# Universal wave function, 20

The physical (synthetic) universal wave function logically cannot be found by any local observers.

The definition of “universe” is “all the things”. So there is no outside.

A global observer has to be outside the universe.

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However, a mathematical (analytic) universal function is possible.

It applies to theoretical/model universe, which can be used to develop interpretations of quantum mechanics and successively approximate the physical universe.

— Me@2012-04-16

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# The fault of optimism

The illusion of peace

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The seemingly rational world is rendered by exceptional good parents.

The seemingly peaceful time is provided by exceptional expense of defense.

— Me@2011.08.19

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# 神的旨意 2.2

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「祂」既可能其實是「邪靈」，亦可能只是你自己的幻覺而已。

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— Me@2018-07-16 07:51:33 PM

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# Chain Rule of Differentiation

Consider the curve $y = f(x)$.

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$\displaystyle{\frac{d}{dx}}$ is an operator, meaning “the slope of the tangent of”. So the expression $\displaystyle{\frac{dy}{dx}}$, meaning $\displaystyle{\frac{d}{dx} (y)}$, is not a fraction.

In order words, it means the slope of the tangent of the curve $y = f(x)$ at a point, such as point $A$ in the graph.

The symbol $dx$ has no relation with the symbol $\displaystyle{\frac{dy}{dx}}$. It means $\Delta x$ as shown in the graph. In other words,

$dx = \Delta x$

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The symbol $dy$ also has no relation with the symbol $\displaystyle{\frac{dy}{dx}}$. It means the vertical distance between the current point $A(x_0, y_0)$, where $y_0 = f(x_0)$, and the point $C$ on the tangent line $y = mx + c$, where $m$ is the slope of the tangent line. In other words,

$dy = m~dx$

or

$\displaystyle{dy = \left[ \left( \frac{d}{dx} \right) y \right] dx}$

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The relationship of $\Delta y$ and $dy$ is that

$\displaystyle{\Delta y = \frac{dy}{dx} \Delta x + \text{higher order terms}}$

$\displaystyle{\Delta y = \frac{dy}{dx} dx + \text{higher order terms}}$

$\Delta y = dy + \text{higher order terms}$

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Similarly, for functions of 2 variables:

$\displaystyle{\Delta f(x,y) = \frac{\partial f}{\partial x} \Delta x + \frac{\partial f}{\partial y} \Delta y + \text{higher order terms}}$

$\displaystyle{df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy}$

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For functions of 3 variables:

$\displaystyle{df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy + \frac{\partial f}{\partial z} dz}$

$\displaystyle{\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y}\frac{dy}{dt} + \frac{\partial f}{\partial z}\frac{dz}{dt}}$

— Me@2018-07-15 09:30:29 PM

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# Problem 14.4b2

Closed string degeneracies | A First Course in String Theory

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(b) State the values of $\alpha' M^2$ and give the separate degeneracies of bosons and fermions for the first five mass levels of the type IIA closed superstrings. Would the answer have the different for type IIB?

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Type IIB closed superstrings

Equation (14.85)

$(NS+, NS+), (NS+, R-), (R-, NS+), (R-, R-)$

— Me@2015.09.16 06:08 AM: Should be the same. But I am not sure whether I have missed something.

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$f_{NS+}(x) = 8 + 128 \, x + 1152 \, x^{2} + 7680 \, x^{3} + 42112 \, x^{4} + ...$

$f_{R-}(x) = 8 + 128 x + 1152 x^{2} + 7680 x^{3} + 42112 x^{4} + ...$

$f_{NS-}(x) = \frac{1}{\sqrt{x}} + 36 \sqrt{x} + 402 x^{\frac{3}{2}} + 3064 x^{\frac{5}{2}} + ...$

$f_{R+}(x) = 8 + 128 x + 1152 x^{2} + 7680 x^{3} + 42112 x^{4} + ...$

— Me@2018-07-14 09:41:10 PM

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# Pointer state

Eigenstates 3

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In quantum Darwinism and similar theories, pointer states are quantum states that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the system after decoherence has occurred through interaction with the environment.

