# Problem 14.3b6

Quick Calculation 14.4b | A First Course in String Theory

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Massive level in the open superstring

Consider the first and second excited levels of the open superstring ($\alpha' M^2 = 1$ and $\alpha' M^2 = 2$). List the states in NS sector and the states in the R sector. Confirm that you get the same number of states.

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When $\alpha' M^2 = 2$, by Equation (14.54), the possible states are

$\{ \alpha_{-2}^I, \alpha_{-1}^I \alpha_{-1}^J, d_{-1}^I d_{-1}^J \} | R_a \rangle, || ...$

$\{ \alpha_{-1}^I d_{-1}^J, d_{-2}^I \} | R_{\bar a} \rangle, || ...$

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For $\alpha_{-2}^I | R_a \rangle$, the number of states is 8.

For $\alpha_{-1}^I \alpha_{-1}^J | R_a \rangle$, the number of states is $\frac{8 \times 7}{2} + 8 = 36$.

For $d_{-1}^I d_{-1}^J | R_a \rangle$, the number of states is $\frac{8 \times 7}{2} = 28$.

For $\alpha_{-1}^I d_{-1}^J | R_{\bar a} \rangle$, the number of states is $8 \times 8 = 64$.

For $d_{-2}^I | R_{\bar a} \rangle$, the number of states is 8.

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However, since each of $a$ and ${\bar a}$ has 8 possible values, there is an additional multiple of 8.

The total number of states is $8 \left[ 8 + 36 + 28 + 64 + 8 \right]$.

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You can check this answer against Equation (14.67):

$f_{NS} (x) = \frac{1}{\sqrt{x}} + 8 + 36 \sqrt{x} + 128 x + 402 x \sqrt{x} + 1152 x^2 + ...$

— Me@2018.02.20 10:57 AM

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# The language of Change 1.2

Energy conservation, 6.2 | Energy 5.2

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time ~ change

energy ~ the ability of _keeping_ changing

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constant velocity ~ the amount of an object’s change of position, measured with respect to its observer’s unit of change, is constant

$s = \Delta x$

$v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}$

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kinetic energy ~ the amount of the ability of keeping changing an object’s position

$\frac{1}{2} m v^2$ ~ the square of (the amount of change of position, relative to the observer’s unit of change)

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Energy difference is _not_ exactly a measurement of the amount of change, time interval is.

— Me@2018-02-20 09:39:30 AM

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# Cat

— Me@2018-02-19 02:33:42 PM

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# 潛行凶間 16

Inception 16

1. 清醒夢

1.1 有些人在某些時候，在夢知道自己在發夢，卻又可以保持住，發夢的狀態。

1.2 那些人之中的部分人，在那些清醒夢時候的部分時候，甚至可以控制著，那些夢境的劇情演變。

（CPK：未。不過，我的姐姐試過。）

《潛行凶間》中的意念，你可以假想，有七成是真的。

2. 多層夢

3. 多重自我

3.1 每一個人，其實有超過一個自我。

3.2 而每一個自我，其實有超過一個層次的意識。

— Me@2018.02.18

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# Creative constraints

Imagine you were asked to invent something new. It could be whatever you want, made from anything you choose, in any shape or size. That kind of creative freedom sounds so liberating, doesn’t it? Or … does it?

If you’re like most people you’d probably be paralyzed by this task. Why?

Brandon Rodriguez explains how creative constraints actually help drive discovery and innovation.

With each invention, the engineers demonstrated an essential habit of scientific thinking – that solutions must recognize the limitations of current technology in order to advance it.

Understanding constraints guides scientific progress, and what’s true in science is also true in many other fields.

Constraints aren’t the boundaries of creativity, but the foundation of it.

— The power of creative constraints

— Lesson by Brandon Rodriguez

— animation by CUB Animation

— TED-Ed

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We cannot change anything until we accept it. Condemnation does not liberate, it oppresses.

— Carl Jung

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# Twelve-step program

A twelve-step program is a set of guiding principles outlining a course of action for recovery from addiction, compulsion, or other behavioral problems. Originally proposed by Alcoholics Anonymous (AA) as a method of recovery from alcoholism, the Twelve Steps were first published in the 1939 book Alcoholics Anonymous: The Story of How More Than One Hundred Men Have Recovered from Alcoholism. The method was adapted and became the foundation of other twelve-step programs.

As summarized by the American Psychological Association, the process involves the following:

– recognizing a higher power that can give strength;

– examining past errors with the help of a sponsor (experienced member);

– making amends for these errors;

– learning to live a new life with a new code of behavior;

– helping others who suffer from the same alcoholism, addictions or compulsions.

— Wikipedia on Twelve-step program

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We cannot change anything until we accept it. Condemnation does not liberate, it oppresses.

— Carl Jung

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# 深淵 2

— 尼采

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As soon as men decide that all means are permitted to fight an evil, then their good becomes indistinguishable from the evil that they set out to destroy.

