Re: Max Tegmark: The Mathematical Universe
I haven't read Max's latest epistle yet, but I feel the need to respond to your points here. On Fri, Sep 21, 2007 at 05:50:12AM -, [EMAIL PROTECTED] wrote: > > It appears to me that to attempt to reduce everything to pure math > runs the risk of a lapse into pure Idealism, the idea that reality is > 'mind created'. Since math is all about knowledge, a successful > attempt to derive physics from math would appear to mean that there's > nothing external to 'mind' itself. As I said, there seems to be a > slippery slipe into solipsism/idealism here." > The Anthropic Principle prevents the slide into solipsism of an idealist theory. The argument is a little subtle, but I'll try to recap. Basically observed reality cannot be completely arbitrary, as it must be consistent with the observer being embedded in the observed reality. Quite why this should be so in an idealist setting is a little mysterious, but is presumably a requirement of consciousness. > --- > > Another major problem is this idea of pure 'baggage free' description > that Max talks about (the removal of all references to obervables , > leaving only abstract relations). The problem with this , is that, by > definition, it cannot possibly explain any observables we actually > see. Notions of space and agency (fundamental to our empirical > descriptions), cannot be derived from pure mathematics, since these > notions involve attaching additional 'non-mathematical' notions to the > pure mathematics. As I pointed out in another recent thread on this > thread, the distinctions required for physical and teleological > explanations of the world appear to be incommensurable with > mathematical notions. We cannot possibly explain anything about the > empirical reality we actually observe without attaching additional > *non-mathematical* notions to the mathematics. > I suspect this comes from limitations in one's imagination of mathematical structures. For me, maths is all about compression, detecting regularities in systems. I think this leads onto your point below about considering OO systems to be mathematical. > > --- > > There are yet more problems with Max's ideas. For instance, he says > in the New Scientist article that: 'mathematical relations, are by > definition eternal and outside space and time'. Certainly, there have > to be *some* mathematical notions that are indeed eternal and platonic > (if one believes in arthematical realism), but it also makes sense to > talk about some kinds of mathematical objects that exist *inside* > space-time and are not static. As I pointed out in another thread > here, implemented algoithms (instantiated computations) are equivalent > to *dynamic* mathematical objects which exist *inside* space-time: > Indeed, how the "inside view" of a mathematical structure relates to the external view of the structure is unclear. There is a bit of the same problem with Bruno's AUDA too. But there must be such a relationship... > "Let us now apply a unique new perspective on mathematics - we shall > now attempt to view mathematics through the lens of the object > oriented framework. That is to say, consider mathematics as we would > try to model it using object oriented programming - what the classes, > methods and objects of math? This is a rather un-usual way of > looking > at math. Mathematical entities, if they are considered in this way > at > all, are not regarded as 'Objects' (things with state, identity and > behaviours) but merely as static class properties. For instance the > math classes in the Java libraries consist of static (class) > variables > and class methods. > See above.. ... -- 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: Max Tegmark: The Mathematical Universe
Max himself posted about this on the everything-list here: http://groups.google.com/group/everything-list/browse_thread/thread/7da9934267f64acf/690ccf0715150a36#690ccf0715150a36 A popular article was also the feature in last week's 'New Scientist': http://www.newscientist.com/channel/fundamentals/mg19526210.500-mathematical-cosmos-reality-by-numbers.html --- Now is a good time for me to summarize my objections once again. As I said recently to Bruno, here's the problem with the idea that everything is mathematics: "I think we need to draw a careful distinction between the *process* of reasoning itself, and the external entities that reasoning is *about* *(ie what it is that our theories are externally referencing). When you carefully examine what mathematics is all about, it seems that it is all about *knowledge* (justified belief). This is because math appears to be the study of patterns and when meaning is ascribed to be these patterns, the result is knowledge. So: so Math <> Meaningful Patterns <> Knowledge. Since math appears to be equivalent to knowledge itself, it is no surprise that all explanations with real explanatory power must use (or indirectly reference) mathematics. That is to say, I think it's true that the *process* of reasoning redcues to pure mathematics. However, it does not follow that all the entities being *referenced* (refered to) by mathematical theories, are themselves mathematical. It appears to me that to attempt to reduce everything to pure math runs the risk of a lapse into pure Idealism, the idea that reality is 'mind created'. Since math is all about knowledge, a successful attempt to derive physics from math would appear to mean that there's nothing external to 'mind' itself. As I said, there seems to be a slippery slipe into solipsism/idealism here." --- Another major problem is this idea of pure 'baggage free' description that Max talks about (the removal of all references to obervables , leaving only abstract relations). The problem with this , is that, by definition, it cannot possibly explain any observables we actually see. Notions of space and agency (fundamental to our empirical descriptions), cannot be derived from pure mathematics, since these notions involve attaching additional 'non-mathematical' notions to the pure mathematics. As I pointed out in another recent thread on this thread, the distinctions required for physical and teleological explanations of the world appear to be incommensurable with mathematical notions. We cannot possibly explain anything about the empirical reality we actually observe without attaching additional *non-mathematical* notions to the mathematics. "I've talked often about 'the three types of properties' (for my property dualism) : Mathematical, Teleological and Physical. These three properties are based on three different kinds of distinction: Mathematics: The distinction is *model/reality* (or mind-body, information, concept). Teleology: The distinction is *observer/observerd* (self- other or 1st person/3rd person, intention) Physics: The distinction is *here/there* (space, geometry). These are simply three incommensurable types of distinction. You (believers in comp) can try to derieve the observer/observed and here/ there distinctions from the model/reality distinction all you want, you just won't succeed." --- There are yet more problems with Max's ideas. For instance, he says in the New Scientist article that: 'mathematical relations, are by definition eternal and outside space and time'. Certainly, there have to be *some* mathematical notions that are indeed eternal and platonic (if one believes in arthematical realism), but it also makes sense to talk about some kinds of mathematical objects that exist *inside* space-time and are not static. As I pointed out in another thread here, implemented algoithms (instantiated computations) are equivalent to *dynamic* mathematical objects which exist *inside* space-time: "Let us now apply a unique new perspective on mathematics - we shall now attempt to view mathematics through the lens of the object oriented framework. That is to say, consider mathematics as we would try to model it using object oriented programming - what the classes, methods and objects of math? This is a rather un-usual way of looking at math. Mathematical entities, if they are considered in this way at all, are not regarded as 'Objects' (things with state, identity and behaviours) but merely as static class properties. For instance the math classes in the Java libraries consist of static (class) variables and class methods. But consider instead that there could be mathematical 'objects' (in the sense of entites with states, identities and behaviours). What could these mathematical 'objects' look like? if there are mathematical objects they have to be dynamic. This conflicts with standard platonic pictures of math as entities which are ete
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 -~--~~~~--~~--~--~---
