Monthly Archives: February 2012

種子意念 2.1.2

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網誌時代 14

這段改編自 2010 年 3 月 20 日的對話。

Every lecture should make only one main point.

The German philosopher G. W. F. Hegel wrote that any philosopher who uses the word “and” too often cannot be a good philosopher. I think he was right, at least insofar as lecturing goes. Every lecture should state one main point and repeat it over and over, like a theme with variations.

— Advice for the Young Scientist

— John Baez

與志同道合的人傾談時，我會在電光火石之間，同時爆發很多條思考線出來，令我「驚惶失措」，不知先講哪一樣比較好。

寫作時會有類似的問題。所以，我迫自己每日最多只寫一篇文章，而文章每篇最多只可以有一個（主要）新點子。那對我來說，有穩定思想、克制情緒的作用。

另外，寫作太多，其實沒有什麼大意思。一來，自己不會有那麼多的時間。二來，讀者亦不會全部閱讀。即使全部閱讀，他們也不會有足夠時間，去把學到的道理付諸實行。「道理」即是「方法」。方法，是用來解決問題的。不能實行，或者不實行的道理，是廢話廢字，不寫也罷。

寫一句讀者會確切執行的東西，勝過寫十篇看過就算的文章。真正重要的，不是我寫了什麼，而是讀者看到什麼、想到什麼 和 做到什麼。

— Me@2012.02.14

2012.02.14 Tuesday (c) All rights reserved by ACHK

Double slit experiment

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Feynman has said that all the surprising wisdom of quantum mechanics is hiding in the double slit experiment. If you think about it carefully enough, you will ultimately figure out all the important and amazing new features of the world that quantum mechanics uncovers.

— Lubos Motl

2012.02.14 Tuesday ACHK

Layer, 3.2

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水平 7.2 | Onion self 5.2 | Inner and outer, 5.2

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One’s deepest self is the universe.

That’s why everyone’s deepest self is the same.

— Me@2012-01-26 4:30:09 PM

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The diagram is not the truth. Instead, it is an analogy. It is a model only. 
— Me@2012.02.11

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Everyone is not a part of the universe, but the whole of the universe.

Everyone is a layer of the universe.

— Me@2012-02-06 11:31:17 PM

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A, B, C are three people.

They are just like three waves of the same underlying ocean (universe).

— Me@2012-02-08 12:55:31 PM

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2012.02.13 Monday (c) All rights reserved by ACHK

二項式係數 2.1

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Binomial coefficient 2.1

這段改編自 2010 年 5 月 25 日的對話。

假設，有一個 3 乘 4 的長方形，由 9 個小正方形組成。

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                    B
       
如果你要沿著格線，由長方形的左上角（A） 走到去右下角（B），總共有多少條可能的路線？

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無論你走哪一條路線，你總共要走 7 步。而那 7 步當中，一定有 4 步是水平，3 步垂直的。所以，我們可以把原本的問題化成：7 步當中，要選擇 4 步走水平的話，總共有多少個可能性？

答案明顯是 7C4，即是「7 選 4」，等於 35。結論是，總共有 35 條可能的路線。
   
— Me@2012.02.13

2012.02.13 Monday (c) All rights reserved by ACHK

Michael Crichton

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    * The best doctors found a middle position where the were neither overwhelmed by their feelings nor estranged from them. That was the most difficult position of all, and the precise balance — neither too detached nor too caring — was something few learned.

