這段改編自 2010 年 3 月 20 日的對話。
很大程度上，所謂「明白」，就是「找到一個適合自己的比喻」。所以，很大程度上，所謂「教學」，就是「利用比喻」，把新知識，轉化成聽眾的舊知識。如果你有才能，把天馬行空、無法感受到的事物，表達成直接具體、切身感受到的東西的話，你就為之有教學的天份。
空間比喻：
事實：原子核的半徑，只有整個原子的十萬分之一。原子核的體積，只有整個原子的 10^15 分之一。
教學：如果一個原子核的大小等於一粒塵埃，一個原子的大小就等於一間房子。
時間比喻：
事實：地球的年齡，是四十六億。
教學：有文字記載的歷史，大概由六千年前開始。先把這個數字，乘以一千。然後，把你得到的數字，再乘以一千。那就相當於地球的年齡。
— Me@2012.03.15
2012.03.15 Thursday (c) All rights reserved by ACHK
It seems that category theory is the new hype — almost nobody actually understands what it is about, or, more importantly, what it is for. Let me tell you what it is for — it’s an important technical tool in mathematical research, which gives you new, coherent language, sometimes provides you with an additional insight in the structure of the stuff you are researching and makes it easier to notice and classify similarities between different kind of structures. Unfortunately, it is almost completely useless and uninteresting by itself — because, well, what’s interesting in objects and arrows anyway?
What make category theory interesting are its connections with various field[s] and [in] math and computer science. That’s why introducing “category theory for dummies” makes completely no sense — it’s like following Erlangen program to teach kids about points, lines and circles on a plane. The need and the significance of Erlangen program arise when you learn about many different geometries, notice what they have in common and what they do not, and try to find out what the geometry is all about. Without it, the Erlangen program is all about abstract bullshit, and the situation is completely the same with category theory. But nobody writes or posts Erlangen program for dummies on HN. Why? “General theory of everything” hype, that’s why. Erlangen program is “general theory of geometry”, but geometry seems a bit pale when compared to everything.
If you really want to understand the significance of category theory, then learn set theory, then algebra, then topology, then algebraic topology and algebraic geometry, or take abstract programming languages theory path. If you don’t care about all this stuff, because you’re hyped on the category theory, then you’re missing the point — it’s like you wanted to learn about algebraic topology, but did not care about algebra or topology.
Also anything that has “for dummies” in title should invariably remind you of Norvig’s essay (google Peter Norvig 21 days).
— xyzzyz 171 days ago
— Hacker News
2012.03.14 Wednesday ACHK
時間管理 4.2
After being as exhaustive as you can, you can be selective. As a beginner, you have to be exhaustive anyway: don’t think that other beginners can have any shortcuts. Remember, no one, even genius, can violate the principle of hardwork.
— Me@2008.10.28
2012.03.14 Wednesday (c) All rights reserved by ACHK
中學實驗報告 3.1
這段改編自 2010 年 5 月 26 日的對話。
不做傻瓜的話，你就要懂得權衡輕重，先做成本效益最高的東西。眾多功課之中，令你的考試分數提升得最多的，就是第一要務。如果時間不足，你就千萬不要企圖，去完成「所有」功課的「所有」部分。你真正必須「完成」的，是第一要務。其他功課，無論你有多麼掛念，都應暫時完全拋諸腦後，直到完成第一要務為止。完成了第一要務後，才開始第二要務，如此類推。
對於公開試的考生來說，校內的功課，通常也沒有什麼大用。真正重要的功課，是 past paper（歷屆試題），或者類似 past paper 的題目。在你眾多功課之中，那是你需要最先完成的東西。
如果你的老師是合理的，他所出功課的形式，自然會貼近公開試題目。即使他間中出了一些無用的功課，只要你向他反映，他亦自然會立刻刪除之。
如果不幸，你的老師是非理性的，你就應該用我之前所講，面對「中學實驗報告」的方法，去對付那堆無用的功課。
— Me@2012.03.14
2012.03.14 Wednesday (c) All rights reserved by ACHK
One of the many articles on the Tricki that was planned but has never been written was about making it easier to solve a problem by generalizing it (which initially seems paradoxical because if you generalize something then you are trying to prove a stronger statement). I know that I’ve run into this phenomenon many times, and sometimes it has been extremely striking just how much simpler the generalized problem is.
edited Sep 26 2010 at 8:34
gowers
Great question. Maybe the phenomenon is less surprising if one thinks that there are ∞ ways to generalize a question, but just a few of them make some progress possible. I think it is reasonable to say that successful generalizations must embed, consciously or not, a very deep understanding of the problem at hand. They operate through the same mechanism at work in good abstraction, by helping you forget insignificant details and focus on the heart of the matter.
answered Sep 26 2010 at 10:27
Piero D’Ancona
— Generalizing a problem to make it easier
— MathOverflow
A general case has less information (details) than a special case.
