Harvard mathematician answers 150-year-old chess problem
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Harvard mathematician answers 150-year-old chess problem
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Re: Harvard mathematician answers 150-year-old chess problem
#2Note that the preprint on arXiv dated back to July 2021.
Re: Harvard mathematician answers 150-year-old chess problem
#3I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
Re: Harvard mathematician answers 150-year-old chess problem
#4I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
Close enough.
- a mathematician
Re: Harvard mathematician answers 150-year-old chess problem
#5I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
There is the always elided “constant coefficient”, which the press release does not even mention.
Re: Harvard mathematician answers 150-year-old chess problem
#6I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
Looking at the actual result, you can really only expect that (92^(1/8))/8 should be close to 0.143. It works out to about 0.22, which is less than double. The result actually says this ratio tends to 1 as n tends to infinity.
Re: Harvard mathematician answers 150-year-old chess problem
#7I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
I noticed the same :-)
Knowing mathematics though, it's quite likely that this result is valid only for some regimes of N, for example assymptotically
Re: Harvard mathematician answers 150-year-old chess problem
#8I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
From the paper
We show that there exists a constant α = 1.942±3×10−3 such that Q(n) = ((1 ± o(1))ne^−α)^n
Dunno what o(1) is.
Re: Harvard mathematician answers 150-year-old chess problem
#9Also featured in this Quanta Magazine article [1]
[1] https://www.quantamagazine.org/mathematician-answers-chess-p...
Re: Harvard mathematician answers 150-year-old chess problem
#10I must be missing something, but when I take the formula (0.143n)^n, for n=8 the result is 2.933, while it should be around 92?
From the paper We show that there exists a constant α = 1.942±3×10−3 such that Q(n) = ((1 ± o(1))ne^−α)^n Dunno what o(1) is.
o(1) is some term that goes to 0 as n goes to infinity.