_: is the verb infinity. You need a noun to get a calculated result. But what is he trying to say? Obviously the sum cannot equal 1r12. So what is (-1/12) supposed to mean?
On Mon, Jan 20, 2014 at 10:23 PM, Richard Hill <[email protected]> wrote: > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