— Wikipedia on Pointer state

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In calculation, if a quantum state is in a superposition, that superposition is a superposition of eigenstates.

However, real superposition does not just includes states that make macroscopic senses.

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That is the major mistake of the many-worlds interpretation of quantum mechanics.

— Me@2017-12-30 10:24 AM

— Me@2018-07-03 07:24 PM

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# Mirror selves, 5.2

Anatta 3.3 | 無我 3.3

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You fight for existence, for being alive.

However, your existence is not “yours”.

The existence of you, is not your property.

The existence of you, is a property of the group you are in.

The existence of you, is a property of other people.

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To meaningfully say the statement “I exist”, you have to specify you exist with respect to whom.

To exist, you have to specify to exist in which people’s world.

— Me@2018-05-22 7:43 AM

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# 神的旨意 2.1

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（問：你閱讀過很多有關「瀕死經驗」的文章？）

（問：那你怎樣分辨，「瀕死經驗」的文章之中，哪些是真，哪些為假？）

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「祂」既可能其實是「邪靈」，亦可能只是你自己的幻覺而已。

— Me@2018-06-28 10:23:28 PM

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# Block spacetime, 9

motohagiography 42 days ago [-]

I once saw a fridge magnet that said “time is natures way of making sure everything doesn’t happen all at once,” and it’s stuck with me.

The concept of time not being “real,” can be useful as an exercise for modelling problems where to fully explore the problem space, you need to decouple your solutions from needing them to occur in an order or sequence.

From an engineering perspective, “removing” time means you can model problems abstractly by stepping back from a problem and asking, what are all possible states of the mechanism, then which ones are we implementing, and finally, in what order. This is different from the relatively stochastic approach most people take of “given X, what is the necessary next step to get to desired endstate.”

More simply, as a tool, time helps us apprehend the states of a system by reducing the scope of our perception of them to sets of serial, ordered phenomena.

Whether it is “real,” or an artifact of our perception is sort of immaterial when you can choose to reason about things with it, or without it. A friend once joked that math is what you get when you remove time from physics.

I look forward to the author’s new book.

— Gödel and the unreality of time

— Hacker News

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2018.06.26 Tuesday ACHK

# Quick Calculation 14.8.2

A First Course in String Theory

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What sector(s) can be combined with a left-moving NS- to form a consistent closed string sector?

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There are no mass levels in NS+, R+, or R- that can match those in NS-. So NS- can be paired only with NS-:

$(NS-, NS-)$

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$f_{NS} (x)$
$= \frac{1}{\sqrt{x}} \prod_{n=1}^\infty \left( \frac{1+x^{n-\frac{1}{2}}}{1-x^n} \right)^8$
$= \frac{1}{\sqrt{x}} g_{NS}(x)$
$= \frac{1}{\sqrt{x}} + 8 + 36 \sqrt{x} + 128 x + 402 x \sqrt{x} + 1152 x^2 + ...$

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$g (\sqrt{x})$
$= \prod_{n=1}^\infty \left( \frac{1+x^{n-\frac{1}{2}}}{1-x^n} \right)^8$
$= 1 + 8 \, \sqrt{x} + 36 \, x + 128 \, x^{\frac{3}{2}} + 402 \, x^{2} + 1152 \, x^{\frac{5}{2}} + 3064 \, x^{3} + ...$

$g (-\sqrt{x})$
$= \prod_{n=1}^\infty \left( \frac{1-x^{n-\frac{1}{2}}}{1-x^n} \right)^8$
$= 1 -8 \, \sqrt{x} + 36 \, x -128 \, x^{\frac{3}{2}} + 402 \, x^{2} -1152 \, x^{\frac{5}{2}} + 3064 \, x^{3} + ...$

