Hi Eugin, > I see, we're at the "prove that the Moon is not made from green cheese > when > nobody is looking" stage. > > I thought this list wasn't about ghosties'n'goblins. > Allright, I seem to have been mistaken about that.
You seem to be getting a little hot under the collar! Here is a justification of why I think arithmetical realism is at least very plausible... Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see "people" laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say "Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so ludicrous!". Now Eugin, you may argue that the existence of this universe depends on the fact that it was simulated by a computer in our universe. I find this a little hard to fathom - because computer simulations are deterministic and they give the same results whether they are run once or a thousand times. I find it hard to imagine that they "leap into existence" when they are run the first time. I'm particularly motivated by the universal dove-tailing program - which eventually generates the trace of all possible programs. Do you say that most of the integers don't exist because nobody has written them down? I can see your point when you say that 2+2=4 is meaningless without the "physical objects" to which it relates. However this is irrelevant because you are thinking of too simplistic a mathematical system! The only mathematical systems that are relevant to the everything-list are those that have conscious inhabitants within them. Within this "self contained" mathematical world we *do* have the context for numbers. It's a bit like the chicken and egg problem. (egg = number theory, chicken = objects and observers). Both come together and can't be pulled apart. - David > -----Original Message----- > From: Eugen Leitl [mailto:[EMAIL PROTECTED] > Sent: Wednesday, 14 January 2004 1:32 AM > To: [EMAIL PROTECTED] > Subject: Re: Is the universe computable? > > On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: > > > > What is the point? Do we have experimental procedure to validate > > the opposite of the fanciful scenario? Giving that we were talking about > > I see, we're at the "prove that the Moon is not made from green cheese > when > nobody is looking" stage. > > I thought this list wasn't about ghosties'n'goblins. > Allright, I seem to have been mistaken about that. > > > first person scenario, in any case it is senseless to ask for > > experimental procedure. (experience = first person view; experiment = > > third person view). > > So the multiverse is not a falsifyable theory? > > > Don't tell me you were believing I was arguing. > > You were asserting a lot of stuff. That's commonly considered arguing, > except > you weren't providing any evidence so far. So, maybe you weren't. > > > About logic, it is a branch of mathematics. Like topology, algebra, > analysis > > it can be *applied* to some problem, which, through some hypothesis, > > can bear on some problem. With the comp hyp mathematical logic makes > > it possible to derive what consistent and platonist machine can prove > about > > themselves and their consistent extension. > > Except that machine doesn't exist in absence of implementations, be it > people, machines, or aliens. > > > >My point is that formal systems are a very powerful tool with very > small > > >reach, > > >unfortunately. > > > > But I never use formal system. I "modelise" a particular sort of machine > by > > formal system, so I prove things *about* machines, by using works > > *about* formal system. I don't use formal systems. I prove things in > > informal > > ways like all mathematicians. > > Above passage is 100% content-free. > > > >Because we know that QM is not a TOE. You haven't heard? > > > > How could be *know* QM is not a TOE? (I ask this independently of > > the fact that I find plausible QM is not a *primitive* TOE). > > Because general relativity and quantum theory are mutually incompatible. > So > both TOE aren't. We have several TOE candidates, and an increased number > of > blips heralding new physics, but no heir apparent yet. > > > You believe that the theorem "there is an infinity of primes" is a human > > invention? (as opposed to "a human discovery"). > > Of course. Not necessarily human; there might be other production systems > which invented them. Then, maybe there aren't. > > Infinity is something unphysical, btw. You can't represent arbitrary > values > within a finite physical system -- all infoprocessing systems are that. > You'll also notice that imperfect theories are riddled with infinities; > they > tend to go away with the next design iteration. So infinities is something > even more primatish than enumerable natural numbers. > > > >I do not see how arithmetic realism (a special case of Platonic > realism, is > > >that correct?) is an axiom. I agree with the rest of > > >your list. > > > > Perhaps I have been unclear. By Arithmetic Realism I mean that > Arithmetical > > Truth is independent of me, you, and the rest of humanity. There exist > > Oh, I disagree with that allright. Nonliving systems don't have an > evolutionary pressure to develop enumerable quantities representation. > > > weaker form of that axiom and stronger form. Tegmark for instance > > defends a much larger mathematical realism (so large that I am not sure > > what it could mean). As I said some ultrafinitist defends strictly > > weaker form of mathematical realism. > > The more quoted argument in favour of arithmetical realism is the one > based > > on Godel's theorem, and presented by him too) which is that any formal > > systems (and so any ideally consistent machines) can prove, even in > > principle, > > that is with infinite time and space, all the true proposition of > > arithmetic. > > Sure. Notice that infinite time and space is unphysical, and of course a > machine which doesn't exist doesn't produce anything. > > I was hoping for a falsifyable argument, showing that this spacetime is an > operation artifact of some finite production system. > > > But look also to the site of Watkins > > http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm > > Oh, basically you're arguing that the unreasonable applicability of > mathematics in physics is anything but unreasonable, and that a TOE arisen > from a formal system is in fact the universe itself? > > > for a lot of evidence for it (evidence which are a priori not related to > > my more theoretical computer science approach). > > Now my goal (here) is not really to defend AR as true, but as > sufficiently > > plausible > > that it is interesting to look at the consequences. You can read some > > I do not deny that a TOE can be immensely useful (but not necessarily so, > higher levels of theory tend to require increasing amounts of crunch to > predict anything useful), but that TOE has anything to do with the > metalayer, > or that in fact that distinction is meaningful. > > You don't seem to disagree, so we're not actually arguing. > > > main post I send to this list where I present the argument according to > > which if we take comp seriously (comp = AR + TC + "yes doctor") then > > physics is eventually a branch of machine's psychology (itself a branch > > of computer science" itself a branch of number theory. > > Ah, some severe leap of faith required here. > > > If you find an error, or an imprecision, please show them. > > I'm experiencing a severe cognitive dissonance, trying to understand why > you > think formal systems do exist in absence of their production systems. > > > Or, if there is a point you don't understand, it will be a pleasure for > me > > to provide more explanations. > > Also, I thought you were postulating an universe, aren't you? (I just > try > > Sure, we're having a conversation (albeit a bit surreal one), so we seem > to exist. > > > to figure out your philosophical basic hypothesis). > > > > Regards, > > > > Bruno > > > -- Eugen* Leitl <a href="http://leitl.org";>leitl</a> > ______________________________________________________________ > ICBM: 48.07078, 11.61144 http://www.leitl.org > 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE > http://moleculardevices.org http://nanomachines.net
