Category Archives: seed | catalyst | 種子論

A Few Tricks

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Every Mathematician Has Only a Few Tricks

A long time ago an older and well-known number theorist made some disparaging remarks about Paul Erdos’s work. You admire Erdos’s contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdos’s work could be “reduced” to a few tricks which Erdos repeatedly relied on in his proofs.

What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over.

Take Hilbert. The second volume of Hilbert’s collected papers contains Hilbert’s papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert’s beautiful results have been completely forgotten. But on reading the proofs of Hilbert’s striking and deep theorems in invariant theory, it was surprising to verify that Hilbert’s proofs relied on the same few tricks. Even Hilbert had only a few tricks!

— Ten Lessons I Wish I Had Been Taught

— Gian-Carlo Rota

2012.05.13 Sunday ACHK

Until it’s obvious

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Feynman’s Blackboard, 3

You don’t truly understand it until you think it’s obvious.

— Chris Oliver

This is akin to how a society comes to understand something and why genius ideas sometimes take so long to become accepted. I believe “context” is the underlying principle here.

Arthur Schopenhauer said, “All truth passes through three stages: First, it is ridiculed; Second, it is violently opposed; Third, it is accepted as self-evident.”

If you present a truth to someone whom doesn’t have sufficient context for what you are saying, it may seem outrageous and ridiculous to them because the gap between their understanding and the insight you presenting is too great.

They would have to build up their understanding of the context around it until it expands to a point where they find a connection to what they already know. Then they can start to relate to it and eventually they may see it as self evident.   

— espeed 254 days ago

— Hacker News

2012.04.26 Thursday ACHK

Luck surface area

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嘗試出現 2

To borrow another bit of wisdom from Jason Roberts, this is a story about “luck surface area”. Given enough exposure, the impossibly lucky becomes the inevitable.

— How I Got a Job From a Hacker News Post

— February 28th, 2012 by Dave Wasmer

2012.04.15 Sunday ACHK

Wittgenstein’s Tractatus

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種子意念 2.1.5

The Tractatus Logico-Philosophicus is an unusual example of a self-refuting argument, in that Ludwig Wittgenstein explicitly admits to the issue at the end of the work:

    “My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it)”. (6.54)

However, this idea can be solved in the sense that, even if the argument itself is self-refuting, the effects of the argument elicit understandings that go beyond the argument itself.

— Wikipedia on Self-refuting idea

2012.04.10 Tuesday ACHK

人生漫步

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King believes that, generally speaking, good stories cannot be called consciously and should not be plotted out beforehand; they are better served by focusing on a single “seed” of a story and letting the story grow itself.

– Wikipedia

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2009.07.01 Wednesday ACHK

連繫智力 2

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無足夠資料 7

這段改編自 2010 年 3 月 20 日的對話。

「Intelligence is the ability to recognize connections. – Carolus Slovinec」

智力的一個核心元素是，連繫意念的能力。

如果沒有足夠資料，一個人多聰明也沒有用。

「沒有足夠資料」就為之「無知」。「無知」不等於「愚蠢」。「無知」的意思是，你沒有足夠資料，來作正確的決定；「愚蠢」的意思是，即使有足夠資料，你也沒有能力做正確的決定。

有足夠資料，仍然做不到決定，或者做錯決定的話，往往是因為你，不能把那堆資料意念，恰當地連繫起來，形成一個大故事，或者上文下理。當你看不出手上的一大堆資料，和當前要做的決定，有何關連時，自然會任務失敗。

智力的核心，在於融會貫通。

（安：你這個講法，有嚴重的問題。如果一個人不能完成任務，你又怎會知道，那是因為他沒有足夠資料，還是他本身愚蠢，導致即使有足夠的資料，也得物無所用呢？）

要分辨兩者，其實十分簡單。只要給予兩個人 相同的任務 和 相同的資料 就可以。如果至少其中一個，能夠做出正確的決定，那就可以肯定，資料充足。例如，你在一個烹飪比賽中，給予兩位參賽者（甲和乙），一模一樣的食物材料。如果甲可以煮到美味的菜色，而乙不可以的話，那就代表乙的失敗成因，並不是食材不足，而是自己的廚藝差。

— Me@2012.03.22

2012.03.22 Thursday (c) All rights reserved by ACHK

Collector 2

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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

功夫種子 2

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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

