# 物理一個字：力學第一步

This is my first created video.

Please click, like, share, and subscribe!

— Me@2021-06-07 05:00:34 PM

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2021.06.07 Monday (c) All rights reserved by ACHK

# What is magic Science is the real magic.

What you know is science; what you do not know is magic.

Life is a process of turning magic into science.

— Me@2016-11-20 09:14:06 AM

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2021.05.28 Friday (c) All rights reserved by ACHK

# 一萬個小時 3.4

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1. 幾乎

2. 過程中的一個重要環節是，會領悟到一些洞見。

3. 雖然要「自己領悟」第二點中的洞見，來自第一點中的「幾年加幾年」過程，但是，如果只是「吸收別人已知的」知識本身，絶不需要花「幾年加幾年」。有時，甚至只是，花數個小時就可以。

「學習」的意思正正就是，自己毋須親身經歷（例如）四年，也可以獲取本來要四年，才發掘得到的成果。

4. (1.) 但是，「知道」本身，並不代表自己有足夠功力去「運用」，而「運用」則是，第一點的水平。不過，如果中途有第三點，即是別人情報資料上的提點，你就可以走少很多冤往路。那樣，原本是（例如）十年的過程，可以壓縮到（例如）三年。

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— Me@2021-05-23 04:39:54 PM

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2021.05.25 Tuesday (c) All rights reserved by ACHK

# 2.10 A spacetime orbifold in two dimensions, 2

A First Course in String Theory

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(a) Use the result of Problem 2.2, part (a), to recast (1) as $\displaystyle{(x^+, x^-) \sim \left( e^{-\lambda} x^+, e^{\lambda} x^- \right)}$, where $\displaystyle{e^\lambda \equiv \sqrt{\frac{1+\beta}{1-\beta}}}$.

What is the range of $\lambda$? What is the orbifold fixed point? Assume now that $\beta > 0$, and thus $\lambda > 0$.

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Range of $\displaystyle{\lambda}$: \displaystyle{ \begin{aligned} 0 &< \beta < \infty \\ 1 &< \frac{1 + \beta}{1 - \beta} < \infty \\ 0 &< \ln \frac{1 + \beta}{1 - \beta} < \infty \\ 0 &< \frac{1}{2} \ln \frac{1 + \beta}{1 - \beta} < \infty \\ 0 &< \lambda < \infty \\ \end{aligned}}

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Fixed points: \displaystyle{ \begin{aligned} \begin{bmatrix} (x^+)' \\ (x^-)' \end{bmatrix} &= \begin{bmatrix} e^{- \lambda} x^+ \\ e^{\lambda} x^- \\ \end{bmatrix} \\ \end{aligned}} \displaystyle{ \begin{aligned} (x^+, x^-) &= (0, 0) \\ \end{aligned}}

— Me@2021-05-16 06:31:12 PM

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2021.05.17 Monday (c) All rights reserved by ACHK

# Logical arrow of time, 9.3

We label the time direction that we can remember as “past”.

If we could remember both time directions, we would remember infinite things, unless the future has an anti-big-bang.

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Also “remembering the future” creates a meta-dox (aka paradox).

— Me@2013-08-11 8:25 AM

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2021.05.16 Sunday (c) All rights reserved by ACHK

# Genius 4

High school teachers are by nature non-intellectuals; students are by nature intellectuals.

— Me@2011.08.23

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As a mathematician there is a story I hear a lot. It tends to come up whenever I tell someone what I do for the first time, and they admit that they don’t really like, or aren’t very good at, mathematics. In almost every case, if I bother to ask (and these days I usually do), I find that the person, once upon a time, was good at and liked mathematics, but somewhere along the way they had a bad teacher, or struck a subject they couldn’t grasp at first, and fell a bit behind. From that point on their experiences of mathematics is a tale of woe: because mathematics piles layer upon layer, if you fall behind then you find yourself in a never ending game of catch-up, chasing a horizon that you never seem to reach; that can be very dispiriting and depressing.

— Zen and the Art of Mathematics

— The Narrow Road

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All children are born geniuses; 9999 out of every 10000 are swiftly, inadvertently degeniusized by grownups.

