# （反對）開夜車 2.5

（問：「只要飛蚊不惡化」？你怎能保證？）

「飛蚊症」只是某個或某些疾病的一個「症」，而不是「疾病」本身。一日不能知道，我飛蚊症的病因，我也不能有力預防，症狀的加劇。

（問：你不是說，長期夜睡少睡，導致你的飛蚊症嗎？）

— Me@2019-04-13 03:34:33 PM

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# Physical laws are low-energy approximations to reality, 1.3.1

Symmetry breaking is important.

When there is symmetry-breaking, the system goes to a low-energy state.

Each possible low-energy state can be regarded as a new “physical world”.

One “physical world” cannot jump to another, unless through quantum tunnelling. But the probability of quantum tunnelling happening is low.

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Low-energy physics theories, such as harmonic oscillator, are often simple and beautiful.

— Professor Renbao Liu

— Me@2019-04-08 10:46:32 PM

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# scmutils

In order to run the SICM code, you need to install the scmutils library. Just go to the official page to download the library and follow the official instructions to install it in a Linux operating system.

When you try to run it, your system may give the following error message:

/usr/local/bin/mechanics: line 16: exec: xterm: not found


If so, you should install the program xterm first.

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Also, in case you like to use Emacs as editor, you can:

Just include the following in your .emacs file:

(defun mechanics ()
(interactive)
(run-scheme
"ROOT/mit-scheme/bin/scheme --library ROOT/mit-scheme/lib"
))


Replace ROOT with the directory in which you installed the scmutils software. (Remember to replace it in both places. If it is installed differently on your system, just make sure the string has the form “/path/to/mit-scheme --library /path/to/scmutils-library“.) Restart emacs (or use C-x C-e to evaluate the mechanics defun), and launch the environment with the command M-x mechanics.

— Using GNU Emacs With SCMUtils

— Aaron Maxwell

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In my Ubuntu 18.04, the paths are:

(defun mechanics()
(interactive)
(run-scheme
"/usr/local/scmutils/mit-scheme/bin/scheme --library
/usr/local/scmutils/mit-scheme/lib"
))


— Me@2019-04-07 02:52:50 PM

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# Confirmation principle

Verification principle, 2.2 | The problem of induction 4

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The statements “statements are meaningless unless they can be empirically verified” and “statements are meaningless unless they can be empirically falsified” are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

— Wikipedia on Self-refuting idea

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In 1936, Carnap sought a switch from verification to confirmation. Carnap’s confirmability criterion (confirmationism) would not require conclusive verification (thus accommodating for universal generalizations) but allow for partial testability to establish “degrees of confirmation” on a probabilistic basis.

— Wikipedia on Verificationism

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Confirmation principle should not be applied to itself because it is an analytic statement which defines synthetic statements.

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Even if it does, it is not self-defeating, because confirmation principle, unlike verification principle, does not requires a statement to be proven with 100% certainty.

So in a sense, replacing verification principle by confirmation principle can avoid infinite regress.

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Accepting confirmation principle is equivalent to accepting induction.

“This is everything to win but nothing to lose.”

— Me@2012.04.17

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# Authenticity

If you seek authenticity for authenticity’s sake, you are no longer authentic.

— Jean Paul Sartre

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2019.04.06 Saturday ACHK

# PhD, 3.5

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（問：實際上呢？）

（問：三重身份，哪有那麼多的時間？）

（問：你上司？）

（問：為什麼呢？）

（問：你的意思是，「誰是主角」和「誰是助手」？）

— Me@2019-04-05 12:00:42 PM

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# Finding trajectories that minimize the action

We have used the variational principle to determine if a given trajectory is realizable. We can also use the variational principle to find trajectories. Given a set of trajectories that are specified by a finite number of parameters, we can search the parameter space looking for the trajectory in the set that best approximates the real trajectory by finding one that minimizes the action. By choosing a good set of approximating functions we can get arbitrarily close to the real trajectory.

— Structure and Interpretation of Classical Mechanics

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We have used the variational principle to determine if a given trajectory is realizable.

How?

— Me@2019-03-29 04:23:36 PM

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Check if the action of that given trajectory is stationary or not.

— Me@2019-03-29 04:25:45 PM

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# Quantum classical logic

Mixed states, 2 | Eigenstates 4

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— This is my guess. —

If the position is indefinite, you can express it in terms of a pure quantum state[1] (of a superposition of position eigenstates);

if the quantum state is indefinite, you can express it in terms of a mixed state;

if the mixed state is indefinite, you can express it in terms of a “mixed mixed state”[2]; etc. until definite.

At that level, you can start to use classical logic.

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If you cannot get certainty, you can get certain uncertainty.

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[1]: Me@2019-03-21 11:08:59 PM: This line of not correct. The uncertainty may not be quantum uncertainty. It may be classical.

[2]: Me@2019-03-22 02:56:21 PM: This concept may be useless, because a so-called “mixed mixed state” is just another mixed state.

