Path: news.eternal-september.org!eternal-september.org!feeder3.eternal-september.org!panix!weretis.net!feeder9.news.weretis.net!news.nk.ca!rocksolid2!i2pn2.org!.POSTED!not-for-mail From: HenHanna Newsgroups: rec.puzzles Subject: Re: Repeated digits in Pi -- the Feynman point Date: Mon, 23 Jun 2025 19:58:59 +0000 Organization: novaBBS Message-ID: <1f87e271f28067836cabd2199a7ea473@www.novabbs.com> References: <103bugr$1bnfr$2@dont-email.me> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Info: i2pn2.org; logging-data="1747350"; mail-complaints-to="usenet@i2pn2.org"; posting-account="4L8HabKtc1alsSAOmk7EUGDHKRhgGhC+6gJMfTsJB0A"; User-Agent: Rocksolid Light X-Rslight-Posting-User: abae1fed5a82111a8790dc84735f550edb4392db X-Rslight-Site: $2y$10$IwKhw4F87bBG/IXpFCwr6utmtkU2zH0ihV7bkhjo5IM7Oyom3Cqmm X-Spam-Checker-Version: SpamAssassin 4.0.0 X-Face: P#KeQ)CUdd!==@fw~Ms1=,Hb`IWtb6:Mw)x3B=H1BfNC\lz?Nb&)M9}$>?'X7l;CuB}utlJ=PHsRBSG6X>dYZ$[>P]$~+`>@V6$t}hTLoQ7XC~W\>:`B3ALU]SH;d(\MEc}znW8m}-ma&yPFkJ2@KSQrz=!Y;><;6a>z6N+mt`ClCt.PAE On Sun, 22 Jun 2025 19:15:32 +0000, HenHanna wrote: > >> The Feynman point refers to the sequence of six consecutive >> nines (999999) that appears in the decimal expansion of pi (π), starting >> at the 762nd digit after the decimal point. This point is notable >> because such a long run of identical digits is statistically rare so >> early in the sequence, leading to its fame as a mathematical curiosity. > > > I didn't immediately see anything surprising about the six consecutive > nines, but I've thought about it... > > If the following isn't right, could you put me straight? I hope you don't mean ME... > > With a number system including ten single-digit integers, zero to nine, > for a base ten number system, if the sequence of numbers is random > (which > pi isn't), Really? i thought Pi was random. > then there is a one in ten probability that any given digit > will be followed by the same digit. There is a nine tenths probability > that the subsequent digit will be different. The probability of three > identical digits is one in ten multiplied by by one in ten, or a > probability of one in one hundred of three identical digits following > each > other. If the sequence of identical digits is n digits long, then the > probability of it happening in a random sequence of digits is one in > 10^(n-1). > > So, the probability of six nines occurring together, in a random > sequence, > would be one in one hundred thousand. If 999999 occurs after the 762nd > digit after the decimal point of pi, I now recognize that is surprising. > > Thanks I feel better for that. _______________________ Almost every day.... i get briefed from my fav AI. I just got tutored by AI on the following.... When flipping a fair coin repeatedly, the expected number of tosses needed to see 6 consecutive heads is: Expected tosses = 126 When randomly selecting digits from 0 to 9, the expected number of digits you need to draw before seeing 6 consecutive 9’s is: Expected digits = 1,111,110 So how unusual or UNexpected is that? (the Actual Feynmann point ) Is that the T-test? p-value? I'll ask my AI maybe tomorrow.