tag:blogger.com,1999:blog-663998076511109850.post5848563908597115345..comments2023-11-05T04:33:11.265-08:00Comments on Maison Fleury: Mathematics: Can +, x and ^ operands be generalized to higher orders?adt43wt342http://www.blogger.com/profile/07557608193924044365noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-663998076511109850.post-55465578344124489602008-05-27T06:23:00.000-07:002008-05-27T06:23:00.000-07:00well, www.tetration.org :)by googling tetration :)...well, <BR/><BR/>www.tetration.org :)<BR/><BR/>by googling tetration :)<BR/> <BR/>There is good stuff on the physics (indeed found in renormalization).<BR/>It has to do with Hopf algebras and 90 pages of stuff I didn't understand at all. But if you want to take a look at what experts are doing in theoretical physics and all the cute little diagrams that look like fishes. I wonder if what we do in software looks dumb in comparison?<BR/><BR/>http://arxiv.org/abs/hep-th/0408145/%7C<BR/><BR/>Don't waste more than 30 seconds, it is completely obscure.adt43wt342https://www.blogger.com/profile/07557608193924044365noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-68800308144508033202008-05-26T14:15:00.000-07:002008-05-26T14:15:00.000-07:00barry! Bingo!As you can see, I was writing my answ...barry! Bingo!<BR/><BR/>As you can see, I was writing my answer while you were writing yours. <BR/><BR/>Yes! this is exactly it. The OP(n) defined here are the Hyper-Operator or the Knuth up arrow notation! Apparently hypothesized in the 76 by Knuth. The OP(3) is called "Tetration or Hyper 4". <BR/><BR/>I browsed what I could from wikipidia and found the material a bit weak. No discussion of derivatives nor discussions of APPLICATION. <BR/><BR/>Tetration is probably FOUND in phenomenas that have their derivative equal to the square of themselves. <BR/><BR/>Very cool barry, thank you, how did you go about finding this information? What did you google for? did you know about it before? from knuth? very cool, thanksadt43wt342https://www.blogger.com/profile/07557608193924044365noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-33995449369677336332008-05-26T14:03:00.000-07:002008-05-26T14:03:00.000-07:00I knew there would be jokes about 42 and mainframe...I knew there would be jokes about 42 and mainframes :)<BR/><BR/>I feel slightly old and very crazy.<BR/><BR/>Come on! there has got to be something somewhere.adt43wt342https://www.blogger.com/profile/07557608193924044365noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-54907144992391113342008-05-26T14:02:00.000-07:002008-05-26T14:02:00.000-07:00At first glance, OP(n) is equivalent to Knuth's up...At first glance, OP(n) is equivalent to <A HREF="http://en.wikipedia.org/wiki/Knuth's_up-arrow_notation" REL="nofollow">Knuth's up-arrow notation</A> for n-1 up-arrows, where n >= 2. Iterated exponentiation, your OP(3), is called <A HREF="http://en.wikipedia.org/wiki/Tetration" REL="nofollow">tetration</A>, and has its own format - a bit like exponentiation in the mirror.Barry Kellyhttps://www.blogger.com/profile/10559947643606684495noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-80459615669676655402008-05-26T11:49:00.000-07:002008-05-26T11:49:00.000-07:00Funny I have been wondering about the same idea fo...Funny I have been wondering about the same idea for many years.Julien Viethttps://www.blogger.com/profile/04710381063905327936noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-35078648521598763432008-05-26T11:46:00.000-07:002008-05-26T11:46:00.000-07:00d((x OP(3) n))/dx = (x OP(3) n) (x OP(3) n-1)/ x ...d((x OP(3) n))/dx = (x OP(3) n) (x OP(3) n-1)/ x = 42<BR/><BR/>There. Now go to sleep.Roy Russohttps://www.blogger.com/profile/09423697973167398758noreply@blogger.comtag:blogger.com,1999:blog-663998076511109850.post-79744368443847070892008-05-26T11:31:00.000-07:002008-05-26T11:31:00.000-07:00If you can count to 7.6 e 12 sheep and still not f...If you can count to 7.6 e 12 sheep and still not fall asleep, you will break the mainframe. <BR/><BR/>That's it.Juha Lindforshttps://www.blogger.com/profile/10913597885618265996noreply@blogger.com