Ken Chan 時光機 1.3

唔識就飛 8.4.2

.

另一個技巧是,考試時「唔識就飛」:想不通的話,就立刻先做下一題,或者同一題的下一部分。

假設我現時記憶正確,Ken Chan 是第一個教我這個技巧的老師;我日校的純數學科老師,則是第二個(亦是最後一個)。

這個技巧,對我來說,實在太重要,因為,在兩年多後的純數學科高考中,如果我不是確切執行這個政策的話,我有極大機會會失手,繼而在當年,升不到大學。

那個故事,現不再詳述,因為已於另一篇文章「唔識就飛 8.4」中講過。請參考該文章。

— Me@2018-10-31 09:39:05 AM

.

.

2018.10.31 Wednesday (c) All rights reserved by ACHK

如有 HKDSE physics 香港中學文憑試之物理問題,歡迎以右邊之電郵地址,聯絡本人。

funcall

In Common Lisp, apply can take any number of arguments, and the function given first will be applied to the list made by consing the rest of the arguments onto the list given last. So the expression

(apply #’+ 1 ’(2))

is equivalent to the preceding four. If it is inconvenient to give the arguments as
a list, we can use funcall, which differs from apply only in this respect. This expression

(funcall #’+ 1 2)

has the same effect as those above.

— p.13

— On Lisp

— Paul Graham

.

Exercise 7.1

Define funcall.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.


(defmacro our-funcall (f &rest p)
  `(apply ,f (list ,@p)))

— Me@2018-10-30 03:24:05 PM

.

.

.

2018.10.30 Tuesday (c) All rights reserved by ACHK

Problem 14.5b2

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

.

(b) Consider the left R’ sector. Write the precise mass-squared formula with normal-ordered oscillators and the appropriate normal-ordering constant.

We have 32 zero modes \displaystyle{\lambda_0^A} and 16 linear combinations behave as creation operators.

As usual half of the ground states have \displaystyle{(-1)^{F_L} = +1} and the other half have \displaystyle{(-1)^{F_L} = -1}.

Let \displaystyle{|R_\alpha \rangle_L} denote ground states with \displaystyle{(-1)^{F_L} = +1}.

How many ground states \displaystyle{|R_\alpha \rangle_L} are there?

~~~

— This answer is my guess. —

\displaystyle{ \begin{aligned} \alpha' M_L^2 &= 1 + \sum_{n \in \mathbf{Z}^+} \left( \bar \alpha_{-n}^I \bar \alpha_{n}^I + n \lambda_{-n}^A \lambda_{n}^A \right) \\ \end{aligned}}

p.315 “Being zero modes, these creation operators do not contribute to the mass-squared of the states. Postulating a unique vacuum \displaystyle{|0 \rangle}, the creation operators allow us to construct \displaystyle{16 = 2^4} degenerate Ramond ground states.”

Following the same logic:

Postulating a unique vacuum \displaystyle{|0 \rangle}, the creation operators allow us to construct \displaystyle{2^{16}} degenerate Ramond ground states.

Therefore, there are \displaystyle{2^{15}} ground states \displaystyle{|R_\alpha \rangle_L}.

— This answer is my guess. —

— Me@2018-10-29 03:11:07 PM

.

.

2018.10.29 Monday (c) All rights reserved by ACHK

Visualizing higher dimensions

The trick of visualizing higher dimension is: not to visualize it.

— Wikipedia

— Me@2011.08.19

.

Besides trying to visualize, there are other methods to understand higher dimensions.

— Me@2018-10-28 04:28:01 PM

.

.

What is the meaning of visualization?

— Me@2018-09-02 4:35 pm

.

feel ~ receive all the data at once

(This definition is not totally correct, but is useful in the meantime.)

visual ~ feel at once through eyes

.

you can visualize a 3D object ~ you can see all of a 3D object at once

you cannot visualize a 4D object ~ you cannot see all of a 4D object at once

.

Actually, you can only visualize a 2D object, such as a square.

You cannot visualize a 3D object, such as a cube.

That’s why the screen of any computer monitor is 2 dimensional, not 3.

— Me@2018-10-28 04:32:41 PM

.

.

2018.10.28 Sunday (c) All rights reserved by ACHK

A pretty girl, 2

Women are directly fitted for acting as the nurses and teachers of our early childhood by the fact that they are themselves childish, frivolous and short-sighted; in a word, they are big children all their life long–a kind of intermediate stage between the child and the full-grown man, who is man in the strict sense of the word. See how a girl will fondle a child for days together, dance with it and sing to it; and then think what a man, with the best will in the world, could do if he were put in her place.

— Of Women

— Arthur Schopenhauer

.

When the elderly Schopenhauer sat for a sculpture portrait by the Prussian sculptor Elisabet Ney in 1859, he was much impressed by the young woman’s wit and independence, as well as by her skill as a visual artist. After his time with Ney, he told Richard Wagner’s friend Malwida von Meysenbug, “I have not yet spoken my last word about women. I believe that if a woman succeeds in withdrawing from the mass, or rather raising herself above the mass, she grows ceaselessly and more than a man.

— Wikipedia on Arthur Schopenhauer

.

Anybody can look at a pretty girl and see a pretty girl. An artist can look at a pretty girl and see the old woman she will become. A better artist can look at an old woman and see the pretty girl that she used to be. But a great artist — a master — and that is what Auguste Rodin was — can look at an old woman, portray her exactly as she is… and force the viewer to see the pretty girl she used to be…. and more than that, he can make anyone with the sensitivity of an armadillo, or even you, see that this lovely young girl is still alive, not old and ugly at all, but simply prisoned inside her ruined body. He can make you feel the quiet, endless tragedy that there was never a girl born who ever grew older than eighteen in her heart…. no matter what the merciless hours have done to her. Look at her, Ben. Growing old doesn’t matter to you and me; we were never meant to be admired — but it does to them. Look at her! (UC)

— Robert A. Heinlein

.

.

2018.10.27 Saturday ACHK