Re: Wolfram 2,3 Turing Machine
Le 26-oct.-07, à 16:21, Juergen Schmidhuber a écrit : > Impressive result by Alex Smith! Absolutely. > Funny though how Wolfram's web sites on this > print Wolfram's name in larger font and more > frequently than Smith's, even trying to sell this > as "New Kind Of Science" although it's just a > continuation of a decades-old search for > small universal Turing machines :-) Yes. > > BTW, check out Marcus Hutter's older posting to > the Kolmogorov Complexity mailing list on whether > such machines should really count as UTMs or not: > http://mailman.ti-edu.ch/pipermail/kolmogorov/2007/000245.html Yes. And I agree with Marcus. The search of small UM in the context of Kolmogorov Complexity is, imo, a red herring. All the interest in such universal notion (of complexity, ...) is that there are equivalent up to a constant. Wanting a special (little) constant cut the interest in such theories at the start. Of course some existence theorem can be made simpler, but that's all. But small UM are interesting for many other reasons. The main one is they put light on the nature of universality in math and computation theory. Wolfram says that the universality of its 2,3 UM adds evidences for the CEP (comp equivalence principle). I don't see one. Idea? Bruno > > JS > http://www.idsia.ch/~juergen/computeruniverse.html > http://www.idsia.ch/~juergen/wolfram.html > > On Oct 24, 2007, at 8:32 PM, Tom Caylor wrote: >> We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine >> Research Prize has been won. >> Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a >> 40-page proof that Wolfram's 2,3 Turing machine is indeed universal. >> This result ends a half-century quest to find the simplest possible >> universal Turing machine. It also provides strong further evidence for >> Wolfram's Principle of Computational Equivalence. The official prize >> ceremony is planned for November at Bletchley Park, UK, site of Alan >> Turing's wartime work. >> For more information about the prize and the solution, see: >> http://www.wolframprize.org >> Stephen Wolfram has posted his personal reaction to the prize at: >> http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html > > http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Wolfram 2,3 Turing Machine
Impressive result by Alex Smith! Funny though how Wolfram's web sites on this print Wolfram's name in larger font and more frequently than Smith's, even trying to sell this as "New Kind Of Science" although it's just a continuation of a decades-old search for small universal Turing machines :-) BTW, check out Marcus Hutter's older posting to the Kolmogorov Complexity mailing list on whether such machines should really count as UTMs or not: http://mailman.ti-edu.ch/pipermail/kolmogorov/2007/000245.html JS http://www.idsia.ch/~juergen/computeruniverse.html http://www.idsia.ch/~juergen/wolfram.html On Oct 24, 2007, at 8:32 PM, Tom Caylor wrote: We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine Research Prize has been won. Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a 40-page proof that Wolfram's 2,3 Turing machine is indeed universal. This result ends a half-century quest to find the simplest possible universal Turing machine. It also provides strong further evidence for Wolfram's Principle of Computational Equivalence. The official prize ceremony is planned for November at Bletchley Park, UK, site of Alan Turing's wartime work. For more information about the prize and the solution, see: http://www.wolframprize.org Stephen Wolfram has posted his personal reaction to the prize at: http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html smime.p7s Description: S/MIME cryptographic signature
Re: Wolfram 2,3 Turing Machine
Le 24-oct.-07, à 20:32, Tom Caylor a écrit : > > This might be of interest to some of you, for instance Bruno, since > one of the ideals expounded here is "keep it simple". Sorry I haven't > been participating here. > >> From Wolfram Science Group: > > We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine > Research Prize has been won. Thanks for that very nice news. We have discussed it a lot in Siena. I am interested in this because, a negative solution would have ruin a conjecture of my own: the existence of of a cubic universal diophantine equation with no more than 8 variables. Today the simplest universal diophantine equation is of degree four and has 154 variables. > > Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a > 40-page proof that Wolfram's 2,3 Turing machine is indeed universal. > This result ends a half-century quest to find the simplest possible > universal Turing machine. It also provides strong further evidence for > Wolfram's Principle of Computational Equivalence. (PCE) I don't see why. I should publish this perhaps, but I can prove that comp entails the falsity of the PCE. Frankly, anyone grasping the UDA should see this. The reasoning is the same as the one showing Schmidhuberian form of physicalist computationalism is incompatible with comp (I have often explain why I cannot be myself a digital machine, and at the same time in a purely computational universe). Ah! I see Wei Dai just posted a message which shows this is not yet clear for every one ... Hmmm... > The official prize > ceremony is planned for November at Bletchley Park, UK, site of Alan > Turing's wartime work. > > For more information about the prize and the solution, see: > > http://www.wolframprize.org > > Stephen Wolfram has posted his personal reaction to the prize at: > > http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html Well Wolfram says: "But is PCE true? I'm sure it is. But--like many fundamental principles in science--it's not the kind of thing one can abstractly prove." It is a good test to see if you have grasped the Universal Dovetailer Argument: shows that it refutes (even without comp) the PCE, at least if you define Nature by what is observable. Note that the QM observables (in any world/branches, or if you prefer Unitary-Evolution+Measurement) refutes it also. If you define Nature by the QM mutiverse, as seen from outside (and thus without measurement) , then the PCE is not violated, but it has to be violated from inside. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Wolfram 2,3 Turing Machine
This might be of interest to some of you, for instance Bruno, since one of the ideals expounded here is "keep it simple". Sorry I haven't been participating here. >From Wolfram Science Group: We're excited to announce that the $25,000 Wolfram 2,3 Turing Machine Research Prize has been won. Alex Smith, a 20-year-old undergraduate in Birmingham, UK, has given a 40-page proof that Wolfram's 2,3 Turing machine is indeed universal. This result ends a half-century quest to find the simplest possible universal Turing machine. It also provides strong further evidence for Wolfram's Principle of Computational Equivalence. The official prize ceremony is planned for November at Bletchley Park, UK, site of Alan Turing's wartime work. For more information about the prize and the solution, see: http://www.wolframprize.org Stephen Wolfram has posted his personal reaction to the prize at: http://blog.wolfram.com/2007/10/the_prize_is_won_the_simplest.html --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
