, but it seems inconceivable how our physical world with material objects might emerge from (or within) this mathematical structure. I wonder if Godel's incompleteness theorem may actually be the bridge between purely mathematical structures and physical structures, or even consciousness.<br /><br />I am no expert on Godel's theorem but from what I've seen it says that within a mathematical structure of sufficient complexity (being able to incorporate arithmetic or something like that) necessarily exist entities or truths that cannot be derived from this structure. So these strange entities are actually new axioms that expand what seemed like a complete structure, and it turns out that the structure is bigger than it seemed. <br /><br />So how do you derive physics from arithmetic, or consciousness from arithmetic? The answer might be that you can't. And yet arithmetic may give rise to both physical objects and consciousness - in a Godelian fashion.Tomas Paleshttp://www.blogger.com/profile/17752614252899277481noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-31698980235220734132014-01-05T18:53:46.950-05:002014-01-05T18:53:46.950-05:00Hi Alastair,
>The Absolute Infinity is an &quo...Hi Alastair,<br /><br />>The Absolute Infinity is an "infinity of infinities."<<br /><br />The absolute infinity is an infinity greater than all other infinities. (I think it's clearer to talk in terms of greater than or less than. I'm not really sure it's clear what an infinity of infinities means.)<br /><br />You gave examples of an infinity (the cardinality of the set of real numbers) which is greater than certain other infinities (e.g. the cardinality of the set of natural numbers). Yet there are infinities which are greater than the cardinality of the set of real numbers. You have not established that there is a coherent concept of an absolute infinity than which there is no greater infinity.<br /><br />> Russell's paradox (I believe that is what you are referring to) never invalidated Cantor's naive set theory.<<br /><br />I didn't say it did. I said the set of all sets was invalid in Zermelo-Fraenkel set theory, and that the argument you had presented for the infinity of infinities was analogous to an argument for the set of all sets. Since your argument wasn't specific to any specific set theory, the conclusion you are drawing is questionable at best.<br /><br />However, if it's true that Cantor's set theory is not axiomatised then it's impossible to say what does or does not work in it because it's vague. Nothing can be proven either way without axiomatisation.<br /><br />>The bottom line is that information processing is a dynamic process, not a static structure.<<br /><br />Agreed. So what? I'm arguing that the universe is a mathematical structure not a running computer process. A computer process allows us to explore certain mathematical structures. It is not the structure itself. If you want to explore causality under the MUH, I have already posted a new start to that conversation I hope you will pick up.<br /><br />>The bottom line is that human intelligence will always be able to take one step more beyond any computer program that has ever been written.<<br /><br />So what? We're agreed that no human-intelligent computer program has ever been written.<br /><br />If you mean that humans can in principle take one step further than any conceivable computer program, you're dead wrong. Godel doesn't prove that at all. If there was a straightforward way to do that trick, you could write a computer program to do it. If there isn't a straightforward way to do it (and there isn't), eventually it becomes too difficult as the program becomes too complex until you get to a point where no human can take that step. Godel only proves that it's possible to do it in principle, not that a human can do it in practice.<br /><br />>It is according to Godel.<<br /><br />No it isn't. Godel's proofs do not apply to all theories, but only to theories of a certain minimum power. But that's nitpicking. Unfortunately you seem to have entirely ignored the correction I posted shortly after this:<br /><br />"what I meant to say here was that it is not true that there are sentences in all systems which humans can see are true but cannot prove within the system."Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-66827484588178536432014-01-05T16:06:24.577-05:002014-01-05T16:06:24.577-05:00@ Disagreeable Me
