Fellow Jedi - There's a New Scientist article about some people who open-sourced some code to attempt to accomplish Ramanujan-like discoveries in the area of continued fractions: https://www.newscientist.com/article/2209213-computer-attempts-to-replicate-the-dream-like-maths-of-ramanujan/ .
Unfortunately it is paywalled, so I will fair-use a little here: *The theorems Ramanujan produced often involved continued fractions, which express a number as the sum of infinitely nested fractions.* *To mimic this approach, Gal Raayoni at the Israel Institute of Technology and his colleagues created the Ramanujan Machine <http://arxiv.org/abs/1907.00205>. It has already come up with tens of conjectures that use continued fractions to approximate π and e.* *One method the program uses to search for new conjectures is a “meet in the middle” approach. This involves generating many mathematical expressions, computing their value for a limited number of iterations and eliminating the expressions that give inaccurate results.* Anyway, the formula for *e* they show in the article renders into J this way: calcRamalikeE=: 13 : '(+`%)/,x:(3+i.y),.->:i.y'"0 calcRamalikeE ([: +`%`:3 [: , [: x: (3 + i.) ,. [: - [: >: i.)"0 calcRamalikeE 10 20 9864101r3628800 6613313319248080001r2432902008176640000 >50j48":&.>calcRamalikeE 10 20 2.718281801146384479717813051146384479717813051146 2.718281828459045235339784490666415886146403434540 All fine and good but when I tried to replicate this from memory at home tonight, I kept getting a "spelling error" on the "(+`%)" part. Eventually I figured out that what I'm typing in is rendering in Unicode and is failing a spelling test. I'm running J64 8.07, Library 8.07.26, and, as always, under Emacs on Windows. I'm afraid it may just be an Emacs thing as I had saved the problematic session as "raw-text" earlier but I'd be pleased to hear from anyone who could replicate or explain this or, even better, make sure it never happens to anyone else ever again. Thanks, Devon -- Devon McCormick, CFA Quantitative Consultant ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
