Pandemonium, 2.2

You get what you FIGHT for, nothing more, nothing less.

— Me < 2008

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反貼士搵笨大行動 1.1

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— Me@2020-02-19 05:33:09 PM

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Problem 2.1b

A First Course in String Theory

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2.1 Exercises with units

(b) Explain the meaning of the unit K (degree kelvin) used for measuring temperatures, and explain its relation to the basic length, mass, and time units.

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${\displaystyle {\frac {1}{T}}=\left({\frac {\partial S}{\partial U}}\right)_{V,N}}$,

where $\displaystyle{U}$ is the internal energy.
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The units of $\displaystyle{k_B T}$ and $\displaystyle{E}$ are the same.

$\displaystyle{[k_B T] = [E]}$

In other words, the Boltzmann constant $\displaystyle{k_B}$ translates the temperature unit $\displaystyle{K}$ to the language of energy unit $\displaystyle{J}$.

However, although the temperature unit $\displaystyle{K}$ and the energy unit $\displaystyle{J}$ have the relation

$\displaystyle{k_B K = J}$,

just $\displaystyle{k_B T}$ would not give the correct value of energy $\displaystyle{E}$, not to mention that we have not yet specified of which the energy $\displaystyle{E}$ is.

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For an ideal gas,

$\displaystyle{pV=Nk_B T}$

and the average translational kinetic energy is

${\displaystyle {\frac {1}{2}}m{\overline {v^{2}}}={\frac {3}{2}}k_BT}$

for 3 degrees of freedom. In 3D space, if there are only translational motions, there are only 3 degrees of freedom.

In other words, just the value of ${k_B T}$ itself gives no physical meaning. Instead, ${\tfrac{1}{2}k_B T}$ can be interpreted as the average translational kinetic energy of the particles in an one dimensional space. Equivalently, $\displaystyle{\tfrac{3}{2}k_BT}$ gives that in our three dimensional space.

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Another main difference is that although energy is an extensive property, temperature is an intensive property.

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We define the temperature unit Kelvin $\displaystyle{K}$ by requiring the water triple point temperature,

$\displaystyle{T_{tp} \equiv 273.16K}$

Once this value is fixed, the Boltzmann constant $\displaystyle{k_B}$ value can be estimated by using, for example, the ideal gas law

$\displaystyle{pV = N k_B T}$,

because $\displaystyle{k_B}$ always comes with $\displaystyle{T}$.

— Me@2020-02-16 11:14:24 AM

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Unix

Linux is headache. It gives you too many choices.

— Me@2011.07.14

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But Linux is necessary.

— Me@2020-01-23 08:53:29 PM

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Applicants must also have extensive knowledge of Unix, although they should have sufficiently good programming taste to not consider this an achievement.

— Hal Abelson

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大腦物理性損毀不是比喻

99.85%的人不會，終身被匪欺騙教育，大腦已經物理性損毀了，假如說匪的謊言灌輸有20層，那麼絕大多數人遭鐵拳之後的反思，最多只能突破一兩層，達到“我愛國所以要說話”的程度，離理解台人港人藏人維人還非常遠，至少還需要十幾個層次的突破。所以覺醒者極少極少，而且沒有力量。很悲哀，但事實如此。

— 李穎

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People do not change. They die, replaced by other people.

Most people do not change. They die, replaced by a new generation of people.

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You cannot change the people around you, but you can change the people you choose to be around.

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2020.02.15 Saturday ACHK

機遇創生論 1.2

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「緣份攻略」都不行，因為感覺有點怪。

（安：那就不如叫做「緣份理論」。）

「理論」很空泛。不應把「理論」，視為名字的一部分。

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— Me@2020-02-15 07:17:00 AM

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scmutils, 2.3

Within the MIT Scheme environment, it is not the original command line (bash) anymore. I can neither repeat the last command by just pressing the up key once, nor select the last command by mouse in order to copy it.

So I think I have to use an older version of scmutils.

However, this method is not easy to implement, because the author’s website does not provide an older version. Luckily, I have found an old version in my computer. You can download it here:

scmutils-20160827-x86-64-gnu-linux

Note: Since the installation of the library scmutils requires the root access of your Linux system, please do NOT use it on your working computer. Instead, create an isolated virtual machine to use it.

— Me@2020-02-09 10:27:32 PM

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So we seem to have a direct contradiction between [QM and unitarity] and [GR and causality]. Both of these principles, unitarity and causality, cannot be exactly correct because a contradiction arises from their explosive mixture.

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As most quantum mechanicians have known from the very beginning, it is the unitarity, a principle of quantum mechanics, that wins in the battle and remains universally valid.

On the other hand, causality becomes an approximate principle that is only valid in the limit of infinitely large causal diamonds. In the presence of black holes, the internal causal structure is modified by quantum phenomena and the information can “tunnel” out of the black hole.

