_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