— Buckminster Fuller

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2021.05.15 Saturday (c) All rights reserved by ACHK

# 千里共嬋娟

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— Me@2021-05-14 11:02:51 PM

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2021.05.15 Saturday (c) All rights reserved by ACHK

# 1990s, 9 — Me@2021-05-11 10:04:18 PM

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2021.05.11 Tuesday (c) All rights reserved by ACHK

# Ex 1.21 The dumbbell, 2.2.2

[guess]


(define (KE-particle m v)
(* 1/2 m (square v)))

(define ((L-free-constrained m0 m1 l) local)
(let* ((extract (extract-particle 2))
(p0 (extract local 0))
(q0 (coordinate p0))
(qdot0 (velocity p0))

(p1 (extract local 1))
(q1 (coordinate p1))
(qdot1 (velocity p1))

(F (ref (coordinate local) 4)))

(- (+ (KE-particle m0 qdot0)
(KE-particle m1 qdot1))
(U-constraint q0 q1 F l))))

(let ((L (L-free-constrained 'm_0 'm_1 'l)))
(show-expression
((compose L (Gamma q-rect)) 't))) $\displaystyle{ \frac{1}{2} m_0 \left( \dot x_0^2 + \dot y_0^2 \right) + \frac{1}{2} m_1 \left( \dot x_1^2 + \dot y_1^2 \right) + \frac{F}{2 l} \left( l^2 - y_1^2 + 2 y_0 y_1 - x_1^2 + 2 x_0 x_1 - y_0^2 - x_0^2 \right) }$ $\displaystyle{ = \frac{1}{2} m_0 \left( \dot x_0^2 + \dot y_0^2 \right) + \frac{1}{2} m_1 \left( \dot x_1^2 + \dot y_1^2 \right) - \frac{F}{2 l} \left[ (y_1 - y_0)^2 + (x_1 - x_0)^2 - l^2 \right] }$


(define ((local_ m0 m1 l) local)
(let* ((extract (extract-particle 2))
(p0 (extract local 0))
(q0 (coordinate p0))
(qdot0 (velocity p0))

(p1 (extract local 1))
(q1 (coordinate p1))
(qdot1 (velocity p1))

(F (ref (coordinate local) 4)))
local))

(show-expression
((compose (local_ 'm_0 'm_1 'l) (Gamma q-rect)) 't)) (define ((p0_ m0 m1 l) local)
(let* ((extract (extract-particle 2))
(p0 (extract local 0))
(q0 (coordinate p0))
(qdot0 (velocity p0))

(p1 (extract local 1))
(q1 (coordinate p1))
(qdot1 (velocity p1))

(F (ref (coordinate local) 4)))
p0))

(show-expression
((compose (p0_ 'm_0 'm_1 'l) (Gamma q-rect)) 't)) (define ((p1_ m0 m1 l) local)
(let* ((extract (extract-particle 2))
(p0 (extract local 0))
(q0 (coordinate p0))
(qdot0 (velocity p0))

(p1 (extract local 1))
(q1 (coordinate p1))
(qdot1 (velocity p1))

(F (ref (coordinate local) 4)))
p1))

(show-expression
((compose (p1_ 'm_0 'm_1 'l) (Gamma q-rect)) 't)) [guess]

— based on /sicmutils/sicm-exercises

— Me@2021-04-27 05:03:59 PM

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2021.05.11 Tuesday (c) All rights reserved by ACHK

# Goodstein’s theorem

[guess]

Goodstein’s theorem is an example that sometimes a finite result requires the existence of infinity in its proof.

— Me@2021-05-09 11:06:34 PM

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Goodstein’s theorem itself assumes that there is an infinite number of natural numbers, so it is not really a finite result.

— Me@2017-02-20 06:16:28 PM

[guess]

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2021.05.09 Sunday (c) All rights reserved by ACHK

# 卡拉OK, 4

Facebook time does not change anything.

Doing things changes things.

If you (and other people) do nothing, the situation stays exactly where it is.

— Me@2016-12-12 03:18:13 PM

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2021.05.09 Sunday (c) All rights reserved by ACHK

# To realize is to realize, 1.2.2

So in theory, there is no free will, because the future is already fixed, by the physical laws.