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$g (\sqrt{x}) + g (-\sqrt{x})$
$= 2(1 + 36 x + 402 x^{2} + 3064 x^{3} + ...)$

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$f_{NS-}(x)$
$= \frac{1}{2 \sqrt{x}} \left[ g (\sqrt{x}) + g (-\sqrt{x}) \right]$
$= \frac{1}{2 \sqrt{x}} \left[ \prod_{n=1}^\infty \left( \frac{1+x^{n-\frac{1}{2}}}{1-x^n} \right)^8 + \prod_{n=1}^\infty \left( \frac{1-x^{n-\frac{1}{2}}}{1-x^n} \right)^8 \right]$
$= \frac{1}{2 \sqrt{x}} \left[ 2(1 + 36 \, x + 402 \, x^{2} + 3064 \, x^{3} + ...) \right]$
$= \frac{1}{\sqrt{x}} + 36 \sqrt{x} + 402 x^{\frac{3}{2}} + 3064 x^{\frac{5}{2}} + ...$

— Me@2018-06-26 07:36:41 PM

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# Eigenstates 2.3.2

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eigenstates

~ classical states

~ definite states

— Me@2012-04-15 11:42:10 PM

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The concept of eigenstate is relative.

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First, you have to specify the eigenstate is of which physical observable.

A physical system can be at an eigenstate of one observable but at a superposition state of another observable.

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Second, you have to specify the state of that observable is eigen with respect to which observer.

— Me@2018-06-16 7:27 AM

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eigenstates

~ of which observable?

~ with respect to which observer?

— Me@2018-06-19 10:54:54 AM

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# 魔間傳奇 4.1

The difference between fiction and reality?

Fiction has to make sense.

— Tom Clancy

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… because fiction is written by one person or one compatible group,

while reality is written by a group with a lot of people who might not want to be together.

— Me@2011

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# 大學經濟

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（問：不一定呀。中學生比較年青，腦袋理應高速一點。）

「中學的你」可以因為腦袋較年青，學習新事物比「大學的你」較快。「大學的你」可能因為知識和經驗較多，學習新事物比「中學的你」較快。

— Me@2018-06-05 11:54:51 AM

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# Plato

trowawee 4 months ago

I’m a little frustrated at the tossed-off reference to Plato and Aristotle at the beginning – “The good life may have sufficed for Plato and Aristotle, but it is no longer enough.” – because I feel like that ignores the fact that both Plato and Aristotle, along with a lot of philosophers, actually had a lot to say about physical fitness. Plato was a champion wrestler, and both he and Aristotle viewed physical education as a fundamental component to living the good life. Xenophon quotes Socrates saying this:

“For in everything that men do the body is useful; and in all uses of the body it is of great importance to be in as high a state of physical efficiency as possible. Why, even in the process of thinking, in which the use of the body seems to be reduced to a minimum, it is matter of common knowledge that grave mistakes may often be traced to bad health.”

The whole article feels a little too mired in presentism, and ignorant of the history of self-improvement ideas.

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coldtea 4 months ago

>Plato was a champion wrestler

And the name Plato is a nickname — meaning “the broad/wide one” given to him for his broad shoulders because of that training and physical appearance. Real name: Aristocles.

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kernelbandwidth 4 months ago

It’s funny to consider that one of the canonically great philosophers in history is known essentially by the equivalent of his WWE wrestling name. It’s like if in the future there were classes taught on the philosophical ideas of “The Rock”.

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coldtea 4 months ago

Some other amusing related stuff: so, Plato, was called for for the ancient greek word for broad/wide.

Modern [English] words that stem from the same root: plateau, platitude, plat, plate — via French and Latin (plattus) from Greek (platis “flat, wide, broad”).

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danohu 4 months ago

Well, the first Pope was literally called The Rock (Peter). Jesus appointed him by saying “you are The Rock, and I’ll build my church on this rock”.

Exactly what he meant has led to centuries of debate between protestants and catholics.

