tag:blogger.com,1999:blog-1784861354684747574.post4928902942472356634..comments2023-11-18T01:36:04.058-08:00Comments on Post-Doc Ergo Propter Hoc: The Nested Logarithm ConstantsAlexhttp://www.blogger.com/profile/06621088380628973769noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-1784861354684747574.post-52033217654550841222016-10-10T12:21:09.378-07:002016-10-10T12:21:09.378-07:00This took about 2 minutes on my machine.
60,000 d...This took about 2 minutes on my machine.<br /><br />60,000 digits would take about twice as long (because the amount required grows by roughly $\sqrt{N}$Anonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-71250103169101705202016-10-10T11:57:12.684-07:002016-10-10T11:57:12.684-07:00Damn that's a lot of digits.Damn that's a lot of digits.Alexhttps://www.blogger.com/profile/06621088380628973769noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-6762516055389670742016-10-10T11:50:54.093-07:002016-10-10T11:50:54.093-07:00I removed my other comment, because this one only ...I removed my other comment, because this one only has the digits, not the whole output.<br /><br />Here are the first 15,000 digits (generated from 50,000 bits).<br /><br />http://hastebin.com/fecaboqese.css<br />Anonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-25334985700575757202016-10-10T11:47:51.374-07:002016-10-10T11:47:51.374-07:00Yes.
The quadratic function of $N$ I posted tells...Yes.<br /><br />The quadratic function of $N$ I posted tells how many bits are accurate after N iterationsAnonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-71098879298299403952016-10-10T11:45:09.440-07:002016-10-10T11:45:09.440-07:00I know what bits are but I'm unsure how it rel...I know what bits are but I'm unsure how it relates to the convergence? Are you talking about the number of converged binary digits in each step after N iterations?Alexhttps://www.blogger.com/profile/06621088380628973769noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-939707794742310972016-10-10T11:39:39.172-07:002016-10-10T11:39:39.172-07:00Bits are binary digits.
Like how we have digits th...Bits are binary digits.<br />Like how we have digits that can be 0, 1, 2, 3, . . . 9<br /><br />The binary equivalent are called bits (each 0 or 1).<br /><br />So we might say that $1242$ (base 10) has 4 digits, and we would say that $110101$ (base 2) has 6 bits.<br /><br />Each digit is roughly $log_(2)(10) \approx 3.3219280$ bits.Anonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-26889692636035614092016-10-10T11:36:24.978-07:002016-10-10T11:36:24.978-07:00Thanks!
What do you mean by bits in this context?Thanks!<br />What do you mean by bits in this context?Alexhttps://www.blogger.com/profile/06621088380628973769noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-35480666686337669582016-10-10T11:33:35.816-07:002016-10-10T11:33:35.816-07:00This comment has been removed by the author.Anonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.comtag:blogger.com,1999:blog-1784861354684747574.post-32004394489439012922016-10-10T11:33:00.947-07:002016-10-10T11:33:00.947-07:00It does converge quite fast.
The number of bits a...It does converge quite fast.<br /><br />The number of bits after N iterations is roughly $.02N^2+2.24N-8.5$<br /><br />This has a correlation coefficient of 1.0 through 5 datapoints.<br /><br />So, this constant is quite easy to compute lots of digits.<br /><br />I used this: http://hastebin.com/jubemuxifu.cpp to compute the first 100000 bits.<br /><br />Anonymoushttps://www.blogger.com/profile/10738016279552190989noreply@blogger.com