> You demonstrated that an i...@ Disagreeable Me<br /><br />> You demonstrated that an infinity can contain infinities. You manifestly did not demonstrate that the absolute infinity is coherent <<br /><br />The Absolute Infinity is an "infinity of infinities." And you previously argued that an "infinity of infinities" is not a coherent concept. I responded to that argument by clearly demonstrating that it was not only a coherent concept, but also a mathematical fact.<br /><br />> Your argument is just like an argument for the set of all sets by giving examples of sets which contain sets. < <br /><br />You appear to be mistaken. <a href="http://en.wikipedia.org/wiki/Russell%27s_paradox" rel="nofollow">Russell's paradox</a> (I believe that is what you are referring to) never invalidated Cantor's naive set theory. (It was Frege's naive set theory, not Cantor's.)<br /><br />"<i>Cantor was aware of some of the paradoxes and did not believe that they discredited his theory. Gottlob Frege explicitly axiomatized a theory in which the formalized version of naive set theory can be interpreted, and it is this formal theory which Bertrand Russell actually addressed when he presented his paradox</i>." (source: Wikipedia: <a href="http://en.wikipedia.org/wiki/Naive_set_theory" rel="nofollow">Naive set theory</a>)<br /><br />> Yes, a running computer process which processes information is a dynamic process, e.g. a process which renders the Mandelbrot Set to a computer screen. What it actually ends up computing is a static mathematical structure, e.g. the Mandelbrot Set itself. The program itself (as opposed to the process which runs the program) is also a static mathematical structure. <<br /><br />The bottom line is that information processing is a dynamic process, not a static structure. And there is nothing in your above response that would suggest otherwise. (That a computer program and the input information it processes may be static does not change the fact that the information processing itself is not.)<br /><br />> It has been established that for any specific computer, there are true statements that specific computer can never prove. This is actually quite different, because for any statement unprovable by computer program A, there may exist a computer program B which can prove it. <<br /><br />The bottom line is that human intelligence will always be able to take one step more beyond any computer program that has ever been written. <br /><br />> It's also not true to say that there are true but unprovable statements in *any* theory. <<br /><br />It is according to Godel. Alastair Paisleyhttp://www.blogger.com/profile/07422653606947285608noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-70498554046520726842014-01-04T16:22:38.811-05:002014-01-04T16:22:38.811-05:00>It's also not true to say that there are t...>It's also not true to say that there are true but unprovable statements in *any* theory. <<br /><br />Sorry, what I meant to say here was that it is not true that there are sentences in all systems which humans can see are true but cannot prove within the system. Some systems may be too complex for humans to construct such Godel sentences.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-14730941168435679552014-01-04T15:40:55.114-05:002014-01-04T15:40:55.114-05:00Hi Alastair,
I think the issue of causality in th...Hi Alastair,<br /><br />I think the issue of causality in the MUH is something that deserves it's own thread. I want to explain how I account for what appears to be causality and I want to understand your objections to it.<br /><br />Firstly, some questions.<br /><br />1. Are you familiar with Conway's Game of Life? If not can you read about it a bit?<br /><br />2. I want to adopt the universe of the GoL as a toy model for a mathematical universe. Can we for the sake of argument pretend that this universe contains intelligent observers?<br /><br />Can you perhaps outline your initial thoughts on whether this universe has causality or not, and compare the causality in this universe with that of ours? How do we know we are not in such a universe?Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-53893652682988023512014-01-04T15:34:46.915-05:002014-01-04T15:34:46.915-05:00> I clearly demonstrated to you that it is not ...> I clearly demonstrated to you that it is not only a coherent concept, but a mathematical fact.<<br /><br />No you didn't. You demonstrated that an infinity can contain infinities. You manifestly did not demonstrate that the absolute infinity is coherent. Your argument is just like an argument for the set of all sets by giving examples of sets which contain sets.<br /><br />>Information processing is a dynamic process, not a static structure.<<br /><br />Yes, a running computer process which processes information is a dynamic process, e.g. a process which renders the Mandelbrot Set to a computer screen. What it actually ends up computing is a static mathematical structure, e.g. the Mandelbrot Set itself. The program itself (as opposed to the process which runs the program) is also a static mathematical structure.<br /><br />>The onus is upon you (not me) to refute Squire's argument. I have already stated it in a previous post. It was a very succinct argument. No counterargument was forthcoming.