Author Archives: rpflee

Index notation

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Symmetries are the result of a redundant, but useful, description of a theory.

In fact, one of the main uses of index notation is just to manifest the symmetry.

— Fields

— Warren Siegel

Siegel authored an extensive (885pg) textbook called Fields, now in its 3rd edition. It is notable in that it follows a very modern approach and incorporates many topics (including string theory) not found in other field theory textbooks. He advocates a “symmetry-based” approach and uses this in his Quantum Field Theory I&II classes. The textbook is also notable in that it is completely an “electronic book” and can be downloaded for free from Siegel’s website.

— Wikipedia on Warren Siegel

2012.02.05 Sunday ACHK

Recursion 8.2

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I am a Strange Loop, 3.2

When I am conscious, different times of myself-s interact.

When different times of the same (software) object interact, there comes consciousness.

The past is part of the present.

So consciousness comes from the whole-part interaction.

— Me@2012-01-24 11:03:37 AM

2012.02.05 Sunday (c) All rights reserved by ACHK

Uncertainty principle, 5

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Universal wave function, 12

The uncertainty principle states the limit of reductionism. Science is based on reductionism, which assumes we can investigate part of the universe. So the uncertainty principle, in effect, states the limit of science.

— Me@2011.11.29

2012.02.05 Sunday (c) All rights reserved by ACHK

Process, not a state, 4

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Excellence is an art won by training and habituation. We do not act rightly because we have virtue or excellence, but we rather have those because we have acted rightly. We are what we repeatedly do. Excellence, then, is not an act but a habit.

— Aristotle (384 BC – 322 BC) Greek Philosopher

* Source: Will Durant, _The Story of Philosophy: The Lives and Opinions of the World’s Greatest Philosophers_ (1926) [Simon & Schuster/Pocket Books, 1991, ISBN 0-671-73916-6] Ch. II: Aristotle and Greek Science; part VII: Ethics and the Nature of Happiness:
   
    “Excellence is an art won by training and habituation: we do not act rightly because we have virtue or excellence, but we rather have these because we have acted rightly; ‘these virtues are formed in man by his doing the actions’; we are what we repeatedly do. Excellence, then, is not an act but a habit: ‘the good of man is a working of the soul in the way of excellence in a complete life… for as it is not one swallow or one fine day that makes a spring, so it is not one day or a short time that makes a man blessed and happy‘” (p. 76).
   
    The quoted phrases within the quotation are from the Nicomachean Ethics, Book II, 4; Book I, 7. The misattribution is from taking Durant’s summation of Aristotle’s ideas as being the words of Aristotle himself.
   
— Wikiquote

Excellence is a process, not a state, nor an event.

An event is a change of state. A process is an infinite chain of events.

— Me@2011.01.01

— Me@2012.02.04

2012.02.04 Saturday (c) All rights reserved by ACHK

種子論起點 10.3.1

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網誌時代 12.3.1

這段改編自 2010 年 3 月 20 日的對話。

我不會好像 Paul Graham 那樣，先寫一篇長文章，然後，再花幾個星期的時間，去不斷修改打磨。我不喜歡那個方法。

寫作，是一項麻煩而沉悶的工序。寫長文章，就即是要在一斷連續的長時間內，處於「寫作」的狀態。我會感到非常厭惡。如果我企圖寫長文章的話，我根本會抗拒到，從來不會開始寫。

寫長文章的麻煩，在於文章一長時，很難可以同時做到，結構嚴謹、內容一致 和 思路清晰。困難的地方，在於一篇文章的複雜程度，會以幾何級數，隨長度而增長。例如，假設「文章乙」的長度，是「文章甲」的兩倍。那樣，「文章乙」的複雜度，隨時會是「文章甲」的四倍。「寫程式」有類似的原理。

所以，我通常也只會寫短文章。每次寫文章時，我會採取「最低消費」策略：在文章內容的發展上，見步行步，行步見步。

— Me@2012.02.04

2012.02.04 Saturday (c) All rights reserved by ACHK

Exponential delay

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We also have some new features to prevent flamewars. The most conspicuous is an exponential delay before reply links appear on deeply nested comments. We’d noticed these were rarely the most interesting comments on the site. We’re hoping that instead of killing stupid arguments, it will be sufficient to apply gradually increasing drag to them.