— Christopher Dawson

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2018.02.16 Friday ACHK

# Problem 14.3b5

Quick Calculation 14.4b | A First Course in String Theory

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Massive level in the open superstring

Consider the first and second excited levels of the open superstring ($\alpha' M^2 = 1$ and $\alpha' M^2 = 2$). List the states in NS sector and the states in the R sector. Confirm that you get the same number of states.

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When $\alpha' M^2 = 2$, by Equation (14.37),

$M^2 = \frac{1}{\alpha'} \left( - \frac{1}{2} + N^\perp \right)$

$N^\perp = \frac{5}{2}$

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$\{ b_{-1/2}^I b_{-1/2}^J b_{-1/2}^K b_{-1/2}^L b_{-1/2}^M,$

$b_{-3/2}^I b_{-1/2}^L b_{-1/2}^M,$

$b_{-5/2}^I,$

$\alpha_{-1}^I b_{-1/2}^J b_{-1/2}^K b_{-1/2}^M,$

$\alpha_{-1}^I b_{-3/2}^J,$

$\alpha_{-2}^I b_{-1/2}^J,$

$\alpha_{-1}^I \alpha_{-1}^J b_{-1/2}^K \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

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There are $\frac{8 \times 7 \times 6 \times 5 \times 4}{5!} = {8 \choose 5} = 56$ states for

$\{ b_{-1/2}^I b_{-1/2}^J b_{-1/2}^K b_{-1/2}^L b_{-1/2}^M |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $8 \times \frac{8 \times 7}{2} = 224$ states for

$\{ b_{-3/2}^I b_{-1/2}^L b_{-1/2}^M \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $8$ states for

$\{ b_{-5/2}^I \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $8 \times {8 \choose 3} = 448$ states for

$\{ \alpha_{-1}^I b_{-1/2}^J b_{-1/2}^K b_{-1/2}^M \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $8 \times 8 = 64$ states for

$\{ \alpha_{-1}^I b_{-3/2}^J \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $8 \times 8 = 64$ states for

$\{ \alpha_{-2}^I b_{-1/2}^J \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

There are $\left( \frac{8 \times 7}{2!} + 8 \right) \times 8 = 288$ states for

$\{ \alpha_{-1}^I \alpha_{-1}^J b_{-1/2}^K \} |NS \rangle \otimes |p^+, \vec p_T \rangle$

So the total number of states is 56 + 224 + 8 + 448 + 64 + 64 + 288 = 1152.

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You can check this answer against Equation (14.67):

$f_{NS} (x) = \frac{1}{\sqrt{x}} + 8 + 36 \sqrt{x} + 128 x + 402 x \sqrt{x} + 1152 x^2 + ...$

— Me@2018-02-16 03:22:13 PM

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# The language of Change

Energy conservation, 6 | Energy 5

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time ~ change

energy ~ the ability of causing change

Assuming

1. a system of one single particle

2. has only kinetic energy

3. and that kinetic energy is conserved.

conservation of energy ~ an object’s potential amount of change of position, measured with respect to its observer’s unit of change, is constant

$s = \Delta x$

$v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}$

— Me@2018-02-15 02:21:20 PM

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Note:

The above argument has a bug:

If the mass m is constant, the kinetic energy $E_K$ should be proportional to velocity squared $v^2$, instead of velocity $v$.

$E_K = \frac{1}{2} m v^2$

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However, the above argument is still technically correct:

When $E_K$ is constant, $v^2$ is constant. In turn, the magnitude of $v$ also remains unchanged.

— Me@2018-02-19 09:37:24 PM

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# Definition of Time, Prime

Energy 4

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time ~ change

energy ~ the ability of causing change

— Me@2018-02-15 10:20:25 AM

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# Importance, 2

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When you give a lot of importance to someone in your life,

you tend to lose your importance in their life.

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2018.02.14 Wednesday ACHK

# 機遇再生論 1.6

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（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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(問：那樣，為什麼要問多一次呢？）

「如果洗牌兩次，起碼一次洗到原本排列 A 的機會率是多少？」

$A_2$ = 兩次洗牌的結果，起碼一次洗到原本排列 A

$A_2$ 的互補事件為「不是 $A_2$」：

= 兩次洗牌的結果，不是起碼一次洗到原本排列 A

= 兩次洗牌的結果，都不是排列 A

$P(\text{not} A_2) = (1 - \frac{1}{N})^2$

$P(A_2)$
$= 1 - P(\text{not} A_2)$
$= 1 - (1 - \frac{1}{N})^2$

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$P(A_m)= 1 - (1 - \frac{1}{N})^m$

$P(A_m)$
$= 1 - (1 - \frac{1}{N})^m$
$= 1 - (1 - \frac{1}{52!})^{10,000,000}$

$1.239799930857148592 \times 10^{-61}$

— Me@2018-01-25 12:38:39 PM

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# Riemann Surfaces

Imaginary Numbers Are Real [Part 1: Introduction]

