Publish! 11

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每個人，都需要有作品。

你的作品，就是你的人生意義。

每個人，都依靠自己的作品來生存。

作品，就是一些，不會隨自己的消失而消失的東西。

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你，有沒有自己的作品？

— Me@2011.07.03

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2019.01.13 Sunday (c) All rights reserved by ACHK

Publish! 11

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每個人，都需要有作品。

你的作品，就是你的人生意義。

每個人，都依靠自己的作品來生存。

作品，就是一些，不會隨自己的消失而消失的東西。

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你，有沒有自己的作品？

— Me@2011.07.03

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2019.01.13 Sunday (c) All rights reserved by ACHK

故事連線 1.1.5.1 | 碩士 4.1 | On Keeping Your Soul, 2.2.1 | Release early. Release often, 3

這段改編自 2010 年 4 月 18 日的對話。

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一般寫博士論文的方法過程，有如 closed source software（閉源軟件）的開發一樣，是不合理的。

那個方法是，花數年時間，編寫一個軟件程式，然後才正式出版。這個方法的危險之處是，如果軟件上市以後，才發現不受市場認同的話，那數年的投資，基本上是血本無歸的。

合理一點的開發模式是，open source software（開源軟件）開發時，一個經常採用的方法，叫做「release early, release often」（極速（而）頻繁（地）出版）。意思是，與其花數年時間，去編寫一個軟件程式的「完美」版，然後才正式出版，倒不如，先把那個軟件的「最粗疏但已經可用」版本，極速完成，然後立刻出版。

那樣，那公司就可以馬上得到，市場的初步反應；從而決定：是否繼續開發那個軟件：如果繼續的話，又應該改進哪些部分。

如果決定繼續開發，就立刻重覆這個「極速出版」流程。亦即是話，再把那個軟件改進部分的，「最粗疏但已經可用」版本，極速完成，然後立刻出版。

— Me@2019-01-13 06:22:43 PM

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2019.01.13 Sunday (c) All rights reserved by ACHK

The generating function is an infinite product:

To evaluate the infinite product, you can use SageMath with the following commands:

`typeset_mode(True)`

(1/x)*prod(((1+x^(n-1/2))^(32)/(1-x^n)^8) for n in (1..oo))

a = (1/x)*prod(((1+x^(n-1/2))^(32)/(1-x^n)^8) for n in (1..200))

F = a.taylor(x,0,6)

g = "+".join(map(latex, sorted([f for f in F.operands()], key=lambda exp:exp.degree(x))))

`g`

— Me@2019-01-11 11:52:33 AM

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2019.01.11 Friday (c) All rights reserved by ACHK

Counting states in heterotic SO(32) string theory | A First Course in String Theory

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d) Write a generating function for the full set of GSO-truncated states in the left-moving sector (include both NS’+ and R’+ states).

Use the convention where counts the number of states with .

Use and an algebraic manipulator to find the total number of states in heterotic string theory at .

~~~

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— This answer is my guess. —

~~~

p.322

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The left NS’+ sector:

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The left R’+ sector:

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~~~

— This answer is my guess. —

— Me@2019-01-10 01:49:43 PM

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2019.01.10 Thursday (c) All rights reserved by ACHK

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an observer ~ a consistent history

— Me@2019-01-05 04:02:43 PM

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2019.01.07 Monday (c) All rights reserved by ACHK

Set your course by the stars, not by the lights of every passing ship.

– Omar Bradley

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2019.01.07 Monday ACHK

聖誕假後的常規課程中，Ken Chan 預計應該不會有時間，教光學和熱學。但是，他認為那兩個課題很淺易，所以，期望我們即使自修，也沒什麼難度。

但是，他後來改變主意，還是決定於，農歷新年的年初一、二、三，為我們補課，教回光學和熱學。

今次，那三天的課，他不單不收我們的學費，他還要自己，花時間找課室、花金錢付租金。

後來，他改為每天收 20 元，即是總共 60 元。他解釋道，補課社的職員因為他的補課，要犧牲那三天的農曆新年假期。那每人 60 元的學費是，全數慰勞他們的。

那三天的補課，好處是光學和熱學；壞處是，由於每天也補多個小時，我少了大量，各科的溫習時間。但是，那個農曆新年長假，因為我自己時間管理不善，而損失的時間，遠多於那三天的補課時間。

