Gauge symmetry

Gauge theory 2

Gauge symmetries can be viewed as analogues of the equivalence principle of general relativity in which each point in spacetime is allowed a choice of local reference (coordinate) frame. Both symmetries reflect a redundancy in the description of a system.

— Wikipedia on Gauge theory

2011.01.31 Monday ACHK

Self de-centralization

自我虛級化 7

The history of ideas is a history of gradually discarding the assumption that it’s all about us. No, it turns out, the earth is not the center of the universe — not even the center of the solar system. No, it turns out, humans are not created by God in his own image; they’re just one species among many, descended not merely from apes, but from microorganisms. Even the concept of “me” turns out to be fuzzy around the edges if you examine it closely.

Conversely, if you have to choose between two theories, prefer the one that doesn’t center on you. This principle isn’t only for big ideas. It works in everyday life, too.

— Paul Graham

2011.01.31 Monday ACHK

The Man of Steel



With the financial and critical success of The Dark Knight, Warners said of the reboot Superman film, “We’re going to try to go dark to the extent that the character allows it.” Legendary Pictures president Thomas Tull added that “Superman needs a powerful antagonist, a worthy opponent,” wanting to evoke Superman as an “angry God”.

Paul Levitz stated in an interview that Batman holds the key to the Superman reboot. He elaborated, “Everyone is waiting for Nolan to sign on for another Batman, once that happens, the release date for Superman and all other future projects will follow.”

— Wikipedia on Superman (film series)




2011.01.31 Monday ACHK

時間定義 7.3 | 8.1

沒有因果關係的東西,就不能標籤為「不同時間」的「同一樣東西」。例如,你不能說,「愛因斯坦」是「2010 安」的「過去」,因為「愛因斯坦」的存在,並不是「2010 安」存在的先決條件。



你突然轉換了話題,令我不知如何答你 …



— Me@2011.01.31

2011.01.31 Monday (c) All rights reserved by ACHK 

Connection (mathematics) 2

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for transporting tangent vectors to a manifold from one point to another along a curve. An affine connection is typically given in the form of a covariant derivative, which gives a means for taking directional derivatives of vector fields: the infinitesimal transport of a vector field in a given direction.

Connections are of central importance in modern geometry in large part because they allow a comparison between the local geometry at one point and the local geometry at another point. Differential geometry embraces several variations on the connection theme, which fall into two major groups: the infinitesimal and the local theory.

— Wikipedia on Connection (mathematics)

2011.01.30 Sunday ACHK

Self Reliance 6

Everybody searching for a hero
People need someone to look up to
I never found anyone to fulfill my needs
A lonely place to be
So I learned to depend on me

– Greatest Love Of All

– by Michael Masser & Linda Creed

想景仰的英雄 我只好改變我

– 至愛

– 鄭國江

– Me@2011.01.30

2011.01.30 Sunday ACHK

CKY 1.3

這段改篇自 2010 年 4 月 30 日的對話。

還有另一個要點要留意。即使你在 section A 做足驗算校對的功夫,你也未必能百分百肯定,可以得到全部分數。所以,為了保證自己可以拿到 C 級或以上的成績,section B 千萬不要真的完全不做。

每題 section B 的題目,你要保證自己都可以完成 a, b 部分。

(CKY:通常 a, b 部分都比較簡單?)

為什麼 section B(乙部)的每一題,都要分 a, b, c, d 四部分呢?

那是因為 section B 都是比較深的題目。如果一開始就問你 d 部分的話,大部分人都不會做到。倒轉來說,a, b 部分的舖排,其實是給考生的提示。由於是提示,所以會比較簡單容易,不會比 section A 的短題目深。

你只要完成 section A 的全部和 section B 每題的 a, b 部分,而做的途中又順道做好驗算,你的成績等級就可以坐 C 望 B。

— Me@2011.01.30

2011.01.30 Sunday (c) All rights reserved by ACHK

Gauge theory

In physics, a gauge theory is a type of field theory in which the Lagrangian is invariant under a continuous group of local transformations.

