所以，如果你想驗算的話，你可以代（例如） x = 0.003217 入左右兩邊，看看左右兩邊是否數值非常近似。
LHS :
RHS :
如果左右兩邊的頭幾個對應數字都相同的話，你的方程式答案
就有很大機會正確。
用這個驗算方法，選擇 x 的數值時，有一些地方要留意。
第一， x 一定要是在 1 和 -1 之間的數字。
第二， x 千萬不要代一些公整的數字。太公整的話，例如 0 和 0.5 等，你很可能會「撞中答案」。即使左右兩邊的數字答案非常接近，你也不能確定，那是因為你的運算正確，還是只是巧合。
第三， x 不要太大。太大的話，例如 0.3217，即使你的方程式答案正確，左右兩邊的數字答案亦未必會接近。
第四， x 不要太小。太小的話，例如 0.000003217，你會校對不到右手邊方程式最後一項（）的係數（281）是否正確。
— Me@2011.03.04
2011.03.05 Saturday (c) All rights reserved by ACHK
String theory 9
U-duality is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the “U-duality (symmetry) group” of M-theory as defined on a particular background space (topological manifold). This is the union of all the S- and T-dualities available in that topology.
The narrow meaning of the word “U-duality” is one of those dualities that can be classified neither as an S-duality, nor as a T-duality – a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example.
— Wikipedia on U-duality
2011.03.04 Friday ACHK
點石成金 2
石的存在目的，是被點成金；種子的存在目的，是長成大樹。
無石不會有金；無種子不會有大樹。
— Me@2011.01.31
The sole purpose of the existence of the first idea is to be rewritten.
— Based on Paul Graham
— Me@2010.09.21
2011.03.04 Friday (c) All rights reserved by ACHK
Startup 6
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In an essay I wrote a couple years ago I advised graduating seniors to work for a couple years for another company before starting their own. I’d modify that now. Work for another company if you want to, but only for a small one, and if you want to start your own startup, go ahead.
— Paul Graham
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2011.03.04 Friday ACHK
最簡單的例子是，一個人的「左腦」和「右腦」，各自都是一個完整的「人」。
對於正常人來說，左腦控制右邊身體，右腦控制左邊身體。左腦和右腦各自控制半個人。它們互相合作，令到一個人能夠過完整的生活。令我驚奇的是，那不是事實的全部。
我看過一輯 BBC（英國廣播公司）的記錄片，描述有一個小童（甲），因為左腦大部分的細胞壞死了，導致他不能有正常的思考，不能過正常的生活。他的家人決定讓醫生移除他左腦的大部分。手術之後，他的右半身失去了左腦的指示，暫時不能正常運作。但是，經過一連串的訓練和治療，他的右腦漸漸地接管了他整個身體的運作，包括了原本由左腦控制的右半身。還有，一般人由左腦負責語言，而甲卻失掉了左腦，本應自此口齒不清。但是，透過不斷學習，他的右腦漸漸地掌握了語言。
甲失掉左腦，結果最後卻可以過正常完整的生活。他的右腦有那麼大的可塑性，主要原因是他還是小童。小童腦部的彈性還是很大。
而我想帶出的是，根本即使是單獨一個左腦，或者是一個右腦，都有潛能掌管一個人的整個身體，負責一個人的整個生活。從這個角度看，左腦右腦各自都是一個完整的「人」。而正常人都有左腦右腦，即是正常人都至少同時有兩個「自我」：左腦和右腦。
我們可以假想一百年後，科技發達。如果你願意的話，你可以要醫生把你的右腦移植去一個機械身體，而左腦則留在原本的身體。那樣，你就由一個人變成了兩個人。
— Me@2011.03.03
2011.03.03 Thursday (c) All rights reserved by ACHK
Left brain functions
sequential
analytical
verbal
logical
linear algorithmic processing
mathematics: perception of counting/measurement
present and past
language: grammar/words, literal
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— Wikipedia on Lateralization of brain function
— Me@2008.01.13
— Me@2022-01-23
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2011.03.03 Thursday ACHK
大世界 3.2
Our hypothetical Blub programmer wouldn’t use either [Cobol or assembly]. Of course he wouldn’t program in machine language. That’s what compilers are for. And as for Cobol, he doesn’t know how anyone can get anything done with it. It doesn’t even have x (Blub feature of your choice).
