Monthly Archives: March 2011

網絡記憶 1.3

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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

M-theory and Loop Quantum Gravity

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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

PayPal

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No, because I think we didn’t know what we were doing. I think the hallmark of a really good entrepreneur is that you’re not really going to build one specific company. The goal — at least the way I think about entrepreneurship — is you realize one day that you can’t really work for anyone else. You have to start your own thing.

— Max Levchin

— Founders at Work

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2011.03.31 Thursday ACHK

多重自我 下世傳奇

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輪迴 4

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假設有輪迴的話，不一定是「一個人變一個人」地輪迴，因為平時所謂的「一個人」，其實有超過一個「人格」。

「靈魂」即「意識」，既可以分開，又可以組合。

一方面，一個人的多重「人格」，可能可以分開，獨立發展。例如，我的左腦人格，輪迴成一個個體，右腦則輪迴成另一個。

另一方面，多個人的不同「人格」，可能可以組合成，一個新的「自我委員會」。例如，我的前生可能是兩個人——一位先生和一位太太。今生，那位先生化成了，我的左腦；而那位太太，則化成右腦。

— Me@2011.03.29

— Me@2022.07.24

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2011.03.29 Tuesday (c) All rights reserved by ACHK

Startup

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The best way to come up with startup ideas is to ask yourself the question: what do you wish someone would make for you?

— Paul Graham

2011.03.29 Tuesday ACHK

Great Idea 4

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If so, this is good news indeed. Good ideas always tend to win eventually. The problem is, it can take a very long time. It took decades for relativity to be accepted, and the greater part of a century to establish that central planning didn’t work. So even a small increase in the rate at which good ideas win would be a momentous change — big enough, probably, to justify a name like the “new economy.”

— Paul Graham

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2011.03.29 Tuesday ACHK

學問潛行凶間

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讀書與睡眠 2

This essay is adapted from a dialogue on 2010.11.11.

CCL: One more question, should I

1. sleep more to maintain a high level of efficiency; or

2. sleep less to prolong the working hours? 

Which one do you think is better?

Me: I suggest you to do BOTH. Let me explain:

2. sleep less to prolong the working hours

Method: shorten the night sleeping hours

1. sleep more to maintain a high level of efficiency

Method: add several 15-minute blocks in your timetable for day-sleeping

Sleeping hours

= 5 hours (night) + 8 x 15 minutes (day)

= 7 hours

Understand?

CCL: OK.

— Me@2010.11.11

— Me@2011.03.27

2011.03.27 Sunday (c) All rights reserved by ACHK

網絡記憶 1.2

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這段改篇自 2010 年 4 月 30 日的對話。

重點是，微分積分有對應的實質意思。如果你知道那些意思的話，很多運算就很易明白和記憶。

就即是找斜率。

就即是求面積。

我的意思是，你千萬不要「死記」（沒有任何理解之下就背誦）。「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？）

— Me@2011.03.25

2011.03.26 Saturday (c) All rights reserved by ACHK

Metric tensor

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In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space. In the same way as a dot product, metric tensors are used to define the length of, and angle between, tangent vectors.

— Wikipedia on Metric tensor

In general relativity, the metric tensor (or simply, the metric) is the fundamental object of study. It may loosely be thought of as a generalization of the gravitational field familiar from Newtonian gravitation. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as distance, volume, curvature, angle, future and past.

— Wikipedia on Metric tensor (general relativity)

2011.03.25 Friday ACHK

I am a Strange Loop, 2.2

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自我委員會 2.2

（安：等一等 … ）

簡化地講，假設你只有兩個人格。「左腦」為之一個人格；「右腦」為之另一個。

你的思考，有時是左腦的意見，有時是右腦的意見。同不同意？

（安：同意。）

但是，在絕大部分情況之下，無論是左腦的意見，還是右腦的意見，你都會覺得：「我就是我。」你都會覺得，你是一個人格，而不是兩個。不知何故，左腦和右腦各自都覺得，「左腦和右腦」是同一個人格。

左腦覺得，「我和右腦」是同一個人格。

右腦覺得，「左腦和我」是同一個人格。

為何他們會有這個根深蒂固的錯覺呢？

一方面，人自小開始，外界會給他這個訊息：一個頭顱內，只會有一個自我，否則就是不正常。另一方面，左腦和右腦再向自己和對方不斷強調，「左腦和右腦」是同一個人格。

— Me@2011.03.23

2011.03.23 Wednesday (c) All rights reserved by ACHK

The computer software industry

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The most amazing achievement of the computer software industry is its continuing cancellation of the steady and staggering gains made by the computer hardware industry.

— Henry Petroski

2011.03.22 Tuesday ACHK

網絡記憶 1.1

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這段改篇自 2010 年 4 月 30 日的對話。

這些微積分的數學操作，背後有對應的 physical meaning（實質意思）。直情發明微積分的那一個人，是一位物理學家。

（CSK：即是微積分和物理有關？）

知不知誰發明微積分？

（CSK：不知。）

頓哥。

（CSK：哪個頓哥？）

牛頓先生。

重點是，微分積分有對應的實質意思。如果你知道那些意思的話，很多運算就很易明白和記憶。

— Me@2011.03.22

2011.03.22 Tuesday (c) All rights reserved by ACHK

The Social Network

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Speaking to an audience at Stanford University, Zuckerberg stated that the film portrayed his motivations for creating Facebook inaccurately; instead of an effort to “get girls”, he says he created the site because he enjoys “building things”. 

— Wikipedia on The Social Network

One of the most interesting things to me was his analysis of what The Social Network got wrong. People in Hollywood couldn’t imagine that someone would build something because they were interested in building things, so they had to create another, perhaps more “movie-compatible,” motivation for him.

— Mark Zuckerberg on What Hollywood Doesn’t Get About Silicon Valley

— Jessica Livingston

2011.03.21 Monday ACHK

Point of view

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“Point of view” is that quintessentially human solution to information overload, an intuitive process of reducing things to an essential relevant and manageable minimum.

— Paul Saffo

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2011.03.21 Monday ACHK