The term gauge refers to redundant degrees of freedom in the Lagrangian. The transformations between possible gauges, called gauge transformations, form a Lie group which is referred to as the symmetry group or the gauge group of the theory. Associated with any Lie group is the Lie algebra of group generators. For each group generator there necessarily arises a corresponding vector field called the gauge field. Gauge fields are included in the Lagrangian to ensure its invariance under the local group transformations (called gauge invariance). When such a theory is quantized, the quanta of the gauge fields are called gauge bosons. If the symmetry group is non-commutative, the gauge theory is referred to as non-abelian, the usual example being the Yang–Mills theory.

— Wikipedia on Gauge theory

2011.01.29 Saturday ACHK

時間定義 7.2



只有當「甲」是「乙」的原因時,你才可以將他們標籤為「不同時間」的「同一樣東西」。我們現在討論的例子是,「甲」是「2000 安」,而「乙」是「2010 安」。「甲」是「乙」的先決條件。沒有「甲」,就不會有「乙」。所以,我們可以把「甲」和「乙」都標籤為「阿安」。他們是不同時間的「阿安」。「2000 安」是「2010 安」的「過去」。

沒有因果關係的東西,就不能標籤為「不同時間」的「同一樣東西」。例如,你不能說,「愛因斯坦」是「2010 安」的「過去」,因為「愛因斯坦」的存在,並不是「2010 安」存在的先決條件。

— Me@2011.01.29

2011.01.29 Saturday (c) All rights reserved by ACHK  

Background independence

String theory 7

A separate and older criticism of string theory is that it is background-dependent — string theory describes perturbative expansions about fixed spacetime backgrounds. Although the theory has some background-independence — topology change is an established process in string theory, and the exchange of gravitons is equivalent to a change in the background — mathematical calculations in the theory rely on preselecting a background as a starting point.

— Wikipedia on String theory

2011.01.28 Friday ACHK

偷天情緣 2

Groundhog Day 2


— 偷天情緣, 維基百科

— Me@2010.10.31

2011.01.28 Friday ACHK

Large organization


Or rather, a large organization could only avoid slowing down if they avoided tree structure. And since human nature limits the size of group that can work together, the only way I can imagine for larger groups to avoid tree structure would be to have no structure: to have each group actually be independent, and to work together the way components of a market economy do.

— Paul Graham




2011.01.28 Friday ACHK

CKY 1.2

這段改篇自 2010 年 4 月 30 日的對話。

或者說,即使你在 section B 一題也不做,一分也得不到,只要你在 section A 運算準確,準確到連一個標點符號都沒有錯的話,你奪取到 C 級成績的機會就會很大,因為 section A 在全卷 110 分之中,佔了 62 分。


正正是因為很難做到,所以我剛才不只叫你「狂轟 section A」,而且還提醒你要「提高運算的準確度。」不同課題會有不同的驗算技巧,你要一一掌握。





還有另一個要點要留意。即使你在 section A 做足驗算校對的功夫,你也未必能百分百肯定,可以得到全部分數。所以,為了保證自己可以拿到 C 級或以上的成績,section B 千萬不要真的完全不做。

每題 section B 的題目,你要保證自己都可以完成 a, b 部分。

— Me@2011.01.28

2011.01.28 Friday (c) All rights reserved by ACHK

The Truth About Lisp

Learning lisp will alter your life.

Your brain will grow bigger than you ever thought possible.

Paul Graham himself was completely written in lisp, by an earlier version of himself, also written in lisp, by an earlier version of lisp. It’s lisp, paul graham, lisp, paul graham, all the way down.

— Leon Bambrick

2011.01.27 Thursday ACHK


Written in anger

I once read that all good non-fiction books are written in anger.

At first I was taken aback by that. Then I realized [that] it was true.

If you do write a book, you are implicitly saying that the world needs this book.

Implicit in that is the accusation that the existing books are either incorrect or incomplete or both.

— How to Write, Publish, and Sell Your Own How-To Book

– John T Reed

2011.01.27 Thursday ACHK