> On 27 Aug 2018, at 20:18, [email protected] wrote: > > > > On Friday, August 24, 2018 at 3:22:39 AM UTC-6, Bruno Marchal wrote: > >> On 24 Aug 2018, at 00:53, [email protected] <javascript:> wrote: >> >> >> >> On Thursday, August 23, 2018 at 5:55:33 PM UTC, [email protected] >> <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, <[email protected] <>> 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 [email protected] <>. >>> To post to this group, send email to [email protected] <>. >>> 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 [email protected] <javascript:>. >> To post to this group, send email to [email protected] >> <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 [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
