On Sunday, May 18, 2014 9:59:10 PM UTC-4, Liz R wrote: > > On 19 May 2014 07:37, Craig Weinberg <[email protected] <javascript:>>wrote: > >> >> >>> You did not provide evidence that they cannot do that. >>> >> >> His evidence was the negative answer to Hilbert's 10th problem. >> >> To be exact, it's claimed to be *how he arrived at* that answer. The > extract says that he arrived at a proof that "no algorithm could have > found". How did he find it? >
>From what I can gather, Matijasevich proved that the already proven unsolvable Halting Problem can be represented as a Diophantine equation, so that there is at least one Diophantine equation that can't be solved by a Turing machine. I'm sure its more complicated than that, but at this point, that's what I'm getting as a general overview. The paper is far too high powered for my little brain, so I am hoping for > an answer for dummies. Did he decide that the answer might have some > particular form using intuition, say, tried it, and found it worked? How > did he (or anyone) then show there was no algorithm for finding it? > > (This is reminiscent of "The Emperor's New Mind", which IIRC attempts to > prove that some gifted mathematicians are not machines!) > > > > -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
