Self-reference

Recursion 12

Self-reference may not be paradoxical, as long as there is a terminating condition / boundary case.

As long as there is a terminating condition, the self-reference is not really “hundred-percent-self”-reference. In other words, it is just self-similar, but not self-identical.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.

Being self-similar is possible, but being self-identical is logically impossible since it creates infinite regress.

— Me@2013.01.12

2013.01.13 Sunday (c) All rights reserved by ACHK

Persuasion

Oran had been reading the work of Robert Cialdini, a former psychology professor and an expert in the power of persuasion. Cialdini had run experiments in southern California trying to get homeowners to reduce their energy use. When Cialdini distributed signs urging people to conserve energy to benefit the environment, or to save money, or to benefit future generations, they didn’t respond. But when Cialdini’s signs informed people that their neighbors were changing their ways to save energy, they responded. Energy use went down.

— The Inside Story of MoveOn’s Secret “Silver Bullet” to Deliver Victory for Obama

— By Andy Kroll

— Mother Jones (magazine)

2013.01.13 Sunday ACHK

對稱情境 1.1

這段改編自 2010 年 6 月 15 日的對話。

有兩個袋。每個袋中都有十張卡紙,而每張卡紙上,都有由 1 到 10 的其中一個數字,沒有重複。現在,甲要由第一個袋中,抽一張卡紙出來。而乙則要在另一個袋中,抽另一張卡紙出來。假設整個過程是隨機的,即是各個可能性的機會均等。

如果甲的數字大過乙,那就為之「甲勝」。如果乙的數字大過甲,那就為之「乙勝」。已知「甲勝」的機會率是 q。問題是,「甲乙打和」的機會是多少?

整個遊戲只有三個可能的結果 ── 「甲勝」、「乙勝」 或者 「打和」 ── 而它們是互斥事件。所以,

P(甲勝)+ P(打和)+ P(乙勝)= 1

因為「甲勝」的機會是 q,而甲乙所面對的情境,又完全相同,所以「乙勝」的機會和「甲勝」一樣,都是 q。

q + P(打和)+ q = 1

P(打和)= 1 – 2q

結論是,「甲乙打和」的機會率是(1 – 2q)。

— Me@2013.01.13

致讀者:如發現本文有思考漏洞,或者運算錯誤,請以電郵告知本人。謝謝!

— Me@2012.10.17

2013.01.13 Sunday (c) All rights reserved by ACHK