Imaginary Numbers Are Real [Part 2: A Little History]

Imaginary Numbers Are Real [Part 3: Cardan’s Problem]

Imaginary Numbers Are Real [Part 4: Bombelli’s Solution]

Imaginary Numbers Are Real [Part 5: Numbers are Two Dimensional]

Imaginary Numbers Are Real [Part 6: The Complex Plane]

Imaginary Numbers Are Real [Part 7: Complex Multiplication]

Imaginary Numbers Are Real [Part 8: Math Wizardry]

Imaginary Numbers Are Real [Part 9: Closure]

Imaginary Numbers Are Real [Part 10: Complex Functions]

Imaginary Numbers Are Real [Part 11: Wandering in 4 Dimensions]

Imaginary Numbers Are Real [Part 12: Riemann’s Solution]

Imaginary Numbers Are Real [Part 13: Riemann Surfaces]

— Welch Labs

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In case the original videos are lost, please use the Internet Archive link:

— Me@2018-02-12 02:14:51 PM

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# English

Yes, English can be weird. It can be understood through tough thorough thought, though.

— David Burge‏

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2018.02.11 Sunday ACHK

# Eyes on me

dziungles 14 days ago

Hey, this is really cool to see natural eyesight topic on the hacker news.
I practice this for more than 10 years. Each day I work with computer for ~10 h., drive a car and do other things, and never wear glasses, even though the traditional ophtalmologic measures clearly indicate that I need strong glasses and I shouldn’t see even the biggest letter on the Snellen chart, but I see not only the biggest, but sometimes even the 20/20.

Doctors can’t explain this, and only congrats me on my achievement. Of course, the eyesight is not perfect. I see clearly in the daytime, but in the nighttime or low light conditions it becomes much harder to distinguish faces.

The best book I found so far is “Relearning to See” by Thomas R. Quackenbush. The originator of this theory was William Bates.

Actually, there is no clear unified theory on how to achieve this. Everyone interprets it differently and the results are inconsistent. There is also a lot of criticism from the medical establishment.

Natural eyesight improvement really works. And the unified theory, in a form of an app, or a good book, maybe including findings from neuroplasticity, would be a great gift for humanity.

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bsder 14 days ago

Natural eyesight improvement really works. And the unified theory, in a form of an app, or a good book, maybe including findings from neuroplasticity, would be a great gift for humanity.

It SORT OF works in stable and predictable situations.

What seems to be happening is that your brain, in all of its neuroplastic glory, is learning to make better inferences from the broken information it receives.

The issue is that this works as long as the inferences are correct. That’s fine when you are reading a newspaper, using the computer, etc. as the situation is stable and predictable.

The problem is that when you are suddenly confronted by a situation where the inferences are NOT correct–such as a nighttime emergency situation while driving. Now you are relying on the “uninferenced” data coming in from your eyes and that data is subpar with all the resultant problems.

The best solution is both: fix the data coming in with corrective lenses for unpredictable situations, and train your brain to make better inferences so you can deal with predictable situations better.

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dziungles 14 days ago

Before, I also had this theory in my mind for a year or so.
But for example, right now I’m in Thailand, traveling here for the first time. Everything is new, unfamiliar and unpredictable, daytime, nightime. I have no problems seeing things, everything is almost perfectly clear and sharp. I needed some time to adapt to a smaller screen of my laptop (I was using 24 inch before), but now I’m doing fine.

Actually, the more you look, the better you see. Like in Aaron Swartz blog post, if you want to retrain your weak legs, you need to walk more. Same with eyes.

https://web.archive.org/web/20180204094207/https://news.ycombinator.com/item?id=16194580

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2018.02.09 Friday ACHK

# Logical arrow of time, 6.2

Source of time asymmetry in macroscopic physical systems

Second law of thermodynamics

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— Bohr

— paraphrased

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Physics should deduce what an observer would observe,

not what it really is, for that would be impossible.

— Me@2018-02-02 12:15:38 AM

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2. Whatever an observer can observe is a consistent history.

observer ~ a consistent story

observing ~ gathering a consistent story from the quantum reality

3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.

4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.

Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.

5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.

— Me@2018-02-02 10:25:05 PM

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# War and Peace

Is peace better than war?

Peace is acceptance of the status quo

You cannot answer the question of whether peace is better than war without reference to the status quo. Preserve peace is another way of saying accept the status quo. Accepting the status quo is OK only if the status quo is acceptable. Sometimes, it is not.

Diplomacy is meaningless unless it is backed by potential use of force.

Nations negotiate diplomatically to prevent war. Were there no threat of war behind international negotiations, each side could just say “No” to the other forever

Objecting to all wars is not an option for anyone unless the objector is protected by someone who does not object to all wars. No one should be willing to risk his life for such people.