感謝 Ken Chan 的額外付出。我亦慶幸，生於那個時空，還是有真人授課的年代。出生遲十年，就已經只能透過錄影帶，來獲得 Ken Chan 的教導。

— Me@2019-01-06 02:18:47 PM

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2019.01.06 Sunday (c) All rights reserved by ACHK

Overview

Clasp is a new Common Lisp implementation that seamlessly interoperates with C++ libraries and programs using LLVM for compilation to native code. This allows Clasp to take advantage of a vast array of preexisting libraries and programs, such as out of the scientific computing ecosystem. Embedding them in a Common Lisp environment allows you to make use of rapid prototyping, incremental development, and other capabilities that make it a powerful language.

— Clasp README.md

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I followed the official instructions to build Clasp:

The building process had been going on for about an hour; and then I got this error:

— Me@2019-01-04 10:11:43 PM

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2019.01.04 Friday (c) All rights reserved by ACHK

Counting states in heterotic SO(32) string theory | A First Course in String Theory

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c) Calculate the total number of states in heterotic string theory (bosons plus fermions) at .

~~~

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— This answer is my guess. —

~~~

spacetime bosons:

Number of states:

Let , the number of ways to put n indistinguishable balls into k boxes.

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Following the same logic:

Postulating a unique vacuum , the creation operators allow us to construct degenerate Ramond ground states.

Therefore, there are ground states .

— Me@2018-10-29 03:11:07 PM

Number of states:

~~~

spacetime fermions:

Number of states:

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Number of states:

~~~

— This answer is my guess. —

— Me@2019-01-03 05:26:59 PM

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2019.01.03 Thursday (c) All rights reserved by ACHK

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What is the relationship between a Maxwell photon and a quantum photon?

— Me@2012-04-09 7:38:06 PM

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The paper Gloge, Marcuse 1969: Formal Quantum Theory of Light Rays starts with the sentence

Maxwell’s theory can be considered as the quantum theory of a single photon and geometrical optics as the classical mechanics of this photon.

That caught me by surprise, because I always thought, Maxwell’s equations should arise from QED in the limit of infinite photons according to the correspondence principle of high quantum numbers as expressed e.g. by Sakurai (1967):

The classical limit of the quantum theory of radiation is achieved when the number of photons becomes so large that the occupation number may as well be regarded as a continuous variable. The space-time development of the classical electromagnetic wave approximates the dynamical behavior of trillions of photons.

Isn’t the view of Sakurai in contradiction to Gloge? Do Maxwell’s equation describe a single photon or an infinite number of photons? Or do Maxwell’s equations describe a single photon and also an infinite number of photons at the same time? But why do we need QED then at all?

— edited Nov 28 ’16 at 6:35

— tparker

— asked Nov 20 ’16 at 22:33

— asmaier

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Because photons do not interact, to very good approximation for frequencies lower than ( = electron mass), the theory for one photon corresponds pretty well to the theory for an infinite number of them, modulo Bose-Einstein symmetry concerns. This is similar to most of the statistical theory of ideal gases being derivable from looking at the behavior of a single gas particle in kinetic theory.

Put another way, the single photon behavior Maxwell’s equations correspondence only holds if you look at the Fourier transform version of Maxwell’s equations. The real space-time version of Maxwell’s equations would require looking at a superposition of an infinite number of photons — one way to describe the taking [of] an inverse Fourier transform.

If you want to think of it in terms of Feynman diagrams, classical electromagnetism is described by a subset of the tree-level diagrams, while quantum field theory requires both tree level and diagrams that have closed loops in them. It is the fact that the lowest mass particle photons can produce a closed loop by interacting with, the electron, that keeps photons from scattering off of each other.

In sum: they’re both incorrect for not including frequency cutoff concerns (pair production), and they’re both right if you take the high frequency cutoff as a given, depending on how you look at things.

