[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80 (1002ﾚｽ)
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114(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2020/01/06(月) 07:16:44.47 ID:t3ENnC2G(1/7) AAS
>>109
貴方のために、下記追加
１）時枝記事の起源
>>86 Hart氏 PDF http://www.ma.huji.ac.il/hart/puzzle/choice.pdf
スレ45 2chｽﾚ:math
(抜粋)
この”ルーマニアあたり”は、地名とよむのが、普通だろうね
で、Sergiu Hartはユダヤ人だがルーマニア生まれなので、ソースは同じかもね
因みに http://www.ma.huji.ac.il/hart/puzzle/choice.html Sergiu Hart Choice Games より PDFには
”1Source unknown. I heard it from Benjy Weiss, who heard it
from ..., who heard it from ... . For a related problem, see
http://xorshammer.com/2008/08/23/set-theory-and-weather-prediction/ ”
と注釈が入っているよ
で、関連部分引用する（＾＾
https://xorshammer.com/2008/08/23/set-theory-and-weather-prediction/
SET THEORY AND WEATHER PREDICTION XOR’S HAMMER Some things in mathematical logic that I find interesting WRITTEN BY MKOCONNOR Blog at WordPress.com. AUGUST 23, 2008
(抜粋)
For some interesting comments on this puzzle, see Greg Muller’s blog post on it here
http://cornellmath.wordpress.com/2007/09/13/the-axiom-of-choice-is-wrong/
(引用終り)
つづく
115(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE [sage] 2020/01/06(月) 07:17:10.15 ID:t3ENnC2G(2/7) AAS
>>114
つづき
２）Generalized Hat Problems との関連
スレ45 2chｽﾚ:math
(抜粋)
ピエロくんの紹介
https://pdfs.semanticscholar.org/8514/a9f8b30546ea81739b9409132673276713d3.pdf
The Mathematics of Coordinated Inference: A Study of Generalized Hat Problems (Developments in Mathematics) 2013 edition by Hardin, Christopher S., Taylor, Alan D.
７章”The Topological Setting”とかなっていて
P9
”In Chapter 7 we start to move further away from the hat problem
metaphor and think instead of trying to predict a function's value at a
point based on knowing (something about) its values on nearby points. The
most natural setting for this is a topological space and if we wanted to
only consider continuous colorings, then the limit operator would serve as
a unique optimal predictor. But we want to consider arbitrary colorings.
Thus we have each point in a topological space representing an agent and
if f and g are two colorings, then f ≡a g if f and g agree on some deleted
neighborhood of the point a. It turns out that an optimal predictor in this
case is wrong only on a set that is "scattered" (a concept with origins going
back to Cantor). Moreover, this predictor again turns out to be essentially
unique, and this is the main result in Chapter 8.”
などとある
さすれば、時枝もそのままじゃ（Topologicalな条件を加えないと）、成り立たないと思う
(引用終り)
以上
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