    * — Travels (1988) Michael Crichton
   
   

2012.02.12 Sunday ACHK

網誌時代 13

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Russell on writing

“I conscientiously tried this, but found that my first draft was almost always better than my second. This discovery has saved me an immense amount of time. I do not, of course, apply it to the substance, but only to the form. When I discover an error of an important kind I re-write the whole. What I do not find is that I can improve a sentence when I am satisfied with what it means. “

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On Russell’s writing

“Russell left a large assortment of writing. From his adolescent years, Russell wrote about 3,000 words a day, in long hand, with relatively few corrections; his first draft nearly always was his last draft, even on the most complex, technical matters. “

– Wikipedia

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2008.04.25 Friday ACHK

Not average

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Those in the print media who dismiss the writing online because of its low average quality are missing an important point: no one reads the average blog. In the old world of channels, it meant something to talk about average quality, because that’s what you were getting whether you liked it or not. But now you can read any writer you want. So the average quality of writing online isn’t what the print media are competing against. They’re competing against the best writing online. And, like Microsoft, they’re losing.

— What Business Can Learn from Open Source

— Paul Graham

2012.02.12 Sunday ACHK

Inner and outer, 5

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Layer, 3 | 水平 7 | Onion self 5

The deeper the consciousness, the more powerful it is.

— Me@2010.08.06

The diagram is not the truth. Instead, it is an analogy. It is a model only.
— 
Me@2012-02-08 12:55:31 PM

The deepest self is the universe.

— Me@2012-01-16 2:20:19 AM

The diagram is not the truth. Instead, it is an analogy. It is a model only.

— Me@2012.02.11

2012.02.11 Saturday (c) All rights reserved by ACHK

二項式係數 1.2

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Binomial coefficient 1.2

這段改編自 2010 年 5 月 25 日的對話。

其實，你毋須透過任何複雜的運算（例如「數學歸納法」），而單靠簡單的思考推理，都可以嚴謹推導得到，只要你對「二項式定理」和「nCr」的 physical meaning（實質意義）足夠了解便行。

首先，你要知道，因為 (x+y)^4 本身是 4 次方，所以展開以後，每一項也是 4 次方的，即是由 4 個英文字母相乘而成。分別是，每一項的 4 個英文字母之中，x 的數目不同。而 y 的數目，亦會項項不同，因為 y 的數目，等於 4 減 x 的數目。例如，有 3 個 x 相乘的話，該項就同時有 1 個 y 。

那樣，總共有多少項是由 3 個 x 和 1 個 y 相乘而成的呢？

其中一種方法是，直接展開 (x+y)^4，把全部 16 項也列出來：

(x+y)^4

= (x + y)(x + y)(x + y)(x + y)

= … + xxxy + … + xxyx + … + xyxx + … + yxxx + …

16 項之中，總共有 4 項，是由 3 個 x 和 1 和 y 組成的。結論是，x^3 y 的係數是 4。

更好的方法是，靠簡單的推理：

每一項也是 4 次方，即是有 4 個空格要填。

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4 個空格之中，要填 3 個 x，總共有多少個填法呢？

答案明顯是 4C3，即是「4 選 3」，等於 4。結論是，x^3 y 的係數是 4。

— Me@2012.02.11

2012.02.11 Saturday (c) All rights reserved by ACHK

Quantum discord

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In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement.

… quantum correlations can be present in certain mixed separable states; In other words, separability alone does not imply the absence of quantum effects. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable (non-entangled) quantum states.

Nonzero quantum discord indicates the presence of correlations that are due to noncommutativity of quantum operators. For pure states, the quantum discord becomes a measure of quantum entanglement, more specifically, in that case it equals the entropy of entanglement.

Evidence has been provided for poignant differences between the properties of quantum entanglement and quantum discord. It has been shown that quantum discord is more resilient to dissipative environments than is quantum entanglement.

… surprisingly, the classical correlation actually decreases as the quantum discord increases.

— Wikipedia on Quantum discord

[Quantum discord is] the amount of entanglement needed in the task of state-merging.

