Monthly Archives: January 2013

Phe-nomenon

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Universal wave function, 19 | Reductionism 4

Impartial/All is the Noumenon, which is logically impossible for any single observer to observe directly, unless the observer is the whole of the universe. But “self-observation” is meaningless.

— Me@2012.04.07

Because “state” is expressed in RQM as the correlation between two systems, there can be no meaning to “self-measurement”.

— Wikipedia on Relational quantum mechanics

The Noumenon is a logical implication. It cannot be observed directly. It can be observed partially only, through senses, or phenomena. An observation is an interaction between the observer and the observed.

To really “observe” the Noumenon, all we can do is to observe as many phenomena as possible. In other words, we consider as many observer-observed pairs as possible.

— Me@2013.01.14

This is because this state would have to be ascribed to a correlation between the universe and some other physical observer, but this observer in turn would have to form part of the universe, and as was discussed above, it is impossible for an object to give a complete specification of itself. Following the idea of relational networks above, an RQM-oriented cosmology would have to account for the universe as a set of partial systems providing descriptions of one another. The exact nature of such a construction remains an open question.

— Wikipedia on Relational quantum mechanics

nomenon = all

phe- = part

noumenon = all aspects of the universe

phenomenon = part of the reality of the universe

— Me@2012.04.07

2013.01.14 Monday (c) All rights reserved by ACHK

生疏荒廢

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石頭永固 2 || use it or lose it || 不進則退 不用即棄

.

人的腦海之中，有一個「機會成本評價系統」，會自動刪除「沒有用」的才能，以節省記憶和時間資源。

「沒有用」既可以指「本身沒有用」，又可以指「本身有用 但不拿出來用」。對於「機會成本評價系統」而言，兩者沒有分別。

才幹以外，感情亦然。

— Me@2013-01-14 10:52:13 AM

.

.

2013.01.14 Monday (c) All rights reserved by ACHK

二次元時間 2.2

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Dimension 1.3.2 | Two dimensional time 2.2 | 孖生宇宙 2.2

這段改編自 2010 年 4 月 3 日的對話。

你可以想像，隨著主角多次的「時間旅行」，改變歷史的次數越多，「平行宇宙」的數目亦會越大。假設，主角除了擁有「時光機」，可以「時間旅行」外，他在後來還發明了「平行宇宙機」，令到自己可以，穿梭遊走於各個「平行宇宙」之間。那樣，我們就可以說，「平行宇宙機」連繫了眾多「平行宇宙」。原本的「平行宇宙」，不再完全「平行」。

那樣，要指清一件事件時，除了要指出它發生的時間 —— 例如「2013 年 1 月 14 日 5 時 20 分」—— 外，還要講清楚，它發生在哪一個宇宙的「2013 年 1 月 14 日 5 時 20 分」。原本的時間標籤，是「第一個時間次元」。多重宇宙的標籤，則可以視為「第二個時間次元」。

（安：我覺得有點奇怪。我覺得「多重宇宙的標籤」，既不可以叫做「空間次元」，因為那個標籤或者數字，並不是用來描述「同一個宇宙」中的空間位置；亦不可以叫做「時間次元」，因為「時間」有「因果鏈」的意思。「多重宇宙」是「平行宇宙」，互不相干，沒有「因果關係」可言。）

所以，我剛才視「多重宇宙標籤」為「第二個時間」次元，是建基於「平行宇宙機」的假設。那個科幻故事的主角，發明了「平行宇宙機」，令到自己可以，由原本的宇宙（甲），走到另一個宇宙（乙）行事。那樣，「宇宙甲」的歷史，就可以透過主角，影響到「宇宙乙」的演化，反之亦然。

（安：依你這個講法，除了在科幻小說外，日常現實生活中 —— 如果用比喻 —— 都會有「二次元時間」的現象。）

什麼意思？

— Me@2013.01.14

2013.01.14 Monday (c) All rights reserved by ACHK

Self-reference

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Recursion 12

Self-reference may not be paradoxical, as long as there is a terminating condition / boundary case.

