網誌時代 9 | 種子意念 6
這段改篇自 2010 年 3 月 6 日的對話。
（安：我最近有看過你那個叫做 Somehow Amazing 的網誌，見到我們對話的紀錄。那真的是 somehow amazing（略帶一點點精采）。）
但是，你有沒有發覺，那些其實不是我們的真正對話？
（安：我正正是想講這一點。那些應該是經過你的修飾後，才公開發表的。尤其是我的那部分內容，比我原本所講的還要清楚簡潔。）
所以，網誌上的「安」，其實不是百分百真正的你，而是我盜用了你的身份。
在寫網誌時，我的心態是，重點不是要分毫不差地紀錄原文，而是透過你我的對話，帶動我的寫作靈感。
我和你的「心靈作業系統」（思考模式）有相似的地方，所以，有時即使是較為深刻抽象的內容，都可以用很精簡的對話來描述。不好處是，其他的大部分人，因為和我們的思考背景不同，如果我把「原聲」輯錄成文字的話，他們不會明白，我們究竟在說什麼。
— Me@2011.04.10
2011.04.10 Sunday (c) All rights reserved by ACHK
An intellectual is someone who has found something more interesting than sex.
— Edgar Wallace
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2011.04.10 Sunday ACHK
隨行不隨想 3
Even if you cannot control your feelings,
you can control your ACTIONS.
— Me@ <= 2007
2011.04.09 Saturday (c) All rights reserved by ACHK
0/0 不能代表任何東西。知不知原因？
（CKY：不知。）
我以前教過你。
（CKY：不記得。）
例如， 等於 3，因為 3 乘以 2 等於 6，即是 3 乘以分母等於分子。又例如，
，因為 4 乘以 3 等於 12。明白嗎？
（CKY：明白。）
同理， 應該是等於 2，因為 2 乘以 0（分母）等於 0（分子）。
（CKY：但是，3 乘以 0（分母），都會等於 0（分子）。）
無錯，所以 又可以代表 3。
一個符號之所以有意思，在於它可以表達唯一的一樣東西。如果一個符號不代表任何東西，又或者可以同時表達超過一樣東西的話，它就會沒有任何意思。
例如，你的名字是 CKY。「CKY」這個名字之所以有意思，是因為「CKY」在這班中，代表了唯一的一個人（你）。如果「CKY」在這班中，不代表任何人的話，它就沒有用處。另一方面，如果「CKY」在這班中，代表超過一個人的話，它亦會沒有用處。
最極端的情形是，這班中的所有人，都叫做「CKY」。那就會很奇怪。當老師宣佈委任「CKY」做班長時，大家也不知道究竟誰會做班長。
而 正正是這個最極端的情形。
可以代表任何一個數，所以它沒有任何用處。
— Me@2011.04.09
2011.04.09 Saturday (c) All rights reserved by ACHK
The quality of a mathematical problem is the mathematics it generates.
— Me, powered by Andrew Wiles
— Me@2010.10.27
2011.04.07 Thursday ACHK
男士希望自己是，女士的第一個對象；
女士則希望自己是，男士的最後一個對象。
— Lee
— Me@2009.02.16
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2011.04.07 Thursday ACHK
這段改篇自 2010 年 2 月 12 日的對話。
總結一下，我們今日討論了「時間定義」。然後就討論了人過身以後，對「時間」的感覺會有什麼不同。接著，我就說其中一個可能性是，過了身以後，人會面對同一個客觀物理世界。即使是那樣，由於我們的存在形式改變了，我們對「同一個客觀物理世界」的主觀認知會有所不同。
跟住，我嘗試解釋人過身時，存在形式 為何會改變 和 如何改變。其中一個要點是，過身以後，一個人的「自我」再不會限制於同一個頭顱之中。
而在相反的另一方面，在生的時候，一個人的頭顱之中，有超過一個「自我」。例如，一個人的左右兩腦，各自可以看成一個完整的「人格」。
— Me@2011.04.06
2011.04.06 Wednesday (c) All rights reserved by ACHK
“In almost all textbooks, even the best, this principle is presented so that it is impossible to understand.” (K. Jacobi, Lectures on Dynamics, 1842-1843). I have not chosen to break with tradition.
— V. I. Arnold, Mathematical Methods of Classical Mechanics, footnote, p. 246
2011.04.05 Tuesday ACHK
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I’m about to become a teacher. How can I be a good one?
The best teachers I remember from school had three things in common:
(1) They had high standards. Like three year olds testing their parents, students will test teachers to see if they can get away with low-quality work or bad behavior. They won’t respect the teachers who don’t call them on it.
(2) They liked us. Like dogs, kids can tell very accurately whether or not someone wishes them well. I think a lot of our teachers either never liked kids much, or got burned out and started not to like them. It’s hard to be a good teacher once that happens. I can’t think of one teacher in all the schools I went to who managed to be good despite disliking students.
(3) They were interested in the subject. Most of the public school teachers I had weren’t really interested in what they taught. Enthusiasm is contagious, and so is boredom.
— Paul Graham
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2011.04.05 Tuesday ACHK
What you have learnt is 100 percent yours,
regardless of your academic results.
