Sidney Coleman

… Nobel laureate Sheldon Glashow told the Boston Globe. “… within the community of theoretical physicists, he’s kind of a major god. He is the physicist’s physicist.”

Coleman’s lectures at Harvard were also legendary. Students in one quantum field theory course created T-shirts bearing his image and a collection of his most noted quotations, among them: “Not only God knows, I know, and by the end of the semester, you will know.” Despite this acclaim, he did not generally enjoy teaching or mentoring graduate students:

I hate [teaching]. You do it as part of the job. Well, that’s of course false … or maybe more true than false when I say I hate it. … But I certainly would be just as happy if I had no graduate students. … Occasionally there is a graduate student who is a joy to collaborate with. Both David Politzer and Erick Weinberg were of this kind, but they were essentially almost mature physicists. They were very bright by the time they came to me. In general, working with a graduate student is like teaching a course. It’s tedious, unpleasant work. A pain in the neck. You do it because you’re paid to do it. If I weren’t paid to do it I certainly would never do it.

— Wikipedia on Sidney Coleman

2012.04.17 Tuesday ACHK

機會率分母

這段改編自 2010 年 6 月 2 日的對話。

機會率是一個分數。分子代表期望的結果;分母代表已知的東西,又名「樣本空間」。

即使期望的事件相同,如果已知的東西不同,都會導致機會率的數值有分別。例如,假設有一粒骰子是公平的,即是各個結果出現的機會率均等。如果要擲到「3」,機會率是多少呢?

期望的結果只有一個,就是擲到「3」,所以機會率分子是 1。樣本空間,就是所有可能結果的集合,即是{1, 2, 3, 4, 5, 6}。樣本空間,顯示總共有 6 個可能的結果,所以機會率分母是 6。答案是,擲到「3」的機會率是 1/6。

但是,如果你已知結果一定是單數,樣本空間就會收窄成{1, 3, 5}。因為現在只有 3 個可能的結果,機會率分母應該改為 3。結論是,擲到「3」的機會率是 1/3。

你現在用「集合論」中的「文氏圖」(Venn diagram),來分析一題機會率題目,理論上是合理的。但是,實際上,你要十分小心,因為「文氏圖」所直接表達的,只有期望的結果,即是「機會率分子」。稍一不留神,你會忘記了,還要考慮「樣本空間」,即是「機會率分母」。

— Me@2012.04.17

2012.04.17 Tuesday (c) All rights reserved by ACHK