— 29 Apr 2009: Faster, Fewer Flamewars

— Paul Graham

2012.02.03 Friday ACHK

Probability 2.4

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這段改編自 2010 年 5 月 25 日的對話。

我現在示範一下，如何寫你的那本「魔法筆記」。

第一句：

「P 方法」和「S 方法」的整體意義相同，因為它們是用來計同一道機會率題目的。如果你的運算無誤，它們的答案，會是相同的數值。

第二句：

但是，「P 方法」和「S 方法」的細節不同，因為「P 方法」的分子，並不是「S 方法」的分子；「P 方法」的分母，亦不是「S 方法」的分母。

第三句：

考試時，「P 方法」和「S 方法」中，你先選定其中一個，用來作答。然後，在草稿紙上，再用另一個方法，以作驗算。

第四句：

（這一點是額外的，可以不寫。）在「P 方法」中，分子和分母都是 permutation（排列）。而在「S 方法」中，分子和分母都是 combination（組合）。

第五句：

在「P 方法」中，分子和分母都是 permutation（排列），重視次序。但是，根據這一題的描述，次序並不重要。或者說，題目所要求的，是 combination（組合）。即使是次序不同，凡是「兩紅兩黑」的排列，你都要採納。那樣，有多少個排列，都符合「兩紅兩點」的規定呢？

4C2 （即是 「4 選 2」，等於 6。）

所以，在「P 方法」中，在四個「機會率分數」之後，你要再乘以一個「4C2」。

即使是個別的要點，你也未必可以立刻明白。更何況，若要保證自己的機會率運算正確，你要每一點也理解清楚。一般人也不能做到。千萬不要做一般人。

— Me@2012.02.03

2012.02.03 Friday (c) All rights reserved by ACHK

Hyperthymesia

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Hyperthymesia, also known as piking or hyperthymestic syndrome is a condition in which the individual possesses a superior autobiographical memory, meaning they can recall the vast majority of personal experiences and events in their lives.

Defining characteristics

Individuals with hyperthymesia can recall almost every day of their lives in near perfect detail, as well as public events that hold some personal significance to them. Those affected describe their memories as uncontrollable associations, when they encounter a date, they “see” a vivid depiction of that day in their heads. Recollection occurs without hesitation or conscious effort.

It is important to draw a distinction between those with hyperthymesia and those with other forms of exceptional memory, who generally use mnemonic or similar rehearsal strategies to memorise long strings of subjective information.

— Wikipedia on Hyperthymesia

2012.02.02 Thursday ACHK

Apple seed

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Like an apple hanging from a tree I picked the ripest one I still got the seed.

— Thinking Of You

— Katy Perry

（以下不是原著的意思，因為我根本不明白，原著是什麼意思。）

即使我拿下的，是蘋果樹上最差的一個蘋果，我仍然可以得到，那棵蘋果樹的種子。

— Me@2012.02.02

2012.02.02 Thursday (c) All rights reserved by ACHK

種子論起點 10.2

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網誌時代 12.2 | 程式員頭腦 12.2

這段改編自 2010 年 3 月 20 日的對話。

你留意一下，我文章的結構，和電腦程式極為相似。

我每一篇文章，就好像一個「大程式」內的一個「小 function」（子程式）。一個「子程式」的特性是，一方面，它本身會有特定的一個完整功能；另一方面，它亦可以被「主程式」利用，與其他「子程式」合作，執行大任務。

同理，我盡量做到，每篇網誌文章「至少有一個意念」和「至多有一個意念」。那樣，我每篇文章就可以各自成篇，自成一國。讀者閱讀我任何的一篇文章，就可以立刻得益，而毋須同時閱讀其他。