<<br /><br />It is very disingenuous to say that no counterargument was forthcoming. Once again, read this: http://disagreeableme.blogspot.co.uk/2013/02/strong-ai-godel-problem.html<br /><br />>(If you can't furnish me with a succinct counterargument, then you really don't have one.)<<br /><br />Yeah, but then you're going to respond to that, and my answer to your response is probably already covered on my blog. If you want to discuss it then my blog is a better place to do it because it's of minimal relevance to this post.<br /><br />But if you want a succinct argument, here goes:<br /><br />Squires:<br />>there are true statements in any theory which a computer can never prove, but which we can see are true. It appears that conscious minds can learn things about any logical system that a computer, following the rules of the system, can never discover.<<br /><br />This argument is based on a gross oversimplification and overinterpretation of the incompleteness theorems. This concise, succint argument is riddled with problems.<br /><br />Firstly, it has not been established that there are true statements which no computer can ever prove. It has been established that for any specific computer, there are true statements that specific computer can never prove. This is actually quite different, because for any statement unprovable by computer program A, there may exist a computer program B which can prove it.<br /><br />However, it is actually quite possible that there are statements that no computer can prove, but then it is just as possible that these statemetns cannot be proven by any human mathematician. There are plenty of unproven conjectures in mathematics which seem to be true but have never been proven. There is no reason to suppose they ever will.<br /><br />It's also not true to say that there are true but unprovable statements in *any* theory. There may be theories too complex for any human to find those Godel sentences, such as those that correspond to the algorithms of their own brains.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-38818192781214565292014-01-03T23:27:48.679-05:002014-01-03T23:27:48.679-05:00@ Disagreeable Me
> I'm not sure I'm r...@ Disagreeable Me<br /><br />> I'm not sure I'm really enjoying this conversation any more. <<br /><br />That probably explains why you have dispensed with the pleasantries.<br /><br />> I would like to make the general observation that you seem to have very rigid definitions of certain concepts such as "physical" and "causality", and when others take different interpretations you find citations which you think bolsters your claim but really are not that persuasive in light of the differing or more flexible interpretations of your interlocutors < <br /><br />You have already gone on record in this particular thread and stated explicitly that both <i>physicality</i> and <i>causality</i> are illusory. You changed your tune afterwards only because you felt it was necessary to muster some kind of counterargument to mine. (If you completely dispense with causality, then all you have are correlations and observations without any causal explanation. And if your metaphysical theory has no causal explanation, then it explains nothing whatsoever.)<br /><br />> Your answer to my point about infinity was misguided. I never denied that an infinity can contain infinities. I denied that it could contain all infinities <<br /><br />My point about infinity was spot on. You previously argued that an "infinity of infinities" is an <i>incoherent</i> concept. I clearly demonstrated to you that it is not only a coherent concept, but a mathematical fact.<br /><br />> You asked, I answered. I remain unconvinced, although I will admit that I am not *certain* that your God is incoherent. It just seems rather so to me. <<br /><br />I asked, you argued, and I promptly responded. You have completely failed to expose any incoherent aspects with my concept of God.<br /><br />> You're tying me in knots with semantic games. <<br /><br />Puhlease! The only one here playing semantic games is you. <br /><br />> The program is a mathematical object. As it sits on the computer, the program itself is not changing, but change does exist within the scope of the simulation - the ball does move after all. <<br /><br />Information processing is a <i>dynamic</i> process, not a <i>static</i> structure.<br /><br />> Time exists as a concept only within the simulation <<br /><br />By your own admission, there can be no process (simulation) without time. <br /><br />> Honestly, how can you not get this? <<br /><br />The mathematical universe hypothesis is a ridiculous hypothesis for reasons already stated.<br /><br />> If you think I'm deluded about Lucas/Penrose then kindly tell me where I went wrong, otherwise don't mention Lucas/Penrose or Godel to me again. <<br /><br />The onus is upon you (not me) to refute Squire's argument. I have already stated it in a previous post. It was a very succinct argument. No counterargument was forthcoming. (If you can't furnish me with a succinct counterargument, then you really don't have one.)Alastair Paisleyhttp://www.blogger.com/profile/07422653606947285608noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-67416602777798104012014-01-02T21:10:53.178-05:002014-01-02T21:10:53.178-05:00@Alastair
