神的旨意 2.1

Posted on June 30, 2018 by rpflee

這段改編自 2010 年 4 月 18 日的對話。

（問：你閱讀過很多有關「瀕死經驗」的文章？）

可以這樣說。

如果你閱讀那些文章的話，要小心一點，因為那類文章良莠不齊——當中有些文章發人深省，有些則謊話連篇。

（問：那你怎樣分辨，「瀕死經驗」的文章之中，哪些是真，哪些為假？）

看看文中所說的，合不合理。

例如，你怎樣知道，我說的話，是真還是假？

合情合理，自圓其說的，就有機會真；無情無理，自相矛盾的，則必定為假。

又例如，如果現在神明顯靈在你面前，你怎樣判斷，那真的是「神明」？

「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

Block spacetime, 9

Posted on June 26, 2018 by rpflee

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

2018.06.26 Tuesday ACHK

Quick Calculation 14.8.2

Posted on June 26, 2018 by rpflee

A First Course in String Theory

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

~~~

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

$(NS-, NS-)$

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

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

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

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

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

— Me@2018-06-26 07:36:41 PM

Eigenstates 2.3.2

Posted on June 19, 2018 by rpflee

eigenstates

~ classical states

~ definite states

— Me@2012-04-15 11:42:10 PM

The concept of eigenstate is relative.

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.

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

— Me@2018-06-16 7:27 AM

eigenstates

~ of which observable?

~ with respect to which observer?

— Me@2018-06-19 10:54:54 AM

魔間傳奇 4.1

Posted on June 10, 2018 by rpflee

The difference between fiction and reality?

Fiction has to make sense.

— Tom Clancy

… 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

大學經濟

Posted on June 7, 2018 by rpflee

這段改編自 2010 年 4 月 18 日的對話。

我猜想，當一個人改變存在型態時，會立刻或者將會，知道很多生時不知道的東西。但是，那些新知識，未必包括你想知道的東西。

比喻說，由中學升到大學，你將會學到，很多超過中學程度的知識。但是，如果你中學時，沒有讀過經濟科的話，單單是「升大學」本身，並不會令你，立刻獲得經濟科的知識。

大學生「由零開始學經濟學」，都同樣要花時間；分別是，通常而言，比中學生「由零開始學經濟學」，速度會高一點。

（問：不一定呀。中學生比較年青，腦袋理應高速一點。）

無錯。

方便起見，暫時用同一個人來比較，例如你。

「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。

視乎情況，因人而異，沒有一定的答案。

但是，至少你會同意一點：

如果你中學時，沒有讀過經濟科，在大學時要「由零開始學經濟學」的話，你會立刻看大學程度的經濟書，而不是由中學教科書開始學。

— Me@2018-06-05 11:54:51 AM

Plato

Posted on June 1, 2018 by rpflee

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.

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.

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”.

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”).

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.

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

— Improving Ourselves to Death

— Hacker News

2018.06.01 Friday ACHK

Physics Town

continues

Monthly Archives: June 2018