— edited Dec 3 ’16 at 6:28

— answered Nov 27 ’16 at 23:08

— Sean E. Lake

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Maxwells equations, which describe the wavefunction of a single noninteracting photon, don’t need Planck’s constant. I find that remarkable. – asmaier Dec 2 ’16 at 14:16

@asmaier : Maxwell’s equations predate the quantum nature of light, they weren’t enough to avoid the ultraviolet catastrophe. Note too that what people think of as Maxwell’s equations are in fact Heaviside’s equations, and IMHO some meaning has been lost. – John Duffield Dec 3 ’16 at 17:45

— Do Maxwell’s equations describe a single photon or an infinite number of photons?

— Physics StackExchange

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2019.01.03 Thursday ACHK

The meaning of life is “entering university”.

Turn your real life into an amazing university, for otherwise, your life has no meaning.

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[At this amazing university,]

Which year (of study) are you in?

Who are your dearest classmates?

— Me@2011.07.01

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2019.01.02 Wednesday (c) All rights reserved by ACHK

PhD, 2.4 | 故事連線 1.1.6 | 碩士 3.4

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…

（問：我也遇過類似的情境。

我和一位好朋友合作做小組習作時，雖然未至於反目，但總會有很多爭拗。和他合作前，明明和他感情要好。各自有什麼困難時，對方總會杖義相助。

為什麼人類會，那麼奇怪呢？）

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簡單地說，即使是同一個人，其實也有不同方面，各樣性格。

做朋友時，你只需要接受小部分—你可以選擇，只接受他，最好的優點。但是，做工作伙伴時，你卻要接收大部分—你未必可以選擇，不接受他，最壞的缺點。

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（問：那樣，如果要「複雜地說」呢？）

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複雜地說，每個個體也透過自己，在這宇宙間的經歷，形成一個「主觀宇宙」，簡稱「世界觀」。

大部分人，也不自覺地，以為他的主觀宇宙，就是客觀宇宙的全部。這個不幸，源於每個人的主觀宇宙，是他唯一能夠觀察到的「客觀宇宙部分」；每個人當時的主觀宇宙，是他當時唯一能夠，觀察到的「客觀宇宙部分」。

只有一些「被選擇的心靈」，簡稱「半神人」，才會想像到，他的主觀世界，只是客觀世界的極小部分。所以，如果兩個人也不是「半神人」，而又要在工作上合作的話，其實就相當於，把兩個（主觀）宇宙的大部分，重疊在一起。

每個宇宙原本，都有各自的運行法則；貿然要求兩個宇宙，互相干涉對方內政，自然會十分危險。

六千五百萬年前，單單是一個小行星與地球相撞，就足以令大部分恐龍滅絕。試想想，兩個宇宙相撞，殺傷力會大多少倍。

— Me@2019-01-01 11:20:57 PM

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2019.01.01 Tuesday (c) All rights reserved by ACHK

EQL5-Android | Common Lisp for Android App Development 2018

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After successfully running the command `./1-make-ecl-host.sh`

, when I tried to run the command `./2-make-ecl-android.sh`

, I got the following errors:

— Me@2018-12-29 11:21:46 PM

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2018.12.30 Sunday (c) All rights reserved by ACHK

Counting states in heterotic SO(32) string theory | A First Course in String Theory

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At any mass level of the heterotic string, the spacetime bosons are obtained by “tensoring” all the left states (NS’+ and R’+) with with the right-moving NS+ states with .

Similarly, the spacetime fermions are obtained by tensoring all the left states (NS’+ and R’+) with with the right-moving R- states with .

c) Calculate the total number of states in heterotic string theory (bosons plus fermions) at .

~~~

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— This answer is my guess. —

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When ,

~~~

The left NS’+ sector:

The left R’+ sector:

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The right-moving NS+ states:

