I know of analytic continuation, but these guys did not mention analytic continuation, nor Abel summation, nor Cesàro summation, nor ... . (They also changed the video since I first viewed it, and flashed up references to alternative proofs.) Please read my original post carefully.
>It would be interesting to see J deal with divergent series... Dealing with _convergent_ series or products would be a good start and interesting enough. See Bring Something Beautiful<http://archive.vector.org.uk/art10500390> . On Tue, Jan 21, 2014 at 9:19 AM, greg heil <[email protected]> wrote: > _1r12 = 1+2+3+4+5+… > > >This is a series used in physics, which is a discipline only slightly > removed from witchcraft (with the emphasis on slightly). As Niels Abel said > "The divergent series are the invention of the devil". > > >i would guess that Roger's reaction is similar to almost every ones. One > however can change the rules, broaden the mind set. Mathematicians are also > in this game see ~analytic_continuation in Wikipedia. And many more > references: see the write up in Slate. > > >It would be interesting to see J deal with divergent series... > > ---~ > > http://www.slate.com/blogs/bad_astronomy/2014/01/18/follow_up_the_infinite_series_and_the_mind_blowing_result.html > > http://en.wikipedia.org/wiki/Grandi's_series > > http://en.wikipedia.org/wiki/Analytic_continuation > > Lubos Motl's physics blog > http://motls.blogspot.com/ > > greg > ~krsnadas.org > > -- > > from: R.E. Boss [email protected] > to: [email protected] > date: 21 January 2014 08:59 > subject: Re: [Jchat] +/i. _: > > Yeah, see also > http://www.gocomics.com/calvinandhobbes/2011/03/09#.Ut6nFBA1iDE > > -- > > from: Ni Bo [email protected] > reply-to: [email protected] > to: [email protected] > date: 21 January 2014 06:46 > subject: Re: [Jchat] +/i. _: > > >*T = 1+1+1+1+ ... = 1+(1+1+1+1+ ...) = 1+T Subtracting T from both > sides, we have 0=1. QED.* > > >Now this is a neat mathematical demonstration for a postmodern approach > to mathematics, physics and reality. How dare one say that 1+1=2? They are > intolerant! I choose to believe that > > 1+1=1 > And who are you to impose your belief system on me? :-) > > Nick > > -- > > from: Don Guinn [email protected] > to: Chat forum <[email protected]> > date: 21 January 2014 05:45 > subject: Re: [Jchat] +/i. _: > > >_: 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? > > -- > > from: Roger Hui [email protected] > to: Chat Forum <[email protected]> > date: 20 January 2014 21:52 > subject: Re: [Jchat] +/i. _: > > >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. > > -- > > from: Richard Hill [email protected] > to: [email protected] > date: 20 January 2014 21:23 > subject: Re: [Jchat] +/i. _: > > >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