I'm not sure I'm really enjoyin...@Alastair<br /><br />I'm not sure I'm really enjoying this conversation any more.<br /><br />I would like to make the general observation that you seem to have very rigid definitions of certain concepts such as "physical" and "causality", and when others take different interpretations you find citations which you think bolsters your claim but really are not that persuasive in light of the differing or more flexible interpretations of your interlocutors.<br /><br />For example, you take as definitive that the universe is not entirely physical because modern physics thinks of reality of consisting of functions. I'm just telling you that many people will not find this argument persuasive. They will adjust the definition of physical to accomodate these findings rather than concluding that the universe is not physical. I think this is reasonable as long as we understand that what physical must mean, ultimately, is that which the universe consists of. If you think that this is moving the goalposts, that is your prerogative, but I'm just telling you now that you won't persuade anyone by quoting physicists about wave-particle duality because you are ignoring that difference of interpretation.<br /><br />Your answer to my point about infinity was misguided. I never denied that an infinity can contain infinities. I denied that it could contain all infinities, just as a set cannot contain all sets in ZF set theory (that does not mean that a set cannot contain sets).<br /><br />I've probably had enough of going in circles explaining why I think God is incoherent. You asked, I answered. I remain unconvinced, although I will admit that I am not *certain* that your God is incoherent. It just seems rather so to me.<br /><br />If you still can't see how my claim about causality makes sense, then I'm lost. It's really simple. You're tying me in knots with semantic games, but it's really obvious to see what I mean if you just imagine it for a second. Imagine a simple computer program that simulates a ball bouncing. The entire future of that bouncing ball is defined by the source code. The program is a mathematical object. As it sits on the computer, the program itself is not changing, but change does exist within the scope of the simulation - the ball does move after all. Time exists as a concept only within the simulation - the program itself exists eternally and changelessly as an abstract object. I am suggesting the universe is like this. Honestly, how can you not get this?<br /><br />If you think I'm deluded about Lucas/Penrose then kindly tell me where I went wrong, otherwise don't mention Lucas/Penrose or Godel to me again.Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-32303443546954115022014-01-01T03:27:44.744-05:002014-01-01T03:27:44.744-05:00@ Disagreeable Me
> I too think we have lost t...@ Disagreeable Me<br /><br />> I too think we have lost track of what we're talking about with the different interpretations of QM and wave/particle duality. <<br /><br />Correction. You lost track; I did not.<br /><br />> My point was, and continues to be, that this duality does not establish that there is a physical and an abstract component to reality. <<br /><br />My argument is that the Copenhagen interpretation holds that the probability wave function is not an actual physical object. I have furnished you with numerous sources to support that claim. You have furnished me with nothing to counter that claim. <br /><br />> This is not a superficial semantic moving of the goalposts <<br /><br />That's exactly what it is. <br /><br />> Kind of, at least in an ultimate, objective sense <<br /><br />Metaphysics is concerned with ultimate reality. And since we are having a metaphysical debate, that's is what we are concerned with. Clearly, mathematical abstractions are nonphysical. Therefore, mathematical monism qualifies as a (twisted) form of "immaterialism."