As long as there is a terminating condition, the self-reference is not really “hundred-percent-self”-reference. In other words, it is just self-similar, but not self-identical.

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. A copy of the license is included in the section entitled GNU Free Documentation License.

Being self-similar is possible, but being self-identical is logically impossible since it creates infinite regress.

— Me@2013.01.12

2013.01.13 Sunday (c) All rights reserved by ACHK

Persuasion

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Oran had been reading the work of Robert Cialdini, a former psychology professor and an expert in the power of persuasion. Cialdini had run experiments in southern California trying to get homeowners to reduce their energy use. When Cialdini distributed signs urging people to conserve energy to benefit the environment, or to save money, or to benefit future generations, they didn’t respond. But when Cialdini’s signs informed people that their neighbors were changing their ways to save energy, they responded. Energy use went down.

— The Inside Story of MoveOn’s Secret “Silver Bullet” to Deliver Victory for Obama

— By Andy Kroll

— Mother Jones (magazine)

2013.01.13 Sunday ACHK

對稱情境 1.1

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這段改編自 2010 年 6 月 15 日的對話。

有兩個袋。每個袋中都有十張卡紙，而每張卡紙上，都有由 1 到 10 的其中一個數字，沒有重複。現在，甲要由第一個袋中，抽一張卡紙出來。而乙則要在另一個袋中，抽另一張卡紙出來。假設整個過程是隨機的，即是各個可能性的機會均等。

如果甲的數字大過乙，那就為之「甲勝」。如果乙的數字大過甲，那就為之「乙勝」。已知「甲勝」的機會率是 q。問題是，「甲乙打和」的機會是多少？

整個遊戲只有三個可能的結果 ── 「甲勝」、「乙勝」 或者 「打和」 ── 而它們是互斥事件。所以，

P（甲勝）+ P（打和）+ P（乙勝）= 1

因為「甲勝」的機會是 q，而甲乙所面對的情境，又完全相同，所以「乙勝」的機會和「甲勝」一樣，都是 q。

q + P（打和）+ q = 1

P（打和）= 1 – 2q

結論是，「甲乙打和」的機會率是（1 – 2q）。

— Me@2013.01.13

致讀者：如發現本文有思考漏洞，或者運算錯誤，請以電郵告知本人。謝謝！

— Me@2012.10.17

2013.01.13 Sunday (c) All rights reserved by ACHK

Everett’s relative-state formulation, 2

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The relative-state interpretation makes two assumptions.

The first is that the wavefunction is not simply a description of the object’s state, but that it actually is entirely equivalent to the object, a claim it has in common with some other interpretations.

The second is that observation or measurement has no special role, unlike in the Copenhagen interpretation which considers the wavefunction collapse as a special kind of event which occurs as a result of observation.

— Wikipedia on Many-worlds interpretation

2013.01.12 Saturday ACHK

二次元時間 2.1

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Dimension 1.3.1 | Two dimensional time 2.1 | 孖生宇宙 2.1

這段改編自 2010 年 4 月 3 日的對話。

（安：我有一點不明白。你說「dimension」（次元）有兩種，可以是「spatial dimension」（空間次元），或者「temporal dimension」（時間次元）。宇宙的次元數目是「三加一」，即是「『三次元空間』加『一次元時間』」。

假設有一個科幻故事，描述一個有「二次元時間」的虛構宇宙。那樣，「二次元時間」是什麼意思？）

其實，「四次元空間」同樣難想像。不過，我們容後再談。我們先討論，何謂「二次元時間」。

一個宇宙，有一個「時間次元」，即是有一條「時間線」。「時間線」又可以稱為「因果鏈」。

如果一個科幻故事，容許「時間旅行」，而又不想引起矛盾，就唯有容許多個「平行宇宙」的存在。例如，二十歲的主角，回到十年之前，殺害十歲時的自己。但是，十歲時的主角既然之死，二十歲的主角又怎會存在呢？