The R- states (that used as right-moving states):

~~~

spacetime bosons:

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spacetime fermions:

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— This answer is my guess. —

— Me@2018-12-28 11:12:59 PM

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2018.12.29 Saturday (c) All rights reserved by ACHK

“Everything has no patterns” (or “there are no laws”) creates a paradox.

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If “there are 100% no first order laws”, then it is itself a second order law (the law of no first-order laws), allowing you to use probability theory.

In this sense, probability theory is a second order law: the law of “there are 100% no first order laws”.

In this sense, probability theory is not for a single event, but statistical, for a meta-event: a collection of events.

Using meta-event patterns to predict the next single event, that is induction.

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Induction is a kind of risk minimization.

— Me@2012-11-05 12:23:24 PM

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2018.12.28 Friday (c) All rights reserved by ACHK

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Seek first to understand, then to be understood

— The Habit 5

— The 7 Habits of Highly Effective People

— Stephen Covey

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To understand does not mean to agree.

— Stephen Covey

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2018.12.28 Friday by ACHK

當年是 1996 年，我 9 月開始上他的課程。每星期上 1.5 小時，由星期六早上 8 時半，上到 10 時正。所以，每個星期六，我也要在還未睡夠時，就很早起床。去補習社的路程中，往往是一邊行，一邊流鼻水；唯有勉勵自己：「即使再辛苦，只要捱過『會考』（公開試），就可以有好日子過。」

記憶所及，大概在聖誕前，剛好完成了力學分部。

然後，他於聖誕假期中，有額外補課—歷時三天的全日課程，不再是每天 1.5 小時。就在那三天，他要完成波動分部。

他在公佈有這個聖誕波動補課時，我有兩點不開心。

第一點是，我要交額外的學費。不過，相對於第二點而言，那也只是小問題。

第二點是，那補課的學額有限，只有常規課程的兩成。我現在的記憶可能有誤，未必真的是兩成，但也必定是，遠少於他常規課程的學生數目。換句話說，如果供不應求，我就可能報讀不到。幸好，正正是因為這個擔憂，我及早報名，爭取到一個補課學位。

— Me@2018-12-27 03:50:13 PM

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2018.12.27 Thursday (c) All rights reserved by ACHK

EQL5-Android | Common Lisp for Android App Development 2018

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The step 2 is to “build cross-compiled ECL for Android”. It should have been straightforward to follow the instructions in the README page of the EQL5-Android project.

**However**, when trying to run the command `./1-make-ecl-host.sh`

, I got the following error messages:

The error was caused by the fact that my Ubuntu 18.04’s 64-bit gcc toolchain could not compile any source code to create 32-bit executables.

The solution is to run the following command to install the 32-bit gcc toolchain first:

`sudo apt-get install g++-multilib libc6-dev-i386`

— Me@2018-12-25 09:51:02 PM

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2018.12.25 Tuesday (c) All rights reserved by ACHK

Counting states in heterotic SO(32) string theory | A First Course in String Theory

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c) … Write out the massless states of the theory (bosons and fermions) and describe the fields associated with the bosons.

~~~

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— This answer is my guess. —

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spacetime bosons:

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**What is the nature of each of the indices ?
**

The vector index runs over eight values.

— c.f. p.323 *A First Course in String Theory* (Second Edition)

— c.f. the blog post Problem 14.5a3

— Me@2018-12-24 10:04:52 PM

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For the states in the form

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they

carry two independent vector indices , that run over eight values. There are therefore 64 bosonic states. Just like the massless states in bosonic closed string theory[,] they carry two vector indices. We therefore get a graviton, a Kalb-Ramond field, and a dilation:

(NS+, NS+) massless fields: .

— p.323 *A First Course in String Theory* (Second Edition)

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Then how about the states in the form

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What kinds of fields do they represent?

— Me@2018-12-24 10:42:03 PM

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— This answer is my guess. —

— Me@2018-12-23 11:16:56 PM

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2018.12.24 Monday (c) All rights reserved by ACHK

Double slit experiment, 8.2

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In the double slit experiment, the screen is used to detect interference pattern itself, causing the photon wavefunctions to “collapse”.

In the Afshar experiment, there is no classically definite position for a photon when the photon passes “through” the vertically wire slits. So there is no interference patterns “formed”, unless you put some kind of screen afterwards. [Me@2015-07-21 10:59 PM: i.e. making the observation, c.f. delayed choice experiment]

— Me@2012-04-09 12:19:52 AM

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Being massless, they cannot be localized without being destroyed…

— Photon dynamics in the double-slit experiment

— Wikipedia on *Photon*

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2018.12.23 Sunday (c) All rights reserved by ACHK