tag:blogger.com,1999:blog-32371144.post4585121499732545023..comments2017-10-19T14:07:45.017-04:00Comments on Room for Doubt: Turing's RevolutionLev Reyzinhttps://plus.google.com/100238312854618140370noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-32371144.post-2373273077190635302015-09-20T11:00:39.224-04:002015-09-20T11:00:39.224-04:00One needs to be cautious in taking a piecemeal app...One needs to be cautious in taking a piecemeal approach to Turing's work, there is an overarching vision and mathematical agenda giving a cohesive form to Turing's career, which is still alive for us now. <br />A comment on Baker-Gill-Solovay: Many mathematicians and computer scientists have become aware over the years that not all computability and complexity theoretic arguments are relativizable. What Baker-Gill-Solovay point to is the fact that certain simple diagonalising techniques do relativize, so pointing to the necessity for something more subtle from the theorist's tool bag.pmt6sbchttps://www.blogger.com/profile/17516781833165880822noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-53646275578145752702013-01-13T23:30:21.571-05:002013-01-13T23:30:21.571-05:00RH is solved and done .RH is solved and done .Sunkhirous Yadegarhttps://www.blogger.com/profile/07351205729018789001noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-32736161051137701952012-12-31T14:23:10.364-05:002012-12-31T14:23:10.364-05:00Thanks -- I was aware of his work on the Riemann H...Thanks -- I was aware of his work on the Riemann Hypothesis but didn't think it important enough to include on the list. However, I hadn't realized the method was more widely used, so I'll add it as # 14.Lev Reyzinhttps://www.blogger.com/profile/09629175455869565423noreply@blogger.comtag:blogger.com,1999:blog-32371144.post-41634301595710852082012-12-29T07:30:19.646-05:002012-12-29T07:30:19.646-05:00Turing’s Zeta Machine & the Riemann Hypothesis...Turing’s Zeta Machine & the Riemann Hypothesis (http://turingos.org/turing-timeline/turings-zeta-machine-the-riemann-hypothesis/)<br />In June 1950 he used the prototype Manchester University Electronic Computer to do some calculations concerned with the distribution of the zeros of the Riemann zeta-function, specifically whether there are any zeros not on the critical line in certain intervals. The pre-war record for the number of zeros located on the line was held by Ted Titchmarsh, confirming that the first 1041 points were OK. Turing extended this to the first 1104 zeros but then, unfortunately, the computer broke down. He devised what is now called “Turing’s method” for easier computational analysis of the function, detailed in his papers “A method for the calculation of the zeta-function” and “Some calculations of the Riemann zeta-function,” which are both widely referenced in modern mathematical publications.Alan Richmondhttps://www.blogger.com/profile/17383150571403817857noreply@blogger.com