「解決」之道是，宣稱在「二十歲的主角」殺害「十歲自己」時，宇宙歷史的發展被改變了，形成一分為二的「歷史分支」。或者說，宇宙的「時間線」，由一條分裂成兩條。

而科幻故事的通常用語是，在「二十歲的主角」殺害「十歲自己」時，宇宙由「一個」，分支成「兩個平行宇宙」。在一個宇宙中，主角活到起碼二十歲；而在另一個宇宙中，主角在十歲已遭人殺害。「平行」的意思是，再互不相干。亦即是話，「二十歲的主角」進入了另一個平行宇宙，再不能回到自己原本的世界。

你可以想像，隨著主角多次的「時間旅行」，改變歷史的次數越多，「平行宇宙」的數目亦會越大。假設，主角除了擁有「時光機」，可以「時間旅行」外，他在後來還發明了「平行宇宙機」，令到自己可以，穿梭遊走於各個「平行宇宙」之間。那樣，我們就可以說，「平行宇宙機」連繫了眾多「平行宇宙」。原本的「平行宇宙」，不再完全「平行」。

— Me@2013.01.12

2013.01.12 Saturday (c) All rights reserved by ACHK

Professor 2

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lisper 4 days ago | link

I was never in academia, but I was a researcher (at NASA) so I played the publishing game. And if you look at my record, I was relatively good at it. Not only was my publications list fairly long, but my work was also pretty widely referenced. But since my career no longer depends on it, I am now free to say that I credit my success almost entirely to gaming the system. This is not to say that I didn’t do good work (I think I did), but there was virtually no correlation between what I thought was quality work and what I actually got rewarded for. The vast majority of my publications were minor tweaks on previous work that were specifically engineered to get past the program committees of key conferences. My best work (by my own quality metric) either went unnoticed, or could not get accepted for publication at all. When it got to the point where I was faced with a very stark choice between continuing to produce bullshit and get rewarded for it, or to do what I thought was good work and eventually get fired, I quit.

   
Evbn 4 days ago | link

Industry isn’t so different. My salary is determined by 2 days of interviews and negotiations, and only slightly perturbed by my performance over the next several years.

— Hacker News

2013.01.11 Friday ACHK

Paul Graham

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zatara 59 days ago | link

I am almost afraid to ask you this, but here it goes.

On the last few weeks/months before starting Viaweb, did you consider yourself a failure for being almost 30, well-educated but out of the formal career track, “poor” and unmarried? If so, was that the fuel behind your many amazing achievements later on?

—–
   
   
pg 59 days ago | link

No, not really. I’d written the two Lisp books, and people liked those. Not a lot of people, but they were people whose opinions I cared about. Actually Viaweb felt like more of a compromise than the way I’d been living before, because it was something I was doing mostly for money.

—–
   
   
sayemm 58 days ago | link

So, you finally had your first taste of startup success at age 34. And you started Y Combinator at 41.

Think your story, along with many others in the Valley (e.g. Jim Clark), goes to show that this is a long-term game, and it only gets better with age and experience.

— Hacker News

2013.01.11 Friday ACHK

抽兩個數

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這段改編自 2010 年 6 月 15 日的對話。

假設有兩個袋。每個袋中都有十張卡紙，而每張卡紙上，都有一個由 1 到 10 的其中一個數字，沒有重複。現在，你要由每個袋中，隨機抽一張卡紙出來。換句話說，各個可能性的機會均等。問題是，你抽到兩個相同數字的機會率是多少？

