現代数学の系譜工学物理雑談古典ガロア理論も読む49

[過去ﾛｸﾞ] 現代数学の系譜工学物理雑談古典ガロア理論も読む49 (658ﾚｽ)
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438: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2018/01/13(土) 10:14:15.84 ID:rUYSYDib

>>437 つづき

http://www.cs.umd.edu/~gasarch/TOPICS/hats/infinite-hats-and-ac.pdf
An Introduction to Infinite Hat Problems Chris Hardin and Alan Taylor THE MATHEMATICAL INTELLIGENCER 2008 Springer Science+Business Media, Inc

２）
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.7027&rank=2
A peculiar connection between the Axiom of Choice and predicting the future THE MATHEMATICAL ASSOCIATION OF AMERICA Monthly February 2008
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.365.7027&rep=rep1&type=pdf

３）Taylorさん
https://en.wikipedia.org/wiki/Alan_D._Taylor
Alan D. Taylor

Alan Dana Taylor (born October 27, 1947) is an American mathematician who, with Steven Brams, solved the problem of envy-free cake-cutting for an arbitrary number of people with the Brams?Taylor procedure.

Taylor received his Ph.D. in 1975 from Dartmouth College.[2]

He currently is the Marie Louise Bailey professor of mathematics at Union College, in Schenectady, New York.

以上

つづく

http://rio2016.5ch.net/test/read.cgi/math/1514376850/438

446: 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE  [sage] 2018/01/13(土) 11:37:38.46 ID:rUYSYDib

>>438 補足

pdf：A peculiar connection between the Axiom of Choice and predicting the future THE MATHEMATICAL ASSOCIATION OF AMERICA Monthly February 2008
については、当時哲学者がいろいろ議論したらしい（下記のpdfご参照）
だが、数学者の投稿は見つからなかった！！（＾＾

そして、過去スレ47にも書いたが、The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D. (2013) （>>439）
では、上記の未来予測可能とか、任意の関数の値が予測可能とする論は、全部捨てられている

その話も、ちょろっと、まとめPDFに入れて貰えると面白いと思うよ
で、時枝も同じだよ

https://link.springer.com/chapter/10.1007/978-3-319-58507-9_10
Philosophical Aspects of an Alleged Connection Between the Axiom of Choice and Predicting the Future, Pawel Pawlowski First Online: 06 September 2017
Abstract
In 2008 Christopher Hardin and Alan Taylor published an article titled
“Peculiar connection between the axiom of choice and predicting the future” in which they claim that if some system can be described as a function from a set of some instants of time to some set of states,
then there is a way to predict the next value of the function based on its previous input. Using their so-called   μμ -strategy one can randomly choose an instant t and the probability that the strategy is correct at t
(i.e. that the output for a strategy for input t is exactly the same as the value of the function) equals 1.
Mathematical aspects of this article are sound, but the background story about the correlation between theorems and philosophical aspects of predicting the future faces certain problems. The goal of my paper is to bring them up.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1514376850/446

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