As long as our hypothetical Blub programmer is looking down the power continuum, he knows he’s looking down. Languages less powerful than Blub are obviously less powerful, because they’re missing some feature he’s used to. But when our hypothetical Blub programmer looks in the other direction, up the power continuum, he doesn’t realize he’s looking up. What he sees are merely weird languages. He probably considers them about equivalent in power to Blub, but with all this other hairy stuff thrown in as well. Blub is good enough for him, because he thinks in Blub.
When we switch to the point of view of a programmer using any of the languages higher up the power continuum, however, we find that he in turn looks down upon Blub. How can you get anything done in Blub? It doesn’t even have y.
By induction, the only programmers in a position to see all the differences in power between the various languages are those who understand the most powerful one. (This is probably what Eric Raymond meant about Lisp making you a better programmer.) You can’t trust the opinions of the others, because of the Blub paradox: they’re satisfied with whatever language they happen to use, because it dictates the way they think about programs.
— Paul Graham
2011.03.02 Wednesday ACHK
You can only rank people with lower rank than you have;
you cannot rank people with higher rank than you have.
— Me@2011.03.02
2011.03.02 Wednesday (c) All rights reserved by ACHK
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… games is a good way to socialize …
– Halcyon Days (book)
– James Hague
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2011.03.02 Wednesday ACHK
二項式定理有一個驗算方法。例如，題目要你把 展開（expand）至
為止。而你運算到的答案是
。你怎樣可以知道，自己有沒有運算錯誤呢？
首先，你要知道，這種題目的目的，是要做近似值，以簡化運算。如果把 的所有項也寫出來的話，你總共要寫 24 項。
如果你只想寫（次方由小至大的）頭幾項，而又要近似值足夠準確的話，x 一定要是在 1 和 -1 之間的一個很小的數值，因為 x 的數值越小， x 越大次方的數值就越可以忽略。例如，x 是百份之一的話， x 二次方就是萬分之一。而 x 三次方就是百萬分之一。
— Me@2011.03.02
2011.03.02 Wednesday (c) All rights reserved by ACHK
Dualities
Before the 1990s, string theorists believed there were five distinct superstring theories: open type I, closed type I, closed type IIA, closed type IIB, and the two flavors of heterotic string theory (SO(32) and E8×E8). The thinking was that out of these five candidate theories, only one was the actual correct theory of everything, and that theory was the one whose low energy limit, with ten spacetime dimensions compactified down to four, matched the physics observed in our world today.
It is now believed that this picture was incorrect and that the five superstring theories are connected to one another as if they are each a special case of some more fundamental theory (thought to be M-theory). These theories are related by transformations that are called dualities. If two theories are related by a duality transformation, it means that the first theory can be transformed in some way so that it ends up looking just like the second theory. The two theories are then said to be dual to one another under that kind of transformation. Put differently, the two theories are mathematically different descriptions of the same phenomena.
— Wikipedia on String theory
2011.02.28 Monday ACHK
by Richard M. Stallman
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My mother on childraising: “All you have to do is love them and show them the world.”
— Paul Graham
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2011.02.27 Sunday ACHK
而我所講的，是「多重人格」。那不是一種病患，那是正常的。每一個人也會有多重人格，而不同人格之間可以互相溝通。互相溝通的速度高到眾多人格，長年累月以來，一直以為他們是同一個「人」。
一個人的「自我」，其實不是一個單獨的「思想意志」，而是一個由很多個委員組成的委員會。委員之間互相溝通商量，然後做出集體決定。（那是正常的。）如果委員之間各自為政，甚至互相爭奪整個委員會的控制權，那就構成「多重人格障礙」（multiple personality disorder）。（那是一種病患。）
— Me@2011.02.27
2011.02.27 Sunday (c) All rights reserved by ACHK
Product progression
Original line
* Windows 1.0
* Windows 2.0
* Windows 2.1 aka Windows/286 and Windows/386
* Windows 3.0
* Windows 3.1
* Windows 3.11 aka Windows for Workgroups
* Windows 3.2
Windows 9x
* Windows 4.0 (Windows 95)
* Windows 4.1 (Windows 98)
* Windows 4.9 (Windows Me)
Windows NT
* Windows NT 3.1
* Windows NT 3.5
* Windows NT 3.51
* Windows NT 4.0
* Windows NT 5.0 (Windows 2000)
* Windows NT 5.1 (Windows XP)
* Windows NT 5.2 (Windows Server 2003 and Windows XP Professional x64 Edition)
* Windows NT 6.0 (Windows Vista and Windows Server 2008)
* Windows NT 6.1 (Windows 7 and Windows Server 2008 R2)
— Wikipedia on History of Microsoft Windows
2011.02.26 Saturday ACHK
Legacy
Windows 3.x was superseded by the release of Windows 95 in August 1995.