<br /><br />> The idea of a mind that operates entirely outside of time is nonsensical, as the only coherent concept of a mind that has ever been presented is that of mind as a process, and processes need something analogous to time to function. <<br /><br />You have already conceded in a previous post that information can be timelessly processed if given infinite computing power. <br /><br />> Maybe the hypothetical absolute infinity would be an actual infinity if it existed. My claim is that the absolute infinity (the infinity of infinities), like the set of all sets in Zermelo–Fraenkel set theory, is not a coherent concept <<br /><br />It's easy to demonstrate that one infinity can contain multiple infinities. For example, the set of real numbers, the set of natural numbers, the set of even numbers, and the set of odd numbers - all four sets - are infinite. Nevertheless, the set of real numbers contains the set of natural numbers, the set of even numbers, and the set of odd numbers. So, with this simple example, I have demonstrated that an "infinity of infinities" is not only a coherent concept, but also a mathematical fact. <br /><br />> Yours is that I have not correctly conceived of God. Mine is that a greatest being is actually inconceivable <<br /><br />Paradoxically, it's actually both. In one sense, our <i>finite</i> minds can<i>not</i> conceive of the <i>infinite</i>. Yet, in another sense, they can. That's why the term "infinite" has meaning for most of us who can intuitively embrace this paradox. It's <i>exactly</i> the same thing with "God." <br /><br />"<i>God is that being of whom no greater can be conceived</i>." - St. Anselm <br /><br />> On the B theory of time, the universe is not changing, but we perceive it to be changing as we move through time. <<br /><br />I have already addressed this. The "A-series," "B-series," and "C-series" are terms coined by <a href="http://en.wikipedia.org/wiki/J._M._E._McTaggart" rel="nofollow">.J.M.E. McTaggart</a> in "<a href="http://en.wikipedia.org/wiki/The_Unreality_of_Time" rel="nofollow">The Unreality of Time</a>" in order to argue for his pantheistic idealism, not mathematical monism. (If time is a subjective illusion, then something still has to be causing the illusion. In idealism, that something is "mind" or "consciousness," not some ridiculous mathematical "pseudo-cause.")<br /><br />> I don't see why. If time is an illusion, nothing is ultimately temporal, including brains and computers. I see no conflict with the computational theory of mind. <<br /><br />The computational theory of mind requires that information be processed. According to you, time is required for any kind of processing to take place. So, if time is illusory, then there can be no information processing.<br /><br />> I've already refuted the Lucas/Penrose argument. <<br /><br />Correction. You have deluded yourself into believing that you have.Alastair Paisleyhttp://www.blogger.com/profile/07422653606947285608noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-57371965254656053152013-12-31T16:15:38.347-05:002013-12-31T16:15:38.347-05:00On whether a greatest being is conceivable, you di...On whether a greatest being is conceivable, you didn't answer my point. If I can conceive of a being greater than God, that has two interpretations. Yours is that I have not correctly conceived of God. Mine is that a greatest being is actually inconceivable. Why should I prefer your interpretation to mine?<br /><br />Suppose I ask you to conceive of the greatest possible number. Now I ask you to raise that number to the power of itself. This number must now be greater than the original number. So, does this mean that I didn't correctly conceive of the greatest number, or does it mean that a greatest number is inconceivable? In this case it's clearly the latter. I see the concept of God the same way.<br /><br />>So, he seems to be presupposing some kind of dualism<<br /><br />Not really. He's just doubtful that this particular universe contains any actual infinities. He also has doubts about whether there can be uncomputable universes (which infinities might lead to), a view I don't share.<br /><br />>And since the universe is clearly evolving and undergoing change, then it requires a causal explanation.<<br /><br />Or a pseudo-causal one which is consistent with and explains our observations.<br /><br />Which I have given, but you have not understood. On the B theory of time, the universe is not changing, but we perceive it to be changing as we move through time. Mathematical entailment, as we see in cellular automata, is perfectly consistent with what we perceive as cause and effect, even though you reject it as true causation.<br /><br />>So, if consciousness is not a byproduct of some temporal 'physical' (actually, in your case,"informational" rather than "physical") process, then the "computational theory of mind" is patently incorrect.<<br /><br />I don't see why. If time is an illusion, nothing is ultimately temporal, including brains and computers. I see no conflict with the computational theory of mind.<br /><br />>Godel's theorem demonstrates that...<<br /><br />Alastair, I've already refuted the Lucas/Penrose argument. Again, please read the blog before mentioning Godel to me again. There's really no point in discussing it until you've read my take on it.<br /><br />Here's the link for you again:<br />http://disagreeableme.blogspot.co.uk/2013/02/strong-ai-godel-problem.htmlDisagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-46690272395290684952013-12-31T16:15:21.743-05:002013-12-31T16:15:21.743-05:00Hi Alastair,
