> On 27 Aug 2018, at 20:18, agrayson2...@gmail.com wrote: > > > > On Friday, August 24, 2018 at 3:22:39 AM UTC-6, Bruno Marchal wrote: > >> On 24 Aug 2018, at 00:53, agrays...@gmail.com <javascript:> wrote: >> >> >> >> On Thursday, August 23, 2018 at 5:55:33 PM UTC, agrays...@gmail.com >> <http://gmail.com/> wrote: >> >> >> On Thursday, August 23, 2018 at 3:28:13 PM UTC, Brent wrote: >> Why don't we all chip in an buy Alan a computer so he can look stuff up on >> Wikipedia. >> >> Brent >> >> I will when you have the courtesy to explain your contradictory statements >> about the instantaneous, infinite extent of the wf. Oh BTW, with your big >> brain, I suppose it never occurred to you that I wanted to hear Bruno's >> definition, which if experience is worth anything, could be wildly DIFFERENT >> from Wiki. While you assess all that, why don't you go fuck yourself, and >> then tell us how it felt. OK? AG >> >> FWIW, comparing Bruno's description with Wiki, which was my intent, >> confirms, at least for me, that the postulates of QM are easier to >> understand, even though many of the defining functions of a Turing Machine >> are known to those who have programmed modern computers, notwithstanding >> that the latter use random access memory. I don't see why the use of RAM is >> decisively important in distinguishing a Turing Machine from how modern >> computers are designed. AG > > > You are right. You can see a von Neumann computer as a Turing machine. As the > set of symbols, and state are arbitrary, you can even see a brain as a Turing > machine. > > From my naive pov, I initially think a Turing machine can manipulate > arbitrary symbols and logical commands, and is limited to computable > functions, whatever they are. If so, and you consider a brain a Turing > machine, what does it do with non-computable functions? AG
I will show that universality (the ability to compute *all* computable function) entails the possibility of ending in a non terminating computation, without any ability to know that that is the case. But for this, we need first to get a definition of what is computable. We will come back on this. You want proceed to much quickly I think. It is good, but there are some subtleties and traps to avoid. Bruno > > That is why eventually Gödel accepted Turing’s argument for the Church’s > thesis. > > Note that the wikipedia is often bad on logic or on computation, ...not > mentioning computationalism. > > Have you understood Cantor’s diagonal proof of the non enumerability of the > set of infinite sequence, in my yesterday post. If not I can explain again, > with different notation. There is a real surprise at the end of that thread, > you will see (I think and hope). > > Bruno > > > > >> >> >> On 8/22/2018 5:58 PM, John Clark wrote: >>> On Wed, Aug 22, 2018 at 8:26 PM, <agrays...@gmail.com <>> wrote: >>> >>> >> Yes, the Busy Beaver Function is not computable. We know that: >>> >>> BB(1) =1 >>> BB(2) =6 >>> BB(3) =21 >>> BB(4) =107 >>> >>> > You haven't *written* the function, just its alleged values for 1,2,3,4. >>> > What is the function? >>> >>> >>> Starting with a all zero tape BB(N) is the number of operations any N state >>> Turing Machine performs after it writes the largest number of 1's and then >>> halts. It is very important that it halt, some machines will go on forever >>> but they don't count. For example we know for sure that BB(5) is at least >>> 47,176,870 because one 5 state Turing Machine has been found that halts >>> after it goes through 47,176,870 operations (and prints 4098 1’s on the >>> tape), but there are 28 other 5 state machines displaying non-regular >>> behavior that are well past 47,176,870 operations and 4098 1's. If one of >>> them eventually halts then that larger number of operations will be BB(5), >>> if none of them ever halts then 47,176,870 really is BB(5); but the trouble >>> is we'll never be able to know it’s 47,176,870 because we'll never know >>> that none of those other 28 5 state machines will never halt because the >>> Halting problem is insolvable. >>> >>> John K Clark >>> >>> >>> -- >>> You received this message because you are subscribed to the Google Groups >>> "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send an >>> email to everything-li...@googlegroups.com <>. >>> To post to this group, send email to everyth...@googlegroups.com <>. >>> Visit this group at https://groups.google.com/group/everything-list >>> <https://groups.google.com/group/everything-list>. >>> For more options, visit https://groups.google.com/d/optout >>> <https://groups.google.com/d/optout>. >> >> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to everything-li...@googlegroups.com <javascript:>. >> To post to this group, send email to everyth...@googlegroups.com >> <javascript:>. >> Visit this group at https://groups.google.com/group/everything-list >> <https://groups.google.com/group/everything-list>. >> For more options, visit https://groups.google.com/d/optout >> <https://groups.google.com/d/optout>. > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