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acangiano 4 months ago

“No man has the right to be an amateur in the matter of physical training. It is a shame for a man to grow old without seeing the beauty and strength of which his body is capable.”

― Socrates

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— Improving Ourselves to Death

— Hacker News

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2018.06.01 Friday ACHK

# Problem 14.4b1.4

Closed string degeneracies | A First Course in String Theory

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What is the meaning of “With $a = 1, ..., 8$ and $\bar b = \bar 1, ..., \bar 8$, …”?

— Me@2015.09.14 12:11 PM

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p.315 “Explicitly, the eight states $| R_a \rangle, a = 1, 2, ..., 8$, with an even number of creation operators are … ”

p.316 “The eight states $|R_{\bar{a}} \rangle, \bar a = \bar 1, \bar 2, ..., \bar 8$, with an odd number of creation operators are … ”

— Me@2018-05-24 11:41:34 AM

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# Life, 3

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We exist in time because time is change.

Growing is part of the definition of life. Growing is a kind of change.

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Also, without time/change, there would be no thinking and no thoughts.

— Me@2017-12-26 11:42 am

— Me@2018-05-23 10:05:03 PM

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time ~ change

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Time is logically necessary if change is necessary.

— Me@2018-02-04 09:07:48 PM

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# 多項選擇題 6

Multiple Choices 6

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（問：哪有那麼多的時間？）

— Me@2018-05-22 06:02:40 PM

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# Quantum Computing, 2

stcredzero 3 months ago

A note for the savvy: A quantum computer is not a magic bit-string that mysteriously flips to the correct answer. A n-qubit quantum computer is not like 2^n phantom computers running at the same time in some quantum superposition phantom-zone. That’s the popular misconception, but it’s effectively ignorant techno-woo.

Here’s what really happens. If you have a string of n-qubits, when you measure them, they might end up randomly in [one] of the 2^n possible configurations. However, if you apply some operations to your string of n-qubits using quantum gates, you can usefully bias their wave equations, such that the probabilities of certain configurations are much more likely to appear. (You can’t have too many of these operations, however, as that runs the risk of decoherence.) Hopefully, you can do this in such a way, that the biased configurations are the answer to a problem you want to solve.

So then, if you have a quantum computer in such a setup, you can run it a bunch of times, and if everything goes well after enough iterations, you will be able to notice a bias towards certain configurations of the string of bits. If you can do this often enough to get statistical significance, then you can be pretty confident you’ve found your answers.

— An Argument Against Quantum Computers

— Hacker News

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2018.05.17 Thursday ACHK

# Van der Waals equation 1.2

Whether $X_{\text{measured}}$ is bigger or smaller than $X_{\text{ideal}}$ ultimately depends on the assumptions and definitions used in the derivation of the ideal gas equation itself.

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In the ideal gas equation derivation, the volume used in the equation refers to the volume that the gas molecules can move within. So

$V_{\text{ideal}} = V_{\text{available for a real gas' molecules to move within}}$

Then, when deriving the pressure, it is assumed that there are no intermolecular forces among gas molecules. So

$P_{\text{ideal}} = P_{\text{assuming no intermolecular forces}}$

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These are the reasons that

$V_{\text{ideal}} < V_{\text{measured}}$

$P_{\text{ideal}} > P_{\text{measured}}$

$P_{\text{ideal}} V_{\text{ideal}} = nRT$

$\left(P_\text{measured} + a\left(\frac{n}{V}\right)^2\right) \left(V_\text{measured}-nb\right) = nRT$

— Me@2018-05-16 07:12:51 PM

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… the thing to keep in mind is that the “pressure we use in the ideal gas law” is not the pressure of the gas itself. The pressure of the gas itself is too low: to relate that pressure to “pressure for the ideal gas law” we have to add a number. While the volume occupied by the real gas is too large – the “ideal volume” is less than that. – Floris Sep 30 ’16 at 17:34

— Physics Stackexchange

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