I too think we have lost track of wh...Hi Alastair,<br /><br />I too think we have lost track of what we're talking about with the different interpretations of QM and wave/particle duality.<br /><br />My point was, and continues to be, that this duality does not establish that there is a physical and an abstract component to reality. Those who believe reality is physical can simply define "physical" so as to describe whatever reality is fundamentally made of, whether that be waves or particles or probability functions or whatever.<br /><br />This is not a superficial semantic moving of the goalposts, as the physical/abstract distinction is still maintained. There remains a difference between (pseudo-physical?) mathematical functions that describe aspects of the physical universe and those (abstract)functions that do not.<br /><br />>Then it necessarily follows that you neither believe the wave is physical nor the particle<<br /><br />Kind of, at least in an ultimate, objective sense. There is no such thing as an objectively physical universe. But it might make sense to describe the particle or the wave as physical from the point of view of an observer in the universe. "Physical" in this sense means "present in my universe".<br /><br />>I have explained this repeatedly to you.<<br /><br />I feel the same way. This is indeed frustrating.<br /><br />God can be timeless, and God can have a mind, but God cannot have a mind that perceives itself and the universe timelessly. The idea of a mind that operates entirely outside of time is nonsensical, as the only coherent concept of a mind that has ever been presented is that of mind as a process, and processes need something analogous to time to function.<br /><br />>"Classical set theory accepts the notion of actual, completed infinities." <<br /><br />I didn't deny actual infinities. I denied the absolute infinity.<br /><br />>The Absolute Infinity is an actual infinity (or, more specifically, it is the actual "infinity of infinities").<<br /><br />Maybe the hypothetical absolute infinity would be an actual infinity if it existed. My claim is that the absolute infinity (the infinity of infinities), like the set of all sets in Zermelo–Fraenkel set theory, is not a coherent concept.<br /><br />(to be continued)Disagreeable Mehttp://www.blogger.com/profile/15258557849869963650noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-76822294196027059332013-12-31T14:55:22.393-05:002013-12-31T14:55:22.393-05:00@ Disagreeable Me
This is part two.
Anyway, all ...@ Disagreeable Me<br /><br />This is part two.<br /><br />Anyway, all this is a digression. You originally argued (contrary to Anselm) that God cannot be that "<i>being of whom no greater can be conceived</i>," because you believe that you can always conceive of a greater being. And my response to that argument is that if you can conceive of some being greater than the Absolute Infinite, then you weren't conceiving of the Absolute Infinite to begin with. (It's impossible, by definition, to conceive of an infinity greater than the Absolute Infinite. Why? Because the Absolute Infinite is the "Infinity of infinities".)<br /><br />Also, you failed to address the point that I made in regards to Tegmark and his position on actual infinities. He considers all actual infinities to be NONPHYSICAL. So, he seems to be presupposing some kind of dualism - the duality between physical mathematical abstractions and nonphysical mathematical abstractions. This appears to be not only unintelligible, but also contradictory - contradictory to the "monism" in mathematical monism.<br /><br />> I'm not moving the goalposts. We just have different interpretations of what "causality" means. <<br /><br />You originally claimed that your mathematical universe was uncaused. So, I countered by arguing that if you are completely dispensing with causality, then all you have are correlations and observations without any causal explanation. And since the universe is clearly evolving and undergoing change, then it requires a causal explanation. However, your metaphysical theory offers none; therefore, it has no explanatory power whatsoever. After digesting my argument, you panicked and immediately started to engage in spin-doctoring by "moving the goalposts." The rest is on record and I don't think there is any need for me to rehash all the tedious details.