反轉意圖

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種子論起點 14.3

這段改編自 2010 年 3 月 20 日的對話。

「種子論」的其中一個可能名字，是「paradoxical intention」（反轉意圖）。

（安：什麼意思？）

例如，當我失眠時，如果刻意迫令自己入睡，反而會更加不能入睡。相反，如果我任由自己繼續睡不著，反而會有機會成功入睡。

入睡的意圖，會增添自己的壓力，令自己緊張起來，導致適得其反。放棄入睡的意圖，會去除自己的壓力，令自己放鬆下來，入睡的機會自然會大增。

（安：那只是「放棄意圖」，而不是「反轉意圖」。）

我有「反轉意圖」的版本。

當你失眠時，身體維持住躺在床上的狀態。但是，你要張開眼睛，心裡迫令自己，千萬不要入睡。那樣，你就有很大機會，在不知不覺間睡著。

但是，「反轉意圖」所描述的，只是「種子論」的一個小部分。

— Me@2012.03.07

2012.03.07 Wednesday (c) All rights reserved by ACHK

Time horizon

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Bezos: It does fit into my view. Our first shareholder letter, in 1997, was entitled, “It’s all about the long term.” If everything you do needs to work on a three-year time horizon, then you’re competing against a lot of people. But if you’re willing to invest on a seven-year time horizon, you’re now competing against a fraction of those people, because very few companies are willing to do that. Just by lengthening the time horizon, you can engage in endeavors that you could never otherwise pursue. At Amazon we like things to work in five to seven years. We’re willing to plant seeds, let them grow—and we’re very stubborn. We say we’re stubborn on vision and flexible on details.

In some cases, things are inevitable. The hard part is that you don’t know how long it might take, but you know it will happen if you’re patient enough. Ebooks had to happen. Infrastructure web services had to happen. So you can do these things with conviction if you are long-term-oriented and patient.

— Jeff Bezos Owns the Web in More Ways Than You Think

— By Steven Levy
   
— Wired December 2011

2012.03.06 Tuesday ACHK

種子論起點 14.2

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這段改編自 2010 年 3 月 20 日的對話。

為「種子論」命名的困難之處，在於它的案例太多，多到一個程度：不例子之間，有時會貌似各不相干。例如，你很難想像，「談情」和「寫作」有什麼關係。又例如，你很難發現，「Google」和「栽花」，有什麼共通之處。

— Me@2012.03.05

2012.03.05 Monday (c) All rights reserved by ACHK

種子論起點 14

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這段改編自 2010 年 3 月 20 日的對話。

長遠來說，在不影響準確度的前提下，我們應該為「種子論」改一個震撼一點的名字。即使是一個十分利害的道理工具，如果沒有一個驚奇的名字，人們就不會留意，不會理會。

— Me@2012.03.03

2012.03.03 Saturday (c) All rights reserved by ACHK

地獄篇（前傳）

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失敗是正常，成功是例外。

人生，是一個尋找例外的過程。

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地獄是正常，天堂是例外。

人生，是一個創造例外的經歷。

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唯有經過地獄的磨難，才有創造天堂的力量。 — 尼采

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— Me@2012.03.01

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2012.03.01 Thursday (c) All rights reserved by ACHK

Enjoy everything, need nothing, 2.2

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種子論起點 12.3 | 兩次測驗 2

有心栽花花不香，無心插柳柳成蔭。當你「需要」一樣東西時，你就會失去它。

又例如，當你「需要」得到好成績時，你就會失去它：你的成績即使不太差，亦一定不會是最好。

如果你「需要」有好成績，才會感到有自信的話，每次在學業上遇到挫折時，你都會覺得那是對 自身人格 和 自我價值 的一個否定。那樣，溫習時，你會戰戰兢兢，自然不能得心應手；考試時，你會惶惶不安，自然不可揮灑自如。沒有豁達的心靈，就沒有靈活的頭腦。你一定不會是一個一流的學生。

正確的心態是，謀事在人，成事在天。你要知道，沒有人可以控制到，究竟自己拿不拿到好成績，因為影響成績的因素，實在有不少。你唯一可以做，唯一可以「控制」的，就是運用最好的策略，把試前十分有限的溫習時間，發揮至最大的功效，盡量提高「拿到好成績」的機會率。

在考試臨場作答時，你要使用同樣的心理結構。你可以控制的，是盡力作答，拿得一分得一分，從而提高「成功」的機會率。至於最終成不成功，或者最終拿到多少分，則完全不在你的控制範圍以內。

把手緊握 什麼都沒有  把手放開 你得到一切  — 臥虎藏龍

— Me@2012.02.28

2012.02.28 Tuesday (c) All rights reserved by ACHK