Ha ha ha ... umm ... clunk. Life's too short for this.
On the slightly more serious side, string theory doesn't seem to generate
much in the way of testable hypotheses, as Feynman pointed out just before
he popped his clogs --- it therefore has little to do with Science. I'm
with Peter Woit here ("Not Even Wrong") --- see e.g.
http://www.edge.org/response-detail/25416 where he points out that even in
the rare circumstances where string theorists make predictions and they
fail, the failed theory is shored up with special pleading. Spare me...
Jo.
On 22 January 2014 06:19, 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