— Jun 10 ’11 at 13:32

— Frederic Grosshans

2012.02.10 Friday ACHK

文章拼圖 1.2

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種子論起點 10.3.4 | 網誌時代 12.3.4

這段改編自 2010 年 3 月 20 日的對話。

（安：坊間有很多書籍，一本只有幾個「思考單位」。它只不過是將每個「思考單位」，化成一篇長一點的文章。然後，再由一篇文章化成（例如）三篇文章。而那三篇文章來來去去，其實，也只是在講述那同一個「思考單位」。）

我不是在描述這個現象。

（安：我想講的是，如果你有很多個「思考單位」，而你又想放它們的大部分，於同一本書的話，寫那本書，將會是一項十分艱鉅的任務。你剛才描述的策略，正正可以化解這個難題。）

— Me@2012.02.10

2012.02.10 Friday (c) All rights reserved by ACHK

Mirror symmetry, 2

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In physics and mathematics, mirror symmetry is a relation that can exist between two Calabi-Yau manifolds. It happens, usually for two such six-dimensional manifolds, that the shapes may look very different geometrically, but nevertheless they are equivalent if they are employed as hidden dimensions of string theory. The classical formulation of mirror symmetry relates two Calabi-Yau threefolds M and W whose Hodge numbers h1,1 and h1,2 are swapped; string theory compactified on these two manifolds lead to identical effective field theories.

… Andrew Strominger, Shing-Tung Yau, and Eric Zaslow have showed that mirror symmetry is a special example of T-duality: the Calabi-Yau manifold may be written as a fiber bundle whose fiber is a three-dimensional torus. The simultaneous action of T-duality on all three dimensions of this torus is equivalent to mirror symmetry.

— Wikipedia on Mirror symmetry (string theory)

2012.02.10 Friday ACHK

Layer, 2

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Everyone is not a part of the universe, but the whole of the universe.

Everyone is a layer of the universe.

— Me@2012-02-06 11:31:17 PM

2012.02.09 Thursday (c) All rights reserved by ACHK

二項式係數 1.1

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Binomial coefficient 1.1

這段改編自 2010 年 5 月 25 日的對話。

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

Binomial theorem（二項式定理）的意思是，例如，

(x+y)^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4

那些係數（1, 4, 6, 4, 1），為什麼會剛巧等如（4C0, 4C1, 4C2, 4C3, 4C4）呢？

其實，你毋須透過任何複雜的運算（例如「數學歸納法」），而單靠簡單的思考推理，都可以嚴謹推導得到，只要你對「二項式定理」和「nCr」的 physical meaning（實質意義）足夠了解便行。

— Me@2012.02.09

2012.02.09 Thursday (c) All rights reserved by ACHK

Reductionism 3

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… systems somehow function as wholes and that their functioning cannot be fully understood solely in terms of their component parts.

— Wikipedia on Holism

Correction:

Actually it can. But to determine the behavior of each component, you have to examine of the effects of all other components on it, which is possible in principle, although maybe difficult in practice.

In this sense, there is no conflict between holism and reductionism. Instead, they support each other.

— Me@2011.11.29

2012.02.08 Wednesday (c) All rights reserved by ACHK

文章拼圖

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種子論起點 10.3.3 | 網誌時代 12.3.3

這段改編自 2010 年 3 月 20 日的對話。

我的文章的特點是，發表以後，就不再作任何修訂。如果我的新文章和舊文章有互動，也只會是被放在一起。

另一個特點是，每篇短文章，只會有一個主要的思考單位。那樣，只要每次選擇一些短文章，把它們放在一起，就自動可以組合成，各式各樣的大文章，而毋須作任何的修改，除了極輕微的剪接外。

甚至，這個工序，並不一定要由我親自完成。

— Me@2012.02.08

2012.02.08 Wednesday (c) All rights reserved by ACHK

Curry–Howard correspondence, 3

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Haskell is a standardized, general-purpose purely functional programming language, with non-strict semantics and strong static typing. It is named after logician Haskell Curry. In Haskell, “a function is a first-class citizen” of the programming language. As a functional programming language, the primary control construct is the function. The language is rooted in the observations of Haskell Curry and his intellectual descendants, that “a proof is a program; the formula it proves is a type for the program“.

— Wikipedia on Haskell (programming language)

2012.02.07 Tuesday ACHK