On March 25, 2016 12:34:51 AM EDT, Antony Prince <ant...@blazrsoft.com> wrote: >On March 24, 2016 11:17:58 PM EDT, "Marcio Barbado, Jr." ><marcio.barb...@gmail.com> wrote: >>Not sure if it's counterintuitive once tossing can be seen as >>abandoning inertia. >> >> >>Marcio Barbado, Jr. >> >> >> >>On Fri, Mar 18, 2016 at 9:18 AM, Peter Lebbing >><pe...@digitalbrains.com> wrote: >>> On 14/03/16 10:37, Fulano Diego Perez wrote: >>>> >>https://www.quantamagazine.org/20160313-mathematicians-discover-prime-conspiracy/ >>> >>> So forgive me for the off-topicness, but something in the text >caught >>my >>> attention: >>> >>>> Soundararajan was drawn to study consecutive primes after hearing a >>>> lecture at Stanford by the mathematician Tadashi Tokieda, of the >>>> University of Cambridge, in which he mentioned a counterintuitive >>>> property of coin-tossing: If Alice tosses a coin until she sees a >>>> head followed by a tail, and Bob tosses a coin until he sees two >>>> heads in a row, then on average, Alice will require four tosses >>while >>>> Bob will require six tosses (try this at home!), even though >>>> head-tail and head-head have an equal chance of appearing after two >>>> coin tosses. >>> >>> I did try this at home; only I wrote a Python script to do all the >>> tedious tossing and accounting. This is its output: >>> >>>> $ ./cointoss HH HT >>>> >>>> H T HH HT >>>> ---------- ---------- ---------- >>---------- >>>> 59821 (49.9%) 60079 (50.1%) 6.044 3.990 >>> >>> >>> After over a million coin tosses, it takes 6 tosses on average until >>you >>> see two heads in a row, but only 4 to see head-tail. Obviously, the >>> script is attached. Supply the patterns on invocation, as shown >>above. >>> Any number of patterns of any length are supported (I think). Well, >>> strictly positive numbers and lengths :). >>> >>> Can someone point me in the direction of the solution to this >>> counterintuitive probability theory result? Any of a common name for >>the >>> property, a mathematical explanation or an intuitive explanation are >>> much appreciated! >>> >>> Anyway, to make up for the off-topicness, let's get slightly >>on-topic... >>> >>> To the OP: Please provide at least a short abstract of the text when >>you >>> post a link. That way people can tell from your mail what the text >>will >>> be about. >>> >>> With regards to the article, I'm surprised by the choice of words in >>its >>> title. Other than to draw in more readers, I don't see what place >the >>> word "conspiracy" has in it. That's like saying 0 and 1 are >>conspiring >>> to be consecutive on the integral number line. Oh no, pretty much >all >>> are computers are based on 0's and 1's and now they are conspiring! >>> Probably against us! Quick, we need neutral numbers without an >>agenda... >>> In my opinion, this title really devalues the article. "Three secret >>> ways to cope with prime conspiracy mathematicians don't want you to >>know >>> about" isn't that much further out. Oh, I hope that phrasing doesn't >>> tickle any spam filters... Ah well. >>> >>> Cheers, >>> >>> Peter. >>> >>> -- >>> I use the GNU Privacy Guard (GnuPG) in combination with Enigmail. >>> You can send me encrypted mail if you want some privacy. >>> My key is available at >><http://digitalbrains.com/2012/openpgp-key-peter> >>> >>> _______________________________________________ >>> Gnupg-users mailing list >>> Gnupg-users@gnupg.org >>> http://lists.gnupg.org/mailman/listinfo/gnupg-users >>> >> >>_______________________________________________ >>Gnupg-users mailing list >>Gnupg-users@gnupg.org >>http://lists.gnupg.org/mailman/listinfo/gnupg-users > >I've followed the thread for a bit now, but the concept definitely >brings some things to light, especially for those less >cryptographically or mathematically inclined. By the basics that I >know, a 50-50 chance is a 50-50 chance. But as has been pointed out, >the chance of getting a specific set of results consecutively is >obviously (according to the data), not 50/50 even though the initial >probability would imply that. I don't really have much more to add to >the discussion other than it made me think a bit more about how >probability and the effect that measuring the probability of >predetermined sequences within that same set might produce results that >are contradictory to the initial expectations. Such is the nature of >these things and I merely found it interesting that the results defied >the expectation. Which is the essence of discovery and progress.
But to reply directly to the post at hand, inertia would definitely be a factor in a physical coin tossing. Even though the coin only has 2 sides, the amount of initial force used to flip it and all the other external factors affecting it before it landed would play a part, so though the beginning ratio might be 50/50, there are external factors that skew the ratio one way or the other in a true physical coin toss, so on that point, I applaud you for that observation. -- Sent from my Android device with K-9 Mail. Please excuse my brevity. _______________________________________________ Gnupg-users mailing list Gnupg-users@gnupg.org http://lists.gnupg.org/mailman/listinfo/gnupg-users
