tag:blogger.com,1999:blog-22973357.post116594805846776009..comments2021-05-13T01:12:55.323-04:00Comments on Sabine Hossenfelder: Backreaction: PISabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger26125tag:blogger.com,1999:blog-22973357.post-1166633739017761092006-12-20T11:55:00.000-05:002006-12-20T11:55:00.000-05:00A question: Suppose you write a trancendental num...A question: Suppose you write a trancendental number in binary, but then interpret the number thus written as a decimal: Is the result always transcendental? I feel sure that it it, but can't immediately prove it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166633304150966062006-12-20T11:48:00.000-05:002006-12-20T11:48:00.000-05:00I did a lesson on computing pi for fifth graders, ...I did a lesson on computing pi for fifth graders, starting with inscribed and circumscribe squares, moving to Archimedes method, and Euler's formula in terms of alternating series. We finished up with a more modern algorithm with which we could compute the first 1500 or so digits, letting Maple draw all the pictures and do the aithmetic.<BR/><BR/>I'm not sure how much they understood, but they Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166401471530462592006-12-17T19:24:00.000-05:002006-12-17T19:24:00.000-05:00Hi Chinmaya,Honestly, I don't know. But mathematic...Hi Chinmaya,<BR/><BR/>Honestly, I don't know. But mathematicians are funny people. They can spend years on a single number, or a function that isn't even named after them. Maybe it's good to easily come up with some coding mechanism? Say, I send you a scrambled text and a ten digit number indicating a starting point in Pi. Then we only need to have agreed on a recipe like: from the starting pointSabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166319393008303042006-12-16T20:36:00.000-05:002006-12-16T20:36:00.000-05:00Maybe he did and Pi is just a code for the bible. ...Maybe he did and Pi is just a code for the bible. After all, if Pi is normal then it should contain the bible in whatever code you could think of...Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166319154272475722006-12-16T20:32:00.000-05:002006-12-16T20:32:00.000-05:00Now why didn't God communicate the first million d...Now why didn't God communicate the first million digit via a prophet, so that it would have appeared in the Bible? :)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166149070648432702006-12-14T21:17:00.000-05:002006-12-14T21:17:00.000-05:00I had a laymen question: Why are they are looking ...I had a laymen question: Why are they are looking for higher and higher digits of pi and whether they are used in anyway? I understand it could be fun in itself. Thank You!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166135092250050992006-12-14T17:24:00.000-05:002006-12-14T17:24:00.000-05:00Hi Gebar,Thanks so much! I'll give it a try if I f...Hi Gebar,<BR/><BR/>Thanks so much! I'll give it a try if I find the time - hopefully soon :-)<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166130345415689142006-12-14T16:05:00.000-05:002006-12-14T16:05:00.000-05:00nice to be able to avoid the axiom of choice.You d...<I>nice to be able to avoid the axiom of choice.</I><BR/><BR/>You don't need the axiom of choice to order a countable set, though it will do the job.Legacy Userhttps://www.blogger.com/profile/06040703073083283966noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166108876815133882006-12-14T10:07:00.000-05:002006-12-14T10:07:00.000-05:00The bible only tells that pi=3 when building the s...The bible only tells that pi=3 when building the sacred tabernacle or so. This place is designed as to be the house of god... And we know that pi=3 in some non-euclidean spaces. So the Bible is telling us about the curvature of space-time from the point of view of G-d, Who is able to see across all the dimensions. So it is telling us that pi=3 in the 11 dimensional space of string theory.<BR/><BRLeucipohttps://www.blogger.com/profile/14505549871207858030noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166108546135085082006-12-14T10:02:00.000-05:002006-12-14T10:02:00.000-05:00Well if I were a mathematician, I could tell if th...Well if I were a mathematician, I could tell if <A HREF="http://www.nersc.gov/~dhbailey/dhbpapers/bcnormal.pdf" REL="nofollow">this paper</A> by Bailey and Crandall includes pi in it's proven class of "normal" constants or not...<BR/>*scratches head*Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166099258625152482006-12-14T07:27:00.000-05:002006-12-14T07:27:00.000-05:00Just a quick note on adding math support to Blogge...Just a quick note on adding math support to Blogger blogs (repeat of post in Clifford's blog).<BR/><BR/>Have a look <A HREF="http://www1.chapman.edu/~jipsen/mathml/asciimath.html" REL="nofollow">here</A>. Peter Jipsen of Chapman University has written ASCIIMathML a great javascript program that converts ASCII notation (more or less the one used in math and physics newsgroups, and of course in Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166087229286043342006-12-14T04:07:00.000-05:002006-12-14T04:07:00.000-05:00" Aaron Bergman said... You can pretty easily w..." Aaron Bergman said...<BR/><BR/> You can pretty easily write down some transcendental numbers with only zeros and ones. Liouville's constant:<BR/><BR/> x= \sum 10^{-(k!)}<BR/><BR/>is trascendental"<BR/><BR/>Hence, 4/9 + 3x is a trascendental number with only 4 and 7 in its decimal expansion :-). It's nice to be able to avoid the axiom of choice.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166082289347520272006-12-14T02:44:00.000-05:002006-12-14T02:44:00.000-05:00You can pretty easily write down some transcendent...You can pretty easily write down some transcendental numbers with only zeros and ones. Liouville's constant:<BR/><BR/>\sum 10^{-(k!)