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However, even if we knew the exact physical laws, it would be still logically impossible to get all the data of the present state of the whole universe, because it is logically impossible for any observer to observe itself, with 100% details, directly. For example, no camera can take a picture of itself directly.

So “in practice”, which is actually also “in principle”, there is free will, because logically, no one can predict, with 100% accuracy, your future actions.

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In one logical sense, the future is already fixed, so there is no free will. In another logical sense, the future is fixed, but no observer can know that “fixed future” with 100% accuracy, so there is free will.

As a result, whether you label your actions are due to “free-will” or “not-free-will” has no real consequence. In other words, whether there is free will or not has no meaningful difference.

The difference that makes no difference makes no difference.

So you can actually transcend the free will problem altogether. You can just ignore it and live your life.

Or, you can somehow capitalize on this freedom of labelling your (future) life as either fixed or free, depending which label is more beneficial for you in a particular situation.

For example, when you are highly under pressure, you know that everything is fixed by the physical laws, from god’s point of view. When you are highly above pressure, you know that you are partially responsible for creating your own reality, because the future is not fixed for any one observer, for there is no “god’s point of view”.

You have the flexibility to label it in one way or another.

— Me@2021-05-07 10:27:04 PM

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2021.05.09 Sunday (c) All rights reserved by ACHK

# 2.10 A spacetime orbifold in two dimensions

A First Course in String Theory

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Consider a two-dimensional world with coordinates $\displaystyle{x^0}$ and $\displaystyle{x^1}$.

A boost with velocity parameter $\displaystyle{\beta}$ along the $\displaystyle{x^1}$ axis is described by the first two equations in (2.36). We want to understand the two-dimensional space that emerges if we identify $\displaystyle{(x^0, x^1) \sim ({x'}^0, {x'}^1)}$.

We are identifying spacetime points whose coordinates are related by a boost!

(a) Use the result of Problem 2.2, part (a), to recast (1) as $\displaystyle{(x^+, x^-) \sim \left( e^{-\lambda} x^+, e^{\lambda} x^- \right)}$, where $\displaystyle{e^\lambda \equiv \sqrt{\frac{1+\beta}{1-\beta}}}$.

~~~ \displaystyle{ \begin{aligned} (x')^0 &= \gamma (x^0 - \beta x^1) \\ (x')^1 &= \gamma (- \beta x^0 + x^1) \\ \end{aligned}} \displaystyle{ \begin{aligned} \begin{bmatrix} (x^+)' \\ (x^-)' \end{bmatrix} &= \begin{bmatrix} \gamma (1-\beta) & 0 \\ 0 & \gamma (1+\beta) \\ \end{bmatrix} \begin{bmatrix} x^+ \\ x^- \end{bmatrix} \\ &= \begin{bmatrix} \frac{1}{\sqrt{1 - \beta^2}} (1-\beta) x^+ \\ \frac{1}{\sqrt{1 - \beta^2}} (1+\beta) x^- \\ \end{bmatrix} \\ &= \begin{bmatrix} e^{- \lambda} x^+ \\ e^{\lambda} x^- \\ \end{bmatrix} \\ \end{aligned}}

— Me@2021-05-04 10:48:28 PM

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2021.05.05 Wednesday (c) All rights reserved by ACHK

# Logical arrow of time, 9.2

To confirm or disconfirm a prediction, you cannot check record; you can only observe the system evolving.

To confirm or disconfirm a retrodiction, you can only check record (or the logical consequence of that retrodiction); you cannot observe that past event directly.

— Me@2013-08-10 08:00 PM

— Me@2021-05-03 12:28 PM

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2021.05.03 Monday (c) All rights reserved by ACHK

# Job: Meaning of Life 3

Life is a copylefting process.

— Me@2011.08.08

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2021.05.02 Sunday (c) All rights reserved by ACHK

# 相逢恨晚 2

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We talked half the night, and in the middle of talk became lovers. — Bertrand Russell

— Me@2021-04-05 06:14:46 PM

— Me@2021-05-01 04:46:18 PM

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2021.05.02 Sunday (c) All rights reserved by ACHK