On Mon, Feb 19, 2018 at 6:56 AM, Lawrence Crowell < [email protected]> wrote:
*> I think it may come down to computers that obey the Church-Turing > thesis,* > It states that a human can compute a function of positive integer s if and only if a Turing Machine (aka a computer) can. Do you have any reason to think it is untrue. > * > which is finite and bounded. Hofstadter's book Godel Escher Bach has > a chapter Bloop, Floop, Gloop where the Bloop means bounded loop or a > halting program on a Turing machine. Biology however is not Bloop, * > Computers can't do that and neither can people becuae Turing proved that nothing has a halting program, such a thing does not exist. > > > The busy beaver algorithm is such a case, which grows in complexity with > each step. > That is a understatement, the busy beaver function is more than just complex is is not computable. The Busy Beaver involves a physical object that could actually be built, a Turing Machine. Starting with a blank tape and a Turing Machine that can be in N states (that is to say have N rules) then BB(N) is the largest* FINITE* number of operations the machine will undergo before it halts ; sometimes the machine will continue forever but ignore them, of the machines that eventually stop BB(N) is the maximum number of operations performed before halting. The Busy Beaver function starts out modestly enough: BB(1)=1 BB(2)=6 BB(3)=21 BB(4)=107 But what is the next element in the series? Nobody knows for sure because at that point the function goes nuts. We know that BB(5) is at least 47,176,870, that is to say one 5 state Turing Machine has been found that halts after 47,176,870 operations, but another 5 state Turing Machine is still going strong well past that point, if it eventually stops then that larger number of operations is BB(5) if not then it’s 47,176,870 ; but if so we'll never be able to prove it’s 47,176,870 because we'll never be able to prove that other 5 state machine will never stop. Turing showed that in general you can’t determine if one of his machines will eventually stop, all you can do is observe it and wait to see if it stops, and you might be waiting forever. So some (perhaps all) BB numbers greater than 4 are not computable. It’s a little like having a perfect watch that will never stop, you can’t make money betting somebody that it will never stop because there is no point where enough evidence is in to allow you to claim you won and get the money. As for BB(6) its at least 7.4* 10^36,534 and probably much larger. BB(7) is greater than or equal to 10^10^10^10^7. Its been proven that BB(7,918) isn't just huge the number is not computable, even a Jupiter Brain will never know what BB(7,918) is, even the universe itself does not know because it does not have sufficient resources to produce it , so I'm not sure it make sense to say such a huge number even exists. It's unknown what the smallest non- c omputable BB number is, all we know is its larger than BB(4) and less than or equal to BB(7,918). > *> For machines to have properties at least parallel to conscious > behavior* > There is no observable difference between conscious behavior and intelligent behavior. > *> we really have to be running in at least Floop and maybe into Gloop.* > Then humans are not conscious. It's true a computer can't calculate BB(7918) , but a human can't either. 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. For more options, visit https://groups.google.com/d/optout.
