I assume you are serious and not jerking people's chains. The sum that these people are talking about does not use the classical definition of infinite sums, which uses the concept of limits (for all epsilon>0, there exists delta etc.). J does not subscribe to the alternative definitions.
I have seen a YouTube video (search for "1+2+3+4") where two people "proved" that +/1 2 3 4 5 ... equals %_12 and mentioned that the fact is used in string theory. Whatever the methods that are used in string theory to justify that that sum equals _12, their "proof" is, ahem, flawed. Using the same logic, I can prove that 0=1: T = 1+1+1+1+ ... = 1+(1+1+1+1+ ...) = 1+T Subtracting T from both sides, we have 0=1. QED. Corollary: m=n for all positive integers m and n. On Mon, Jan 20, 2014 at 9:23 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