另一方面，如果你一次過閱讀，連續幾篇標題相同的文章，你會發現，它們會合體，變成一篇大文章。在一個額外的上文下理中，你或者會有新的體會。

— Me@2012.02.02

2012.02.02 Thursday (c) All rights reserved by ACHK

Digital physics, 2

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The last decade in theoretical physics has simply settled this question – whether someone likes it or not – and the answer is “No”. The spacetime geometry cannot be fundamental at the Planck scale. It is subject to transitions, dualities, and holography, among other phenomena that prove that it must be flexible and it cannot arise from a graph because a graph is too local. In neither of the existing descriptions we can find a discrete spacetime and it seems rather unlikely that there exists a description where it is discrete.

— Quantum Graphity

— Lubos Motl

2012.02.01 Wednesday ACHK

Probability 2.3

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這段改編自 2010 年 5 月 25 日的對話。

在完全熟習 P 方法和 S 方法之前，為免干擾自己的思考，最好不要研究，它們為何可以針對同一題題目，而得到同樣的答案。

在完全熟習之後，如果想研究一下，可以用這個提示：

在 P 方法中，分子和分母都是 permutation（排列）。而在 S 方法中，分子和分母都是 combination（組合）。

— Me@2012.02.01

2012.02.01 Wednesday (c) All rights reserved by ACHK

Digital physics

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The answer to all questions is No. In fact, even the right reaction to the first sentence – that the Planck scale is a “discrete measure” – is No.

The Planck length is a particular value of distance which is as important as 2π times the distance or any other multiple. The fact that we can speak about the Planck scale doesn’t mean that the distance becomes discrete in any way. We may also talk about the radius of the Earth which doesn’t mean that all distances have to be its multiples.

In quantum gravity, geometry with the usual rules doesn’t work if the (proper) distances are thought of as being shorter than the Planck scale. But this invalidity of classical geometry doesn’t mean that anything about the geometry has to become discrete (although it’s a favorite meme promoted by popular books). There are lots of other effects that make the sharp, point-based geometry we know invalid – and indeed, we know that in the real world, the geometry collapses near the Planck scale because of other reasons than discreteness.

— Is reality discrete at the quantum level?

— Lubos Motl

2012.01.31 Tuesday ACHK

Buddha 2

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Lessons from the Light, 2

The revelations coming from the light seemed to go on and on, then I asked the light, “Does this mean that humankind will be saved?”

Then, like a trumpet blast with a shower of spiraling lights, the Great Light spoke, saying, “Remember this and never forget; you save, redeem and heal yourself. You always have. You always will. You were created with the power to do so from before the beginning of the world.”

In that instant I realized even more. I realized that WE HAVE ALREADY BEEN SAVED, and we saved ourselves because we were designed to self-correct like the rest of God’s universe. This is what the second coming is about. 

— Mellen-Thomas Benedict

The way to be saved is to realize that

you are already saved.

— Me

2012.01.31 Tuesday (c) All rights reserved by ACHK

種子論起點 10

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網誌時代 12 | 程式員頭腦 12

這段改編自 2010 年 3 月 20 日的對話。

（安：Paul Graham 講過，他 寫文章的模式 和 寫電腦程式的模式 差不多。他要寫一篇文章時，會先高速把第一個版本寫好。然後，他會花幾個星期的時間，去不斷 debug（修正）該篇文章。）

雖然，我不是用 Paul Graham 那個版本的方法，但是，我寫文章的模式，都和寫程式差不多。那不單是指工作模式的相似。我發覺我寫文章時的思考模式，和一個程式員的幾乎沒有分別。例如，我需要不斷監察住，我的作品有沒有邏輯矛盾。

「寫文章」和「寫程式」的步驟相同，不足為奇，因為，所謂「文章」，其實就是人腦的程式。

— Me@2012.01.31

2012.01.31 Tuesday (c) All rights reserved by ACHK