— Me@2009.03.06
2011.04.04 Monday (c) All rights reserved by ACHK
這裡很麻煩：由 -2 變成 -3，應該叫做「變大」還是「變小」？
無論怎樣答，都好像不妥當。為了清晰起見，這裡應該避用「大/小」這個字眼。我們可以這樣說， -3 比 -2 更加「負」； +3 比 +2 更加「正」。
如果斜率是正數的話，越正越斜：越正的斜率數值，代表越斜的斜線；如果斜率是負數的話，越負越斜。
— Me@2011.04.04
2011.04.04 Monday (c) All rights reserved by ACHK
Again, the time reversal of macroscopic processes can only exist if we “saturate” the second law of thermodynamics: if the entropy stays constant. The time reversal of such processes keeps the entropy constant, too. These processes are not real processes because nothing much is changing. Instead, they describe a physical system at equilibrium.
— Lubos Motl
2011.04.04 Monday ACHK
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Socialising on the internet is to socialising, what reality TV is to reality.
— Aaron Sorkin
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2011.04.04 Monday ACHK
When you think about it, love is just another search problem. And we’ve thought about it. A lot. Google Romance is our solution.
— Google Romance
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2011.04.03 Sunday ACHK
靈魂軟件論 2 | 輪迴 5
還有，之前提過，人的心靈，其實是一個軟件/程式。軟件可以複製。輪迴的時候，究竟如何複製？而又會複製成怎麼樣？有很多可能。
所以，現實世界，其實很 magical（神奇）。
— Me@2011.04.02
2011.04.02 Saturday (c) All rights reserved by ACHK
I think there’s a general principle at work here: the less energy people expend on performance, the more they expend on appearances to compensate. More often than not, the energy they expend on seeming impressive makes their actual performance worse.
In big companies, there’s always going to be more politics and less scope for individual decisions.
The time may soon be coming when instead of startups trying to seem more corporate, corporations will try to seem more like startups. That would be a good thing.
— Paul Graham
2011.04.02 Saturday ACHK
Peirce’s law in logic is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic.
In propositional calculus, Peirce’s law says that ((P→Q)→P)→P. Written out, this means that P must be true if there is a proposition Q such that the truth of P follows from the truth of if P then Q. In particular, when Q is taken to be a false formula, the law says that if P must be true whenever it implies the false, then P is true. In this way Peirce’s law implies the law of excluded middle.
Peirce’s law does not hold in intuitionistic logic or intermediate logics and cannot be deduced from the deduction theorem alone.
Under the Curry-Howard isomorphism, Peirce’s law is the type of continuation operators, e.g. call/cc in Scheme.
— Wikipedia on Peirce’s law
2011.04.02 Saturday ACHK
The greatest enemy of “the best” is “the second best”.
Remember, you have only one life in this life.
In another life, you will be another person.
So, treasure this life as much as possible.
— Me@2010.11.14
2011.04.02 Saturday (c) All rights reserved by ACHK
融會貫通 | 故事連線 3
這段改篇自 2010 年 4 月 30 日的對話。
我的意思是，你千萬不要「死記」。「死記」的不好處是，一方面你心裡會很不舒服；另一方面，你很容易會遺忘。
（CSK：但是，你剛才又叫我們不要期望可以自己想出那些數學技巧，而一定要在考試前背誦好。現在，你又叫我們不要背誦？）
我剛才是叫你不要「死記」，而不是叫你不要「記」。「死記」的意思是，在沒有任何理解之下，就把那些東西生硬背誦下來。只要精神狀態稍為波動，所有「死記」的東西就會不見了。
那樣，如何可以「生記」呢？
先理解那些公式背後的 幾何意義 或者 物理意思，然後把上文下理一併背誦下來。例如，如果你有 4 樣東西 —— A、B、C、D —— 要記的話，其實你有超過 4 樣東西要記。除了要各自記得 A、B、C、D 以外，你還要記得它們之間的關係，例如：
1. A
2. B
3. C
4. D
5. AB （原來 B 是由 A 推算出來的。）
6. BC （原來 B 和 C 只不過是同一個意思的不同講法。）
7. AD （原來 D 只是 A 的一個特例。）
8. CD （原來 D 可以用來驗算 C 的運算結果。）
9. etc.
那樣，A、B、C、D 對你來說，除了是 4 樣東西以外，還形成了一個知識網絡。
萬一你遺忘了（例如）A 的話，你可以立刻由 B、C、D 把 A 推斷出來，因為在這一個知識網絡中，你有遠多於一條路可以走到 A，亦即是你有遠多於一個方法回憶到 A。即使你不能直接回憶到 A，你仍可以由 B 去 A，又可以由 C 去 A，等等。只要其中一條路行得通，你就可以到達 A。反而，要遺忘 A 的話，你需要一個奇蹟。
— Me@2011.03.31
2011.03.31 Thursday (c) All rights reserved by ACHK
The odd thing is that there are a lot of mathematical connections between string theory and the loop representation. Gradually, as time went on, I became more and more convinced that maybe the layfolk were right – maybe the loop representation of quantum gravity really WAS string theory in disguise, or vice versa. This made a little embarrassed by how much I had been making fun of string theory.
I decided to write a paper about this, and as I did some research I was intrigued to find more and more connections between the two approaches, to the point where it is clear that while they are presently very distinct, they come from the same root, historically speaking.
So what I’m hinting at, in brief, is that a bunch of category theory may provide the links between modern string theory with its conformal fields and the loop representation of quantum gravity. This is not as outre as it may appear. The categories being discussed here are really just ways of talking about symmetries (see my stuff on categories and symmetries for more on this). As usual in physics, the clearest way to grasp the connection between two seemingly disparate problems is often by recognizing that they have the same symmetries.
September 11, 1993
This Week’s Finds in Mathematical Physics (Week 18)
John Baez
2011.03.31 Thursday ACHK
Physics Town 
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