P 方法：

總共要抽兩個數字：

（＿）（＿）

第一個數字，什麼也可以接受，所以機會率分是一。

（1）（＿）

第二個數字，則要同第一個數字吻合，而十個數字中，只有一個和第一個相同。所以，第二格的機會率是十分之一（1/10）。

（1）（1/10）

結論是，抽到兩個相同數字的機會率是 1/10。

（1）（1/10）= 1/10

S 方法：

我們先考慮所有可能結果的總數，放於分母；然後，再考慮可以接受的結果有多少，放於分子。

（＿）
（   ）

總共要抽兩個數字。每個數字各自有十個可能性。所以，整體有（10 x 10）個可能結果。

（＿＿＿）
（10）（10）

而眾多可能之中，只有十組是可以接受的，包括（1,1）、（2,2）……（10,10）。所以，分子是十（10）。

　（10）
＿＿＿＿
（10）（10）

結論是，抽到兩個相同數字的機會率是 1/10。

　（10）
＿＿＿＿
（10）（10）

= 1/10

— Me@2013.01.10

致讀者：如發現本文有思考漏洞，或者運算錯誤，請以電郵告知本人。謝謝！

— Me@2012.10.17

2013.01.11 Friday (c) All rights reserved by ACHK

Metamathematics

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In particular, arguably the greatest achievement of metamathematics and the philosophy of mathematics to date is Godel’s incompleteness theorem: proof that given any finite number of axioms for Peano arithmetic, there will be true statements about that arithmetic that cannot be proved from those axioms.

— Wikipedia on Metamathematics

2013.01.09 Wednesday ACHK

比喻

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Dimension 1.2

這段改編自 2010 年 4 月 3 日的對話。

該片的另一個問題是，它只用了一些比喻作為 argument（論據）。

「比喻」的作用，在於輔助理解，加深記憶。但是，「比喻」本身，並不可以作為論據。所以，我們要清楚知道，「以比喻來輔助解釋」和「以比喻本身作為解釋」的分別。前者合理，後者荒謬。

當一個所謂的「科學作品」，只提供一些比喻，而背後卻沒有提供，實質的內容和具體的論據時，那就只可算是「偽科學」和「偽作品」。

— Me@2013.01.09

2013.01.09 Wednesday (c) All rights reserved by ACHK

Digital physics, 3.2

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… what changes continuously is not the eigenvalue, namely the quantity that you measure, but rather the probabilities of measuring one or the other of those eigenvalues.

— Jan 26 ’11 at 23:51

— Carlo Rovelli

2013.01.08 Tuesday ACHK

Mind uncertainty

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People like talking because that can give them a feeling of decreasing uncertainty within their minds, although sometimes, that feeling is an illusion.

— Me@2013.01.07

The more emotional unstable you are, the more talking your need.

— Me@2013.01.08

2013.01.08 Tuesday (c) All rights reserved by ACHK

Past papers 26.7

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這段改編自 2010 年 6 月 15 日的對話。

這次考完試以後，如果你想知道，我這類讀書方法的詳情，你可以參考我的「魔法網誌」。

（CPK：但是，我上次收不到那個網址。）

不要緊，我再電郵給你。不過，你千萬不要在這個時期閱讀，因為你現在臨近考試，我怕那會令你分心。你應在這次大考後，才開始閱讀我的網誌。如果你要極度專心讀書，你就應該極度減少用電腦。

（LMC：那很難做到。）

可以做到。我年青時，高考課程的那兩年中（1997 年 9 月 至 1999 年 4 月），我從來沒有開過電腦。

（CPK：但是，如果我們需要打實驗報告呢？那又怎樣辦？）

很簡單。你用一部不能上網的電腦就可以。考試前，即使在必須用電腦的情況，只要不連上互聯網，就不易分心。

— Me@2013.01.07

2013.01.08 Tuesday (c) All rights reserved by ACHK

Information lost, 3.3

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Unitarity 3

The laws of Quantum Mechanics are very subtle — so subtle that they allow randomness to coexist with both energy conservation and information conservation.

— The Black Hole War, p.89

— Leonard Susskind

2013.01.06 Sunday ACHK