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It shouldn’t be so surprising that unitarity survives completely while causality doesn’t. After all, the basic postulates of quantum mechanics, including unitarity, the probabilistic interpretation of the amplitudes, and the linearity of the operators representing observables, seem to be universally necessary to describe physics of any system that agrees with the basic insights of the quantum revolution.

On the other hand, geometry has been downgraded into an effective, approximate, emergent aspect of reality. The metric tensor is just one among many fields in our effective field theories including gravity. In string theory, there are, in some sense, infinitely many such fields besides the metric tensor – the whole “stringy tower”. The metric tensor doesn’t have to exist as a good degree of freedom at the Planck scale or in other extreme conditions. We know many other fields that are only good enough at low energies – e.g. the pion field.

— Black hole information puzzle

— Lubos Motl

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2020.02.09 Sunday ACHK

魔間傳奇

Hell Is Empty, and All the Devils Are Here

— The Tempest

— William Shakespeare

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2020.02.08 Saturday ACHK

Ken Chan 時光機 3.4

（問：何出此言呢？）

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— Me@2020-02-08 11:36:41 AM

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Problem 2.1

A First Course in String Theory

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2.1 Exercises with units

Construct and evaluate a dimensionless number using the charge $\displaystyle{e}$ of the electron (as defined in Gaussian system of units), $\displaystyle{\hbar}$, and $\displaystyle{c}$. (In Heaviside-Lorentz units, the Gaussian $\displaystyle{e^2}$ is replaced by $\displaystyle{\frac{e^2}{4 \pi}}$.)

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\displaystyle{ \begin{aligned} \alpha &= \frac{e^2}{(4 \pi \varepsilon_0)\hbar c} \\ \alpha &= \frac{1}{137.035\,999\,679(94)} \\ \end{aligned} }

— Me@2010

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Spacetime interval

Two contrasting viewpoints on time divide prominent philosophers.

One view is that time is part of the fundamental structure of the universe – a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.

The opposing view is that time does not refer to any kind of “container” that events and objects “move through”, nor to any entity that “flows”, but that it is instead part of a fundamental intellectual structure (together with space and number) within which humans sequence and compare events.

This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, and thus is not itself measurable nor can it be travelled.

— Wikipedia on Time

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Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light.

— The Fabric of the Cosmos: Space, Time, and the Texture of Reality

— Brian Greene

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Space is relative, in the sense that the space interval, $\Delta d$, (aka distance) between two events can have different values for different observers.

\displaystyle{ \begin{aligned} \Delta {d} &= \sqrt{{\left(\Delta {x}\right)}^{2}+{\left(\Delta {y}\right)}^{2}+{\left(\Delta {z}\right)}^{2}} \\ \end{aligned} }

Time is relative, in the sense that the time interval, $\Delta t$, (aka duration) between two events can have different values for different observers.

Spacetime is absolute, in the sense that the spacetime interval, $(\Delta s)^2$, between two events cannot have different values for different observers.

\displaystyle{ \begin{aligned} (\Delta s)^{2} &= (\Delta ct)^{2}-(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2} \\ &= (\Delta ct)^{2}-(\Delta d)^{2} \\ \end{aligned} }

— paraphrasing The Fabric of the Cosmos

— Me@2020-01-26 12:46:41 AM

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機遇創生論

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（安：除了創作那個大理論的名字外，還有什麼話題？）

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（安：不行。我都想過這個名字。但它非常誤導。「合體機械人」只是比喻。整個理論和機械人無關。）

「副作用機械人」？

（安：不如直接用你的名字，命名那個理論。）

「種子論」是起點，「果實論」是終點。然後，每個果實內，其實又有很多新種子。

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「緣份管理學」？

（安：我覺得「管理學」好像令個理論降級了一點，因為一般而言，「管理學」並不是，太高深的學問。）

「緣份機械人」？

（安：叫做「人生攻略理論」？）

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「緣份攻略」都不行，因為感覺有點怪。

（安：那就不如叫做「緣份理論」。）

「理論」很空泛。不應把「理論」，視為名字的一部分。

— Me@2020-01-29 12:23:38 AM

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1986

I keep this picture here as a backup.

— Me@2020-01-27 06:33:01 PM

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scmutils, 2.2

Either use an older version of scmutils in order to follow the previous instructions for setting up Emacs for scmutils, or give up using Emacs for scmutils for the time being.

Using command line is the best way to go, so far.

The “using command line” method does not really work.

Within the MIT Scheme environment, it is not the original command line (bash) anymore. I can neither repeat the last command by just pressing the up key once, nor select the last command by mouse in order to copy it.

So I think I have to use an older version of scmutils.

— Me@2020-01-26 07:38:31 PM

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