The following statement is copied from Lubos Motl's physics blog... the sum of positive integers should be assigned the value \(-1/12\). However, this profound truth reigns not only in string theory but in any theory where some free fields periodically depend on two dimensions. That's why one may verify that the sum equals \(-1/12\) even in QED, by measuring the Casimir force between two plates. It's really an important insight in all of physics and all approaches to mathematics of functions that wants to respect the same kind of "deep mathematical wisdom and elegance" that is exhibited by Nature through quantum field theory and string theory.
He says this was known to Euler When I try it in J 604 I get +/i.@ _: ┌─────┬──┬──┐ │┌─┬─┐│i.│_:│ ││+│/││ │ │ │└─┴─┘│ │ │ └─────┴──┴──┘ but +/ i. 10E7 5e15 And +/ i. 10E8 |limit error | +/ i.1000000000 Which is what I expected Is there any way the "profound truth" can be expressed in J? ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