— Me@2012.03.10
2012.03.13 Tuesday (c) All rights reserved by ACHK
We cannot change anything until we accept it. Condemnation does not liberate, it oppresses.
— Carl Jung
2012.03.13 Tuesday ACHK
這段改編自 2010 年 3 月 20 日的對話。
我以前提過，有一本書叫做「I am a Strange Loop」。書內研究的其中一個要點是，怎樣才為之「明白」？
作者發現，在很大程度上，「明白」就是「比喻」。
（安：什麼意思？）
你試想想，我們學習新東西時，在什麼情況下，才有「明白」的感覺呢？
第一種情況是，把新東西表達成舊東西。例如，「3 乘以 2」為什麼會等如「6」呢？
那是因為「乘」的意思是，把同一個數，加很多次：
3 x 2 = 3 + 3 = 6
第二種情況是，把新東西反覆背誦和運用，令到自己對它熟練到，成為一個習慣為止。那樣，即使沒有任何實質的理解，你也會有「明白」的幻覺。例如，小時候你背誦了「乘數表」，所以你覺得自己明白，為何「九八七十二」。
9 x 8 = 72
但是，你之所以「明白」，並不是因為，你曾經把「9 x 8」化成加數，真正如實地運算「9 + 9 + 9 + 9 + 9 + 9 + 9 + 9」。
第三種情況是，把新東西類比成熟悉的事物。例如，如果你教一個小孩「物質是由粒子組成的」，他可能會一頭霧水。要他「明白」的話，你可以試試這樣說：
物質，是由一些超微小的彈珠（波子）組成的。那些超微小的彈珠，叫做「粒子」。
（安：第三種情況，可以看成第一種的一個特例，因為它都是把未知的東西，翻譯成已知的事物。）
可以這樣說。但是，第一種中的翻譯，是「解釋」；而第三種的，是「比喻」。或者我這樣分比較好：
第一種「明白」，是通過「解釋」而得來的。
第二種是通過「熟習」。
第三種是用「比喻」。
我現在想集中討論的，是第三種情況。
— Me@2012.03.13
2012.03.13 Tuesday (c) All rights reserved by ACHK
During this period, Tom Banks, Willy Fischler, Stephen Shenker and Leonard Susskind formulated matrix theory, a full holographic description of M-theory using IIA D0 branes. This was the first definition of string theory that was fully non-perturbative and a concrete mathematical realization of the holographic principle. It is an example of a gauge-gravity duality and is now understood to be a special case of the AdS/CFT correspondence.
— Wikipedia on String theory
2012.03.12 Monday ACHK
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The foundation of all mental illness is the avoidance of true suffering.
– Carl Jung
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2008.06.02 Monday ACHK
中學實驗報告 2 | 間時間表 3.2
這段改編自 2010 年 5 月 26 日的對話。
無論是你過份懶惰，還是你的老師過份勤力，都足以令你欠下功課鉅債。更加不幸的是，很多時，這兩種情況會同時發生。所以，深明「歸還功課」之道，至關重要。歸還功課的有效方法，可參考我「間時間表 2」和「間時間表 3」兩篇文章。
但是，如果考試臨近，就千萬不要期望，自己可以有足夠時間，去「追回」以前所有欠交的功課。
你要記住，做功課的最終目的，並不是「完成功課」。做功課的最終目的，是透過做功課，去奪取最多的學術知識和考試分數，從而升上大學。所以，真正重要的，並不是你完成了多少份功課，而是你入不入到大學。
即使你以前在校內，間中有欠交功課，如果公開試的成績上佳，一定會有大學取錄你。相反，即使你在校內，一份功課也沒有欠，如果公開試的成績不足，大概也沒有大學會取錄你。勤奮做功課，而成績仍然差，就足以證明，你是一個傻瓜。
不做傻瓜的話，你就要懂得權衡輕重，先做成本效益最高的東西。眾多功課之中，令你的考試分數提升得最多的，就是第一要務。如果時間不足，你就千萬不要企圖，去完成「所有」功課的「所有」部分。你真正必須「完成」的，是第一要務。其他功課，無論你有多麼掛念，都應暫時完全拋諸腦後，直到完成第一要務為止。完成了第一要務後，才開始第二要務，如此類推。
— Me@2012.03.12
2012.03.12 Monday (c) All rights reserved by ACHK
Apple’s revenues may continue to rise for a long time, but as Microsoft shows, revenue is a lagging indicator in the technology business.