<br /><br />> OK, so even if that's the case, what's the problem? <<br /><br />The problem is that <a href="" rel="nofollow">pseudo</a>-causality is not real causality by definition. You're making a spurious argument that explains nothing. Clearly we are experiencing a world of change. And if your metaphysical theory cannot explain that, then it has no explanatory power whatsoever. <br /><br />> OK? <<br /><br />So, if consciousness is not a byproduct of some temporal 'physical' (actually, in your case,"informational" rather than "physical") process, then the "<a href="http://en.wikipedia.org/wiki/Computational_theory_of_mind" rel="nofollow">computational theory of mind</a>" is patently incorrect. <br /><br />> I don't. <<br /><br />Godel's theorem demonstrates that "<i>there are true statements in any theory which a computer can never prove, but which we can see are true. It appears that conscious minds can learn things about any logical system that a computer, following the rules of the system, can never discover</i>." - Euan Squires, pg 150, "Conscious Mind in the Physical World" Alastair Paisleyhttp://www.blogger.com/profile/07422653606947285608noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-59636513929942032892013-12-31T14:49:50.606-05:002013-12-31T14:49:50.606-05:00@ Disagreeable Me
This is part one of a two-part ...@ Disagreeable Me<br /><br />This is part one of a two-part response.<br /><br />> I think that might be close enough to the definition of physical property for some people. <<br /><br />The Copenhagen interpretation says that it isn't. And that's the interpretation that is accepted by the majority of physicists.<br /><br />> Another interpretation might consider the wave function to be physical as it is what the physical world is built of. <<br /><br />But we're debating what the Copenhagen interpretation says about the issue, not what another interpretation might or might not say. (Perhaps I should refresh your memory. I presented Massimo with the argument that nature is fundamentally dualistic - the wave/particle duality. I also argued that this implies that nature has a physical aspect (the particle aspect) and a nonphysical aspect (the wave aspect). I cited numerous sources to support that claim. You took exception to my claim, saying that that was my interpretation of the "wave/particle" duality. I countered that by arguing that that is the Copenhagen interpretation, not my interpretation.)<br /><br />> My position is that there is no physical stuff, and that the concept of an objectively physical universe is incoherent. <<br /><br />Then it necessarily follows that you neither believe the wave is physical nor the particle. So, by arguing for the <i>physicality</i> of the wave, you are actually arguing against mathematical monism and undermining your own position. (IOW, you're engaging in an inherently self-defeating argument. It's bizarre!)<br /><br />> Agreed, but not that such a mind is omniscient. It cannot know what it will think next, because thoughts occur in a sequence, even if that sequence is infinitely fast. <<br /><br />I have explained this repeatedly to you. God's existence is timeless. Unfortunately, you keep placing God in time and presupposing that God has a past and a future. But God does <i>not</i> have any past or future. So, God does <i>not</i> have any past thoughts or future thoughts. In fact, properly speaking, God only has one thought, and it is happening in the ever-present "now." The whole of time (past and future) is, as it were, spread out before God. (Tegmark presupposes something analogous to this timeless state - a.k.a. the "<a href="http://en.wikipedia.org/wiki/Eternalism_%28philosophy_of_time%29" rel="nofollow">block universe or block time</a>" - for his MUH. So, I am failing to see why you can't grasp this.) From God's nontemporal perspective, God sees and responds to all temporal contingencies all-at-once - in one simultaneous act, in one simultaneous thought.<br /><br />> It's not clear from the Wikipedia article that this is accepted as a valid or useful concept by mathematicians in general. <<br /><br />"<i>Classical set theory accepts the notion of actual, completed infinities</i>." (source: Wikipedia: <a href="http://en.wikipedia.org/wiki/Actual_infinity#Classical_set_theory" rel="nofollow">Actual infinity</a>) <br /><br />> An actual infinity is not the same as an absolute infinity. <<br /><br />The Absolute Infinity is an actual infinity (or, more specifically, it is the actual "infinity of infinities").<br /><br />"<i>The <b>actual infinite</b> arises in three contexts: first when it is realized in the most complete form, in a fully independent otherworldly being, in Deo, where I call it the <b>Absolute Infinite</b> or simply Absolute; second when it occurs in the contingent, created world; third when the mind grasps it in abstracto as a mathematical magnitude, number or order type</i>." - Georg Cantor (source: Wikipedia: <a href="http://en.wikipedia.org/wiki/Absolute_Infinite#Cantor.27s_view" rel="nofollow">Absolute Infinite</a>)Alastair Paisleyhttp://www.blogger.com/profile/07422653606947285608noreply@blogger.com