}<BR/><BR/>does the trick.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166060822673536132006-12-13T20:47:00.000-05:002006-12-13T20:47:00.000-05:00carlbrannen--actually, it shouldn't do too difficu...carlbrannen--actually, it shouldn't do too difficult to find transcendental numbers on a line segment. After all, Georg Cantor discovered that there are more irrational numbers than rational numbers, and more transcendental numbers than algebraic ones. Restated, most real numbers are irrational; and among irrational numbers, most are transcendental.<BR/><BR/>Hence, transcendentals are--by far-Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166060154308656522006-12-13T20:35:00.000-05:002006-12-13T20:35:00.000-05:00You should also link to the rather well-known blog...You should also link to the rather well-known blog that has the PI favicon. ;-)Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166056101067952722006-12-13T19:28:00.000-05:002006-12-13T19:28:00.000-05:00To make a transcendental number with just 4s and 7...To make a transcendental number with just 4s and 7s in the decimal expansion:<BR/><BR/>Algebraic means that the number is the root of a rational polynomial. Transcendental means not algebraic.<BR/><BR/>The algebraic numbers (which includes all the rationals) are countable. So one lists them in one order or another, as a countably infinite list {a_n}. Many such orderings are known.<BR/><BR/>To Legacy Userhttps://www.blogger.com/profile/06040703073083283966noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166041710661527522006-12-13T15:28:00.000-05:002006-12-13T15:28:00.000-05:00Dear Cynthia,I admit, I also like Euler's number b...Dear Cynthia,<BR/><BR/>I admit, I also like Euler's number better, or the function e^z defined through it, respectively. Is there anything more beautiful than a function that reproduces itself under derivation? <BR/><BR/>d/dz e^z = e^z<BR/><BR/>Best,<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166041478017919332006-12-13T15:24:00.000-05:002006-12-13T15:24:00.000-05:00Without question, Pi's a symbol to be reckoned wit...Without question, Pi's a symbol to be reckoned with. Admittedly, though, I hold a special fondness for e. Oh sure, Pi and e are equally two of the most celebrated transcendental numbers.<BR/><BR/>In comparison to Pi, I'll remark, not only does e seem to allow one to perform more mathematical tricks, e also seems to have a stronger connection to Nature. Granted, this is nothing more than a hunch..Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166041223336320582006-12-13T15:20:00.000-05:002006-12-13T15:20:00.000-05:00Hi Georg, Hi Carl,Thanks for pointing this out! No...Hi Georg, Hi Carl,<BR/><BR/>Thanks for pointing this out! Now that you mention it, I recall there was a subtlety... I have corrected the sentence. So the status is, one thinks Pi is normal, but there's no prove? <BR/><BR/><I>It's easy to write down a transcendental number whose decimal digits are, for example, all 7s and 4s.</I><BR/><BR/>What exactly do you mean with 'write down'? I can imagine Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166040505906880912006-12-13T15:08:00.000-05:002006-12-13T15:08:00.000-05:00georg is right. It's easy to write down a transce...georg is right. It's easy to write down a transcendental number whose decimal digits are, for example, all 7s and 4s.Legacy Userhttps://www.blogger.com/profile/06040703073083283966noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166036741050935562006-12-13T14:05:00.000-05:002006-12-13T14:05:00.000-05:00Pi is a transcendental number, which means [...] e...<I>Pi is a transcendental number, which means [...] every possible sequence appears at some point.</I><BR/><BR/>That's not strictly true. Pi is transcendental, of course, but it is not known that every transcendental number must be "normal" (have every possible finite sequence appearing with equal probability). Pretty much all that is known is that the set of non-normal numbers has measure zero. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166032759899236012006-12-13T12:59:00.000-05:002006-12-13T12:59:00.000-05:00Ah, found the book:The Visiting Professor by Rober...Ah, found the book:<BR/><BR/><A HREF="http://www.amazon.com/Visiting-Professor-Novel-Chaos/dp/1585678163/sr=1-2/qid=1166032505/ref=sr_1_2/002-4696541-9320850?ie=UTF8&s=books" REL="nofollow">The Visiting Professor</A> by Robert Littel<BR/><BR/>Here's the blurb:<BR/><BR/><I><BR/>Forsaking his customary thriller territory, Littell ( The Revolutionist ) here finds fertile new ground in the farther Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166032171890912742006-12-13T12:49:00.000-05:002006-12-13T12:49:00.000-05:00Hi Uncle,that's nice :-) I once read a book which ...Hi Uncle,<BR/><BR/>that's nice :-) I once read a book which evolved around a sequence of 23 23-s in Pi, but I can't really remember the details (not the name of the book, will try to find out). You know where to find the sequence? <BR/><BR/>Best,<BR/><BR/>B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166030426326670742006-12-13T12:20:00.000-05:002006-12-13T12:20:00.000-05:00Yasumasa Kanada 6,442,450,000 decimal digits, M...Yasumasa Kanada<BR/><BR/> 6,442,450,000 decimal digits, March 1996.<BR/> 51,539,600,000 decimal digits, August 1997.<BR/> 206,158,430,000 decimal digits, September 1999.<BR/>1,241,099,999,501 decimal digits, December 2002. <BR/><BR/>Frequency distributions for (pi minus 3)<BR/><BR/> 1.2x10^12 <BR/>==================<BR/>0: 119,999,636,735<BR/>1: 120,000,035,569<BR/>2: Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1166030350602303102006-12-13T12:19:00.000-05:002006-12-13T12:19:00.000-05:00Missing a factorial.Missing a factorial.Anonymousnoreply@blogger.com