tag:blogger.com,1999:blog-264226589944705290.post3672221763887264219..comments2022-08-07T01:05:01.413-07:00Comments on God Plays Dice: Interesting fact of the dayMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-264226589944705290.post-15605936029980847262008-10-12T18:36:00.000-07:002008-10-12T18:36:00.000-07:00Yeah. Papers are way easier to read when they rest...Yeah. Papers are way easier to read when they restate the axioms in every sentence that discusses a conclusion.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-11049238596578878202008-10-11T16:01:00.000-07:002008-10-11T16:01:00.000-07:00Yes, but the solution wasn't phrased that way. If...Yes, but the solution wasn't phrased that way. If so, it would have read something like "an even number expressed with at most three ones can only have two". Or even: "In the situations under consideration in this problem, an even number can be expressed as the sum of at most two ones". <BR/><BR/>As I said, it was easy to understand from context, but at first glance it read like (an obviously wrong)general statement.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-64517169559789476802008-10-11T14:30:00.000-07:002008-10-11T14:30:00.000-07:00@anonymous 2: Read the problem statement more care...@anonymous 2: Read the problem statement more carefully. The problem only considers representations which use each summand at most three times.Michael Lugohttps://www.blogger.com/profile/15671307315028242949noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-14981730391055600482008-10-11T14:27:00.000-07:002008-10-11T14:27:00.000-07:00I was a little surprised that the solution to the ...I was a little surprised that the solution to the problem included a few obviously wrong statements. From context you could figure out what the author was trying to say, but it was still jarring. (For example, the claim that an even number would not be expressed as the sum of more than two 1's. Um, how about 4 = 1 + 1 + 1 + 1?)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-91267285726181238612008-10-10T19:40:00.000-07:002008-10-10T19:40:00.000-07:00Yeah, it's interesting stuff. I came across that p...Yeah, it's interesting stuff. I came across that paper in the course of solving one of the problems at projecteuler.net (which is awesome, btw).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-11747670245442967932008-10-10T13:25:00.000-07:002008-10-10T13:25:00.000-07:00This reminds me of the simplest adder used in digi...This reminds me of the simplest adder used in digital electronics. It has 3 inputs and two outputs. The three input bits are of the same magnitude and can give results of 0, 1, 2, or 3. This requires two bits to code.<BR/><BR/>The high output bit is called the "carry out", and one of the three inputs is called the "carry in". One can use N of these to add two N-bit numbers.<BR/><BR/>I suspect that one could also use N of these to correct the binary description of a number which had as much as 3 copies of a given bit.<BR/><BR/>Also, "each rational number" should presumably be "each positive rational number".CarlBrannenhttps://www.blogger.com/profile/17180079098492232258noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-45350380900295301652008-10-10T13:24:00.000-07:002008-10-10T13:24:00.000-07:00Phillie is playing the on team that no matter who ...Phillie is playing the on team that no matter who they play I want to lose.<BR/><BR/>In fact I'd love to see them lose every game in a season.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-40449664409449013812008-10-09T23:51:00.000-07:002008-10-09T23:51:00.000-07:00Wow, that's great! I'll have to share this around-...Wow, that's great! I'll have to share this around--it's very interesting.Anonymousnoreply@blogger.com