tag:blogger.com,1999:blog-8666091.post5135769360054628339..comments2017-11-17T11:28:58.387+01:00Comments on The Reference Frame: There are no 't Hooft's ontological basesLuboš Motlhttp://www.blogger.com/profile/17487263983247488359noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-8666091.post-17204030073503225452014-05-20T08:34:28.261+02:002014-05-20T08:34:28.261+02:00As an ignorant layman, I'm just wondering how ...As an ignorant layman, I'm just wondering how anyone who understands this essay might not know of the letter aleph and its usage in mathematics.Smoking Frognoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-61792848942587012102014-05-20T02:30:51.849+02:002014-05-20T02:30:51.849+02:00you are really a sad waste of life lubosyou are really a sad waste of life lubosjemoinoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-19755271978165914192014-05-20T00:37:42.688+02:002014-05-20T00:37:42.688+02:00Dear Lubos,
thank you very much. I will study thi...Dear Lubos, <br />thank you very much. I will study this article carefully. I was really hoping for some time that you would write this article as I couldn't fully make up my mind about the work of Prof. 't Hooft. Especially after the article on Weinberg I was thinking that it could be a natural next step for you and luckily I was right. While your remarks about the relevance of the relative phases of the state vector and about the spin 1/2 system appear elementary, yet relevant to me I still struggle with your remarks on the permutation group. In particular I don't see why a granular enough discrete time couldn't mimick a continuous but maybe this understanding will come if I read this part again tomorrow.Mikaelnoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-12380670151037137742014-05-19T20:20:33.558+02:002014-05-19T20:20:33.558+02:00"the mesh of time variables" - Lubos, ha..."the mesh of time variables" - Lubos, has anybody considered a string theory with several time-like dimensions?Curious Georgenoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-39266918351998722592014-05-19T19:39:23.686+02:002014-05-19T19:39:23.686+02:00Lubos - You're the only other person that I kn...Lubos - You're the only other person that I know of who was attracted to Phil Gibbs' essay. Although I haven't thought about it in nearly twenty years, your reference somehow evoked a memory of the interest I felt at the time, like Proust with his tea.<br /><br />It is strange that t'Hooft can keep going down this road when , as you show, the simplest possible example proves him wrong.<br /><br />Over the same two weeks that t'Hooft and Weinberg were having their senior moments there were a couple of papers about which I thought you might have something to say. On the chance that they escaped your attention, they were:<br /> http://arxiv.org/abs/1405.2933 and <br />http://arxiv.org/abs/1405.3743.<br /><br />Cheers!!!RAF IIInoreply@blogger.comtag:blogger.com,1999:blog-8666091.post-40857826274971878632014-05-19T18:06:37.981+02:002014-05-19T18:06:37.981+02:00Right, I know this fact about cardinals, sorry for...Right, I know this fact about cardinals, sorry for my being sloppy. What I really wanted to say is that for a large N, N! is parameterically larger than exp(N). Stirling's formula makes N! close to <br /><br /><br />sqrt(2*pi*N) (N/e)^N,<br /><br /><br />roughly speaking to N^N. But yes, at the levels of cardinals, N^N and e^N cannot be distinguished for N=Aleph_0.Luboš Motlhttp://motls.blogspot.com/noreply@blogger.comtag:blogger.com,1999:blog-8666091.post-54479844139346339622014-05-19T18:05:00.804+02:002014-05-19T18:05:00.804+02:00∞! = exp(∞), see http://mathoverflow.net/questions...∞! = exp(∞), see http://mathoverflow.net/questions/27785/cardinality-of-the-permutations-of-an-infinite-set<br /><br />as to what topologies can be applied to S_∞, any group can be given the discrete topology, but theres this clam here http://mathoverflow.net/questions/15591/topologies-on-an-infinite-symmetric-group that the topology of pointwise convergence is also compatible with the group structureSage Basilnoreply@blogger.com