Problem 13.6

Posted on August 26, 2019 by rpflee

A First Course in String Theory

13.6 Orientifold Op-planes

(a) For an O23-plane the two normal directions $\displaystyle{x^{24}, x^{25}}$ can be represented by a plane. A closed string at a fixed $\tau$ appears as a parameterized closed curve $\displaystyle{X^a(\tau, \sigma)}$ in this plane. Draw such an oriented closed string that lies fully in the first quadrant of the $\displaystyle{(x^{24}, x^{25})}$ plane. Draw also the string $\displaystyle{\tilde{X}^a(\tau, \sigma) = -X^a(\tau, 2\pi - \sigma)}$ .

~~~

d_2019_08_26__22_32_32_PM_a

This one is wrong.

d_2019_08_26__22_31_55_PM_b

— Me@2019-08-26 10:31:07 PM

Quantum Computing, 3

Posted on August 24, 2019 by rpflee

Instead of requiring deterministic calculation, you allow (quantum) probabilistic calculation. What you gain is the extra speed.

— Me@2018-02-08 01:50:06 PM

年年齡 10.2

Posted on August 24, 2019 by rpflee

We don’t stop playing because we grow old; we grow old because we stop playing.

—

年紀越大，熱情越減，並不是因為你年紀變大，而是因為你選擇了原地踏步。

— Me@2011.10.11

— Me@2019.08.24

財政自由 1.1

Posted on August 23, 2019 by rpflee

（問：根據你的講法，好像大部分情況下，都不應該讀研究院似的。）

在理想的情況下，你可能應該讀研究院。

（問：那樣，你心目中的理想情況是什麼？）

假設你已經有財政自由，你就有可能，適合讀研究院；…

（問：那就即是話，要在還年青時，就賺到一生夠用的金錢？
為什麼要選擇，那麼難的目標？）

.

（問：但是，財政自由，又可以如何實現呢？）

首先，要有一個概念，就是：

長遠而言，為生不可靠「售賣時間」，而要靠「創造價值」。

例如，你是一位音樂演奏家。如果你的收入，主要來自去現場演出的話，那就為之，以「售賣時間」為生。

「售賣時間」的致命傷是，收入不可倍增放大。那就是所謂的「一分耕耘，一分收穫」。

（問：「一分耕耘，一分收穫」有什麼問題？）

連基本正常的生活，也可能推持不到。

例如，衣食住行是必須的。即使只講「住」，如果你的收入來源，只有薪金的話，你也要花十至三十年（或以上）的時間，才可以累積到有足夠的金錢，去支付買房子所需的首期。

— Me@2019-08-21 07:40:35 PM

Physical laws are low-energy approximations to reality, 1.6

Posted on August 19, 2019 by rpflee

d_2019_01_31__23_13_36_PM_a

QM GR

too many particles

when you cool down the system, you see something that your equations cannot predict

only by experiment, you discover that you can go to there

the system state goes from one local minimum to another

Since each theory is valid only when near a particular energy local minimum, we cannot use it to predict other local minima (other physical realities). That’s why we need to keep doing experiments that are designed for stress-testing existing theories. For example, one experiment can put a system in extreme high pressure. Another experiment can put a system in extreme high temperature.

Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. From there, we construct new theories to explain those phenomena.

d_2019_01_31__23_13_36_PM_b

Once a theory breaks down in one of those experiments, we see phenomena that we have never seen before. In this sense, experimental physics is much richer.

Computational physics goes further in only one direction. Only experiments let you try randomly.

— Me@2019-08-18 07:51:05 PM

Literal numbers

Posted on August 17, 2019 by rpflee

All primitive mathematical procedures are extended to be generic over
symbolic arguments. When given symbolic arguments, these procedures
construct a symbolic representation of the required answer. There are
primitive literal numbers. We can make a literal number that is
represented as an expression by the symbol “a” as follows:

(literal-number 'a)        ==>  (*number* (expression a))

The literal number is an object that has the type of a number, but its
representation as an expression is the symbol “a”.

(type (literal-number 'a))          ==>  *number*

(expression (literal-number 'a))    ==>  a

— SCMUTILS Reference Manual

2019.08.17 Saturday ACHK

Multiple dimensions of time

Posted on August 11, 2019 by rpflee

Two dimensional time 5.2 | 二次元時間 5.2

What would be the implications of multiple dimensions of time?

That means the (past) history itself can change, as commonly seen in time travel stories.

But wouldn’t that be the case with one dimension also?

In reality, there is only one dimension of time, meaning that the state of a system keeps changing, forming the timeline. But the timeline itself cannot be changed once formed. In other words, (past) history cannot be changed.

— Me@2019-08-11 04:07:48 PM

Transcender

Posted on August 4, 2019 by rpflee

Transcender ~ 架空俠

— Me@2019-07-13 09:11:02 AM

（反對）開夜車 4.2

Posted on August 3, 2019 by rpflee

…

平均而言，你仍必須要有，充足的睡眠。亦即是話，某一天睡少了，就必須於在當個星期，還回「睡債」。

例如，如果你的充足睡眠是，每天七小時，而你在某一天只睡了六小時的話，你就有義務，在當個星期的另一天，睡多一小時。一般而言，「另一天」是指週末，或者其他假日。

另外，有時，只要跳出框框，破格思考，你會發現，或者，只要你的時間表稍改一點，就根本毋須「開夜車」。

例如，我在大學一年級時，發覺日間的課堂，加課外活動，異常充實。回到家時，就已經累到，根本集中不到精神研習。

我當時靈機一觸想到，與其沒有精神地研習，倒不如每晚九時半就睡，凌晨三或四時才起床。那樣，七時多出門前，我就會有，三至四個小時的專心時空。

— Me@2019-07-30 11:11:42 PM

Physics Town

continues

Monthly Archives: August 2019