Windows 3.1 found a niche market as an embedded operating system after becoming obsolete in the PC world. Up until November 2008, both Virgin Atlantic and Qantas employed it for some of the onboard entertainment systems on long-distance jets. It also sees continued use as an embedded OS in retail cash tills.
On 9 July 2008, it was announced that Windows for Workgroups 3.11 for the embedded devices channel would no longer be made available for OEM distribution as of 1 November 2008.
— Wikipedia on Windows 3.1x
2011.02.26 Saturday ACHK
Windows API itself is a virtual machine.
Windows API abstracts the hardware away from the application programs.
With Windows API, a programmer does not need to care exactly which hardware the computer is based on.
— Me@2011.02.25
2011.02.26 Saturday (c) All rights reserved by ACHK
Chrono Trigger 2
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An Ancient Fort-
Chasing phantoms in one’s dreams…
Arni Village –
Where the tides start to turn…
Opassa Beach –
A calling from beyond time…
Arni Village –
Nothing has changed but everything!
Cape Howl –
A reminder of one’s former self…
Heading North –
In search of some answers…
The Port Town of Termina –
The pride of the Acacia Dragoons…
Viper Manor –
Where lies the key to the past…
Guldove –
Where ripples become waves…
Hermit’s Hideaway –
Meeting with the ‘other’ swordsman…
From Pirate Ship to Ghost Ship –
A mariner’s worst nightmare…
On to Water Dragon Isle –
In search of the dragon blue…
Fort Dragonia –
Ancient dragons’ dream in ruins…
Temporal Vortex –
Where lost souls wander…
The Lost Portal –
Isolation of people from the world…
Termina –
Knight or day…?
Marbule –
The village of the demi-humans…
The Masamune –
The blood-stained sword of evil…
The Dead Sea –
A place forsaken by the gods…
A Portal Reopened –
And the planet began to shake…
Back to Viper Manor –
A captive audience awaits…
Surprise Attack!!! –
Pursuers with heavy-hearts…
To the Sea of Eden –
Through the hidden holes in time…
The Arbiter of Time –
On whom the three Fates smile…
Terra Tower –
Caught in an echo of time…
Chrono Cross –
The point where destinies meet…
For all the Dreamers –
Our planet’s dream is not over yet…
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– Chrono Compendium
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2011.02.26 Saturday ACHK
權力，來自於被控制者的恐懼。
權力的強弱，反映被控制者的心理狀態。
當被控制者不在恐懼時，權力以光速消失。
— Me@2011.02.24
2011.02.25 Friday (c) All rights reserved by ACHK
50 50, 2
這段改篇自 2010 年 4 月 30 日的對話。
如果「文科」和「理科」之中，二者只能擇其一的話，我建議你跟興趣。年級越高，讀書的工作量越大。如果不是面對自己極有興趣的科目的話，你會極不開心。
如果，你對「文科」和「理科」的興趣竟然是一模一樣，分毫不差的話，我建議你選「理科」，因為「理科」可以後悔，「文科」不可以。如果你在高中時選了「理科」而後悔的話，你可以在大學選科時，選一些「非理科」的科目。但是，如果你在高中時選了「文科」，而發現自己的最大興趣是「理科」的話，你大概沒有可能，在大學選科時，選一些「理科」的科目。
— Me@2011.02.25
2011.02.25 Friday (c) All rights reserved by ACHK
Physics Town 
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