tag:blogger.com,1999:blog-2802439507214383806.post4817272626289479509..comments2023-03-27T07:22:51.195-05:00Comments on Recursively Enumerable: Can humans solve the halting problem?Tyson Diddleyhttp://www.blogger.com/profile/16010423170589014571noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-2802439507214383806.post-39824114658588230222017-04-26T15:53:58.219-05:002017-04-26T15:53:58.219-05:00(Coming reeeeaaaally late to this but better late ...(Coming reeeeaaaally late to this but better late than never :)<br />The issue I find with your argument is that it involves human non-omniscient. <br />However the halting problem is deeper than that in the sense that even if we were to grant someone omniscience (e.g. suppose we are talking about Laplace's demon) he/she would still be unable to decide all problems.<br />So even if one knows the answer to any conjecture conceivable they would still be unable to, say, enumerate the real numbers.<br /><br />The halting problem has nothing to do with human limitations but rather with the nature of nature itself. <br /><br />Of course your argument works quite nicely to demonstrate to someone who does not want to bother with diagonilization arguments and so forth and they just claim that humans are more clever than computers (without assuming that humans are all omniscient though)<br /><br />My question to such a person though would be "how on earth an animal such as the homo sapiens differs from a Turing machine." <br /><br />-NickZeushttps://www.blogger.com/profile/04150879879392862954noreply@blogger.comtag:blogger.com,1999:blog-2802439507214383806.post-7168360644154966682013-09-05T21:31:48.585-05:002013-09-05T21:31:48.585-05:00I thought the same thing after learning about the ...I thought the same thing after learning about the halting problem, and your article is the first satisfactory answer I've come across. Very good examples. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2802439507214383806.post-8466929051201437862013-03-27T18:02:23.943-05:002013-03-27T18:02:23.943-05:00Yes, of course you are right. That is why the Chur...Yes, of course you are right. That is why the Church-Turing Thesis is just that, a thesis, not a theorem. The argument above is for those that think humans are "clearly" smarter/better than computers. The point here is that this is in no way "clearly" true.Tyson Diddleyhttps://www.blogger.com/profile/16010423170589014571noreply@blogger.comtag:blogger.com,1999:blog-2802439507214383806.post-65654727982150143752013-03-27T13:12:37.888-05:002013-03-27T13:12:37.888-05:00I don't think this argument works.
What you&#...I don't think this argument works.<br /><br />What you've done is to show that, for a human to solve the halting problem, he'd have to be able to solve those other problems -- but you haven't shown that humans *can't* solve them, only that they haven't.<br /><br />You'd have to tie it to something that we know humans *can't* solve -- but then you'd have to show a program that solves it and ask whether *that* halts.Anonymoushttps://www.blogger.com/profile/13999428910548345163noreply@blogger.com