For example, the mixture of mixed states

$\displaystyle{p |\psi_1 \rangle \langle \psi_1 | + (1-p) |\psi_2 \rangle \langle \psi_2 |}$

and

$\displaystyle{q |\phi_1 \rangle \langle \phi_1 | + (1-q) |\phi_2 \rangle \langle \phi_2 |}$

is

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\displaystyle{\begin{aligned} &w \bigg[ p |\psi_1 \rangle \langle \psi_1 |+ (1-p) |\psi_2 \rangle \langle \psi_2 | \bigg] + (1-w) \bigg[ q |\phi_1 \rangle \langle \phi_1 | + (1-q) |\phi_2 \rangle \langle \phi_1 | \bigg] \\ &= w p |\psi_1 \rangle \langle \psi_1 | + w (1-p) |\psi_2 \rangle \langle \psi_2 | + (1-w) q |\phi_1 \rangle \langle \phi_1 | + (1-w) (1-q) |\phi_2 \rangle \langle \phi_1 | \\ \end{aligned}}

— This is my guess. —

— Me@2012.04.15

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# Find one, organize two

Technical debt

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dna113 1 day ago [-]

I recently needed an HDMI cord for a monitor and realized that my cord drawer was accruing technical debt.

Whenever I am done with a cord I just throw it in there… it gets all tangled up with all the others. When I inevitably need one of those cords I impatiently pull it out and it makes all the other cords more tangled.

Here I am needing an HDMI cable that won’t just come out easily, I have to pay off my past laziness. But I have choices/tradeoffs/opportunities here.

I can just hurry up and get the minimum untangled and get back to watching TV.

I could untangle all of them since untangling one of them will help me untangle the others and wrap and label them.

I could just untangle the minimum, but also throw a roll of tape and a marker in there and wrap and label all future cords that go into that drawer, eventually they’ll all be nicely wrapped up and well documented.

¯\_(ツ)_/¯

jolmg 1 day ago [-]

Wow. I never thought of clutter in the home as technical debt, but it’s as similar as you describe. That really makes me see home organization in a whole new light.

— Technical Debt Is Like Tetris

— Hacker News

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Whenever you have to search for something, once you have found it, organize an additional thing.

— Me@2019-03-12 11:12:28 AM

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# （反對）開夜車 2.4

（問：但你剛才說，飛蚊症「會帶來精神困擾」？）

（問：為什麼呢？）

（問：立刻要求商戶更換。新買的電器，必定在保養期內，可以更換。）

（問：如果只是一兩點的話，應該不會太明顯。我會先用它，直到幾年後才再換。

（問：永久有死點？）

（問：那又真的，十分不自在。

（問：「只要飛蚊不惡化」？你怎能保證？）

「飛蚊症」只是某個或某些疾病的一個「症」，而不是「疾病」本身。一日不能知道，我的飛蚊症的病因，我也不能有力預防，症狀的加劇。

（問：你不是說，長期夜睡少睡，導致你的飛蚊症嗎？）

— Me@2019-03-18 04:47:58 PM

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# Physical laws are low-energy approximations to reality, 1.2

When the temperature $\displaystyle{T}$ is higher than the critical temperature $\displaystyle{T_c}$, point $\displaystyle{O}$ is a local minimum. So when a particle is trapped at $\displaystyle{O}$, it is in static equilibrium.

However, when the temperature is lowered, the system changes to the lowest curve in the figure shown. As we can see, at the new state, the location $\displaystyle{O}$ is no longer a minimum. Instead, it is a maximum.

So the particle is not in static equilibrium. Instead, it is in unstable equilibrium. In other words, even if the particle is displaced just a little bit, no matter how little, it falls to a state with a lower energy.

This process can be called symmetry-breaking.

This mechanical example is an analogy for illustrating the concepts of symmetry-breaking and phase transition.

— Me@2019-03-02 04:25:23 PM

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# Lagrangians in generalized coordinates

The function $\displaystyle{S_\chi}$ takes a coordinate path; the function $\displaystyle{\mathcal{S}}$ takes a configuration path.

\displaystyle{\begin{aligned} \mathcal{S} [\gamma] (t_1, t_2) &= \int_{t_1}^{t_2} \mathcal{L} \circ \mathcal{T} [\gamma] \\ S_\chi [q] (t_1, t_2) &= \int_{t_1}^{t_2} L_\chi \circ \Gamma [q] \\ \end{aligned}}

\displaystyle{\begin{aligned} \mathcal{S} [\gamma] (t_1, t_2) &= S_\chi [\chi \circ \gamma] (t_1, t_2) \\ \end{aligned}}

# Computing Actions

$\displaystyle{\texttt{literal-function}}$ makes a procedure that represents a function of one argument that has no known properties other than the given symbolic name.

The method of computing the action from the coordinate representation of a Lagrangian and a coordinate path does not depend on the coordinate system.