— Frighteningly Ambitious Startup Ideas
— March 2012
— Paul Graham
2012.03.11 Sunday ACHK
Knowing your own darkness is the best method for dealing with the darknesses of other people.
— Carl Jung
2012.03.11 Sunday ACHK
Douglas Richard Hofstadter (born February 15, 1945) is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics. He is best known for his book Godel, Escher, Bach: an Eternal Golden Braid, first published in 1979, for which he was awarded the Pulitzer Prize for general non-fiction and the National Book Award for Science.
Hofstadter has said that he feels “uncomfortable with the nerd culture that centers on computers”. He admits that “a large fraction [of his audience] seems to be those who are fascinated by technology”, but when it was suggested that his work “has inspired many students to begin careers in computing and artificial intelligence” he replied that he was pleased about that, but that he himself has “no interest in computers.”
— Wikipedia on Douglas Hofstadter
2012.03.10 Saturday ACHK
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The only thing that saves us from the bureaucracy is inefficiency. An efficient bureaucracy is the greatest threat to liberty.
* Eugene McCarthy, quoted in Time magazine, 12 February 1979
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2010.08.25 Wednesday ACHK
That being said, there is a mechanism in place to combat the obvious consequences. Extreme deflation would render most currencies highly impractical: if a single Canadian dollar could suddenly buy the holder a car, how would one go about buying bread or candy? Even pennies would fetch more than a person could carry. Bitcoin, however, offers a simple and stylish solution: infinite divisibility. Bitcoins can be divided up and trade into as small of pieces as one wants, so no matter how valuable Bitcoins become, one can trade them in practical quantities.
In fact, infinite divisibility should allow Bitcoins to function in cases of extreme wallet loss. Even if, in the far future, so many people have lost their wallets that only a single Bitcoin, or a fraction of one, remains, Bitcoin should continue to function just fine. No one can claim to be sure what is going to happen, but deflation may prove to present a smaller threat than many expect.
— Won’t loss of wallets and the finite amount of Bitcoins create excessive deflation, destroying Bitcoin?
— Bitcoin Wiki on FAQ
2012.03.09 Friday ACHK
種子論起點 15
這段改編自 2010 年 3 月 20 日的對話。
小時候所背的詩詞歌賦、所聽的人生道理 和 所學的無用知識，即使當時體會不到，也不會是浪費時間。年紀大了，歷練多了，就自然會明白，自然會受用。
— Me@2012.03.09
2012.03.09 Friday (c) All rights reserved by ACHK
Well, in some sense, the Wheeler-DeWitt equation is nothing else than Einstein’s equations that you encountered elsewhere – potentially simplified and reduced in a minisuperspace formulation.
But if something like the Wheeler-DeWitt equation is the only equation that defines what can happen in a quantum gravity system, your task actually becomes harder, not easier. You must artificially reparameterize your physical states according to a new observable (e.g. the total volume of the Universe at some “moment”) that will play the role of your time (recall that there’s no preferred choice of coordinates in general relativity) – and with this new “gauge-fixed” choice of your time, you will find out that the Wheeler-DeWitt “H=0” equation becomes non-trivial.
— Why and how energy is not conserved in cosmology
— Lubos Motl
Bryce DeWitt first published this equation in 1967 under the name “Einstein–Schrodinger equation”; it was later renamed the “Wheeler–DeWitt equation”.
…
Solutions to the Wheeler-DeWitt equation have therefore been interpreted as the Universal wave function.
This property is known as timelessness [disambiguation needed]. The reemergence of time requires the tools of decoherence and clock operators.
— Wikipedia on Wheeler–DeWitt equation
Timelessness is a property of the Wheeler-deWitt equation in canonical quantum gravity.
— Wikipedia on Timeless
2012.03.08 Thursday ACHK
You cannot choose not to worry. You can only choose what to worry. So choose wisely.
— Me@2012.03.07
2012.03.08 Thursday (c) All rights reserved by ACHK
有東西不明白，就應該盡量立刻發問。千萬不要有一個逃避的心態：
在學校有東西聽不明白，就打算回家才慢慢看教科書；在家裡有東西看不明白，就打算回校才問老師。
結果，被這個循環的邏輯結構鎖死了。不明白的東西，永遠也不明白。
— Me@2012.03.08
2012.03.08 Thursday (c) All rights reserved by ACHK
Physics Town 
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