# Problem 13.6

A First Course in String Theory

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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 $\displaystyle{\tilde{X}^a(\tau, \sigma) = -X^a(\tau, 2\pi - \sigma)}$.

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This one is wrong.

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— Me@2019-08-26 10:31:07 PM

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# Quantum Computing, 3

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

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# 年年齡 10.2

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

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— Me@2011.10.11

— Me@2019.08.24

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# 財政自由 1.1

（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。）

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（問：那樣，你心目中的理想情況是什麼？）

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（問：那就即是話，要在還年青時，就賺到一生夠用的金錢？

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（問：但是，財政自由，又可以如何實現呢？）

「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？）

— Me@2019-08-21 07:40:35 PM

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# Physical laws are low-energy approximations to reality, 1.6

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

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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.

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

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# Literal numbers

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

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2019.08.17 Saturday ACHK

# Multiple dimensions of time

Two dimensional time 5.2 | 二次元時間 5.2

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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

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# （反對）開夜車 4.2

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— Me@2019-07-30 11:11:42 PM

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