# Exercise 1.4. Lagrangian actions

For a free particle an appropriate Lagrangian is

\displaystyle{\begin{aligned} L(t,x,v) &= \frac{1}{2} m v^2 \\ \end{aligned}}

Suppose that $x$ is the constant-velocity straight-line path of a free particle, such that $x_a = x(t_a)$ and $x_b = x(t_b)$. Show that the action on the solution path is

\displaystyle{\begin{aligned} \frac{m}{2} \frac{(x_b - x_a)^2}{t_b - t_a} \\ \end{aligned}}

— Structure and Interpretation of Classical Mechanics

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\displaystyle{\begin{aligned} L(t,x,v) &= \frac{1}{2} m v^2 \\ \end{aligned}}

\displaystyle{\begin{aligned} S_\chi [\gamma] (t_1, t_2) &= \int_{t_1}^{t_2} L_\chi (t, q(t), Dq(t)) dt \\ &= \int_{t_2}^{t_1} \frac{1}{2} m v^2 dt \\ &= \frac{1}{2} m v^2 \int_{t_2}^{t_1} dt \\ &= \frac{1}{2} m v^2 (t_2 - t_1) \\ &= \frac{1}{2} m (\frac{x_2 - x_1}{t_2 - t_1})^2 (t_2 - t_1) \\ &= \frac{1}{2} m \frac{(x_2 - x_1)^2}{t_2 - t_1} \\ \end{aligned}}

— Me@2006-2008

— Me@2019-03-10 11:08:29 PM

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# Distinguishing hardware and software

If

X is a pattern of Y,

then

Y is hardware

and

X is software.

— Me@2019-03-10 12:10:20 AM

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# Time as other things, 3

Time travel, 3.1.3

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~ Flowers look the same as before, but the people do not.

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~ Flowers go into the future.

— Me@2011.08.23

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# PhD, 3.4

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（問：他們大概毋須，任何博士學位吧？

（問：什麼意思？）

（問：那即是應該攻讀研究院？

（問：什麼「資源」？）

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（問：實際上呢？）

— Me@2019-03-06 12:11:31 AM

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# Configuration Spaces

The set of all configurations of the system that can be assumed is called the configuration space of the system.

## Generalized Coordinates

1. In order to be able to talk about specific configurations we need to have a set of parameters that label the configurations. The parameters used to specify the configuration of the system are called the generalized coordinates.

2. The $\displaystyle{n}$-dimensional configuration space can be parameterized by choosing a coordinate function $\displaystyle{\chi}$ that maps elements of the configuration space to $n$-tuples of real numbers.

3. The motion of the system can be described by a configuration path $\displaystyle{\gamma}$ mapping time to configuration-space points.

4. Corresponding to the configuration path is a coordinate path $\displaystyle{q = \chi \circ \gamma}$ mapping time to tuples of generalized coordinates.

The function $\displaystyle{\Xi \chi}$ takes the coordinate-free local tuple $\displaystyle{( t, \gamma (t), \mathcal{D} \gamma (t), ... )}$ and gives a coordinate representation as a tuple of the time, the value of the coordinate path function at that time, and the values of as many derivatives of the coordinate path function as are needed.

\displaystyle{ \begin{aligned} \text{generalized coordinate representation} &= \Xi (\text{local tuple}) \\ (t, q(t), Dq(t), ...) &= \Xi_\chi (t, \gamma(t), \mathcal{D} \gamma(t), ...) \\ \end{aligned} }

\displaystyle{ \begin{aligned} \text{generalized coordinates} &= q \\ &= \chi \circ \gamma \\ \\ q(t) &= \chi(\gamma(t)) \\ \end{aligned} }

\displaystyle{ \begin{aligned} t &\to \gamma: \text{configuration path} \to \chi: \text{generalized coordinates} = q \\ \end{aligned} }

\displaystyle{ \begin{aligned} (t, q(t), Dq(t), ...) &= \Xi_\chi (t, \gamma(t), \mathcal{D} \gamma(t), ...) \\ \\ \Gamma[q](t) &= (t, q(t), Dq(t), ...) \\ \Gamma[q] &= \Xi_\chi \circ \mathcal{T}[\gamma] \\ \end{aligned} }

— 1.2 Configuration Spaces

— Structure and Interpretation of Classical Mechanics

— Me@2019-03-01 03:09:25 PM

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2019.03.01 Friday ACHK

# The Door 1.1

The following contains spoilers on a fictional work.

In Westworld season 2, last episode, when a person/host X passed through “the door”, he got copied, almost perfectly, into a virtual world. Since the door was adjacent to a cliff, just after passing through it, the original copy (the physical body) fell off the cliff and then died.

Did X still exist after passing through the door?

Existence or non-existence of X is not a property of X itself. So in order for the question “does X exist” to be meaningful, we have to specify “with respect to whom”.

With respect to the observer Y, does X exist?

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There are 3 categories of possible observers (who were observing X passing through the door):

1. the original person (X1)
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X_1 == X

2. the copied person (X2) in the virtual world
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For simplicity, assume that X2 is a perfect copy of X.

3. other people (Y)

— Me@2019-02-09 1:09 PM

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# 心懷混亂 6

I tell you: one must have chaos within oneself, to give birth to a dancing star.

— Friedrich Nietzsche

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— 尼采

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— 林夕

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2019.02.27 Wednesday ACHK