微積分 2

這段改編自 2010 年 5 月 1 日的對話。

留意,我只是說做了一個「不定積分」(indefinite integration)後,你可以對答案式子做一次「微分」(differentiation),看看是否得回題目的式子。是的話,你答案正確的機會就十分高。

但是,我從來沒有說過,你做了一題「微分」題目後,可以透過對答案做一次「不定積分」,以作驗算。那是不行的。

「微分」是機械程序,「不定積分」不是。「微分」比「不定積分」簡單容易很多。所以,你應該用「微分」來驗算「不定積分」題目,而不應該用「不定積分」來校對「微分」題目。

如果要驗算「微分」題目的話,你要用其他方法。其中一個方法是,用一部有「微積分」功能,而又被考試局認可的計數機。

— Me@2011.05.18

2011.05.18 Wednesday (c) All rights reserved by ACHK

From Heisenberg to Godel

My student Mike Stay did computer science before he came to UCR. When he was applying, he mentioned a result he helped prove, which relates Godel’s theorem to the Heisenberg uncertainty principle:

2) C. S. Calude and M. A. Stay, From Heisenberg to Godel via Chaitin, International Journal of Theoretical Physics, 44 (2005), 1053-1065. …

Now, this particular combination of topics is classic crackpot fodder. People think “Gee, uncertainty sounds like incompleteness, they’re both limitations on knowledge – they must be related!” and go off the deep end. So I got pretty suspicious until I read his paper and saw it was CORRECT… at which point I definitely wanted him around! The connection they establish is not as precise as I’d like, but it’s solid math.

— This Week’s Finds in Mathematical Physics (Week 230)

— John Baez

2011.05.18 Wednesday ACHK