[math-fun] Some silly arithmetic ...
For some reason, this maths-chat turned up on the Chessbase site ... http://en.chessbase.com/post/a-math-break Someone, please tell me that some formula is being used outside its 'zone of convergence' ... and that 'String Theory' is not using dodgy arithmetic. Thanks in advance, Guy
Summing up the naturals gives infinity, but you can analytically continue the Riemann zeta function to -1 and get -1/12. Here's the story about bosonic string theory: http://math.ucr.edu/home/baez/numbers/24.pdf On Fri, Oct 6, 2017 at 11:39 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
For some reason, this maths-chat turned up on the Chessbase site ... http://en.chessbase.com/post/a-math-break
Someone, please tell me that some formula is being used outside its 'zone of convergence' ... and that 'String Theory' is not using dodgy arithmetic.
Thanks in advance,
Guy
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
.5 Grumble. Write 1/(1-x)^2 = 1 + 2x + 3x^2 + 4x^3 + ... Substitute x = 1 to get 1/infinity^2, a double pole. Why choose zeta, rather than a simple rational function, to do your extrapolation? Rich -------------- Quoting Mike Stay <metaweta@gmail.com>:
Summing up the naturals gives infinity, but you can analytically continue the Riemann zeta function to -1 and get -1/12. Here's the story about bosonic string theory: http://math.ucr.edu/home/baez/numbers/24.pdf
On Fri, Oct 6, 2017 at 11:39 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
For some reason, this maths-chat turned up on the Chessbase site ... http://en.chessbase.com/post/a-math-break
Someone, please tell me that some formula is being used outside its 'zone of convergence' ... and that 'String Theory' is not using dodgy arithmetic.
Thanks in advance,
Guy
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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I don't think (1/1-x) is summable by any means at x=1, let alone 1/(1-x)^2, whereas there's no pole at zeta(-1). On Fri, Oct 6, 2017 at 1:22 PM, <rcs@xmission.com> wrote:
.5 Grumble.
Write 1/(1-x)^2 = 1 + 2x + 3x^2 + 4x^3 + ... Substitute x = 1 to get 1/infinity^2, a double pole. Why choose zeta, rather than a simple rational function, to do your extrapolation?
Rich
--------------
Quoting Mike Stay <metaweta@gmail.com>:
Summing up the naturals gives infinity, but you can analytically continue the Riemann zeta function to -1 and get -1/12. Here's the story about bosonic string theory: http://math.ucr.edu/home/baez/numbers/24.pdf
On Fri, Oct 6, 2017 at 11:39 AM, Guy Haworth <g.haworth@reading.ac.uk> wrote:
For some reason, this maths-chat turned up on the Chessbase site ... http://en.chessbase.com/post/a-math-break
Someone, please tell me that some formula is being used outside its 'zone of convergence' ... and that 'String Theory' is not using dodgy arithmetic.
Thanks in advance,
Guy
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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