tag:blogger.com,1999:blog-1918995924244969903.post7443747642870054360..comments2017-04-28T14:48:33.089+12:00Comments on Kiwi Hellenist: Pi DayPeter Gainsfordhttps://plus.google.com/112181800578852902474noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-1918995924244969903.post-39920345140954351582017-03-26T20:18:35.426+13:002017-03-26T20:18:35.426+13:00Thanks again Peter! Yep, it's been a while... ...Thanks again Peter! Yep, it's been a while... hope all is well with you. Would be great if you could come, it's the 4th of April, 6pm, Hunter building. Cheers -<br />-- NoamErlkoenighttp://www.blogger.com/profile/12003295977825280784noreply@blogger.comtag:blogger.com,1999:blog-1918995924244969903.post-89828745424434649732017-03-21T00:01:09.741+13:002017-03-21T00:01:09.741+13:00Noam! It's been a while, hasn't it? Good t...Noam! It's been a while, hasn't it? Good to hear of your impending inaugural. Yes, I'd love to come!<br /><br />Archimedes' "almost inventing calculus" is a reference to his work with infinitesimals, using the "method of exhaustion" (https://en.wikipedia.org/wiki/Method_of_exhaustion). The polygon method I mentioned above is an example of the principle. You might say it had the potential for exhaustion to be to calculus as geometry is to algebra. But that potential wasn't achieved: the ancient Greeks never developed the idea of limits.<br /><br />We don't have nearly as much surviving of Archimedes' predecessors, but it does sound rather like the popularity of the technique owes more to Eudoxus. Who was no slouch (http://dx.doi.org/10.1163/1574-9347_bnp_e404350).<br /><br />Having said that, Archimedes may have come up with a much more precise measurement of pi, to four or even five significant figures. This isn't in his /Measurement of the circle/, but in Heron of Alexandria's /Metrica/. Unfortunately the text of the numerals is problematic, so it's impossible to be sure what Archimedes actually wrote: but the revised figures Heron quotes involve numerators and denominators with four or five digits each, so it was apparently a much more precise calculation. The numbers that Heron quotes are incorrect, though, so it's either a textual corruption or else Archimedes made a boo-boo.<br /><br />Of course nothing I've said should be taken as a slight on Archimedes himself! He was a genius, but he stood on the shoulders of other geniuses. My concern is about slighting all those /other/ geniuses. When you celebrate Archimedes and /only/ Archimedes, that leads to things like people inferring that the Antikythera mechanism must have been Archimedes' design ... just because he's famous.<br /><br />The liar paradox: yes, that seems to be accurate. With two minor provisos: when the article calls Epimenides "semi-mythical", there's nothing "semi" about it. There were however real literary works attributed to the mythical Epimenides. As for Euboulides/Eubulides, apparently there's some doubt over the exact wording of his paradox -- the New Pauly encyclopaedia quotes Cicero for the wording: "If you say that you are lying and say it truly, are you lying or telling the truth?" (/Academics/ 2.96, https://archive.org/stream/academicscicero00cicegoog#page/n72/mode/2up). Elsewhere, Cicero also attributes the "heap paradox" to him -- "With which additional grain will a number of individual grains become a heap?" I haven't checked the reference to Jerome, but I'd assume that relates to Paul quoting the "All Cretans are liars" line in one of his letters in the New Testament, but that's a quotation from the playwright Menander, not from Epimenides. I can't answer for the later, non-Greco-Roman itesm, I'm afraid.Peter Gainsfordhttp://www.blogger.com/profile/17448862214081111386noreply@blogger.comtag:blogger.com,1999:blog-1918995924244969903.post-9541189761705554672017-03-20T20:24:28.672+13:002017-03-20T20:24:28.672+13:00Very interesting Peter!
Among mathematicians, Ar...Very interesting Peter! <br /><br />Among mathematicians, Archimedes is definitely considered a giant who was ahead of his time. I've heard several times that he "almost invented calculus". I'm not sure what this really means.<br /><br />Another question (for my upcoming inaugural talk, perhaps you'd like to come?) -- is the history of the liar paradox given in https://en.wikipedia.org/wiki/Liar_paradox correct? Thanks! <br />-- NoamErlkoenighttp://www.blogger.com/profile/12003295977825280784noreply@blogger.comtag:blogger.com,1999:blog-1918995924244969903.post-23102571027219726722017-03-20T10:16:53.367+13:002017-03-20T10:16:53.367+13:00Certainly true - I just wasn't going to be too...Certainly true - I just wasn't going to be too picky about that. (But in fact there are some fields where it /is/ customary to refer to a year zero! In archaeoastronomy, for example: so 0 = 1 BCE, -1 = 2 BCE, -2 = 3 BCE, etc. I've seen confusion arise from that convention more than once...)Peter Gainsfordhttp://www.blogger.com/profile/17448862214081111386noreply@blogger.comtag:blogger.com,1999:blog-1918995924244969903.post-54230055488950482862017-03-18T03:50:22.285+13:002017-03-18T03:50:22.285+13:00Not to mention that John Conway's comment abou...Not to mention that John Conway's comment about 'year zero' shows a certain lack of understanding about the difference between numbers in maths and in chronology.David J. Colwillhttp://www.blogger.com/profile/00936595519854071302noreply@blogger.com