# Factors

factors = independent causes

product = the results of factors multiplying together

multiply

— Me@2013-02-28 8:16 pm

# 微積分 5

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{f(x + \Delta x) – f(x)}{(x + \Delta x) – x}

\Delta y = f(x + \Delta x) – f(x)

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}

— Me@2013.02.28

# Exchange symmetry

Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 180 degrees (and so to the rotation of one particle’s frame by 360 degrees), the symmetric nature of the wave function depends on the particle’s spin after the rotation operator is applied to it. Integer spin particles do not change the sign of their wave function upon a 360 degree rotation — therefore the sign of the wave function of the entire system does not change. Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin-statistics theorem).

— Wikipedia on Exchange symmetry

2013.02.27 Wednesday ACHK

# Blogging

Writing a blog is an entertainment against loneliness.

— Me@2009.12.18

— Me@2013.02.27

# Elementary particles, 2

Tommaso Dorigo’s comrade Vladimir Lenin believed that an electron was a galaxy with many electrons, and so on, indefinitely. That’s what he meant by the statement that matter was “inexhaustible”. This hierarchical picture of the Matryoshka Universe was clearly indefensible already during Lenin’s life. First, it has to stop at the Planck scale because distances shorter than the Planck scale are unphysical, or at least don’t follow the normal laws of geometry. Second, two electrons must be exactly identical to allow chemistry to work, so they can’t carry any substructure that would be as variable as one of a galaxy (or even a high entropy, which must be zero).

— Composite vs elementary particles

— Lubos Motl

2013.02.27 Wednesday ACHK

# Records

— Me@2013-02-25 5:35 pm

# 無理數 2.2

「有理數」（rational number）的意思是，兩個整數的比例。亦即是話，它是一個分數，而分子和分母都是整數。如果表達成小數，它會是一個「有盡小數」或者「循環小數」。

「有理數」英文「rational number」中的「rational」，在日常生活的意思是「合理的」。但是，在這個數學的情境下，應該解讀成「ratio-nal」。「ratio」即為「比例」。根據現在的上文下理，「rational number」應該翻譯成「比例數」。「比例數」這個詞，比「有理數」直接易明。

— Me@2013.02.26

# Hiring

We rely on the Lake Wobegon Strategy, which says only hire candidates who are above the mean of your current employees.

— Hiring: The Lake Wobegon Strategy

— Peter Norvig, Director, Google Research

— 12th March 2006

2013.02.25 Monday ACHK

# Consultant

Be a consultant, not a teacher.

Being a teacher makes me old; being a consultant makes me young.

— Me@2009.12.11

# 無限蘋果 1.5

lim_{x -> infinity} x^2/(x^3 + 6)

= …

= 0

lim_{x -> infinity} x^3/(x^2 + 6)

= …

-> infinity

lim_{x -> infinity} (2 x^3 + 3 x + 7)/(5 x^3 + 3 x^2 + 6)

= lim_{x -> infinity} (2 x^3 + …)/(5 x^3 + …)

= …

= 2/5

— Me@2013.02.24

# Anger 4

gbog 15 hours ago | link

“Brilliant marketing play”

Maybe, but where the idealism gone? Both on HN, in tech circles, and, yes, at Google, there was some healthy dose of idealism. You know, this thing that make people do thing for something else than money, for the better good of humanity for example.

Idealism (and anger) brought us Linux, Vim, the Web, etc.

— Google has killed Android (the brand)

— Hacker News

2013.02.22 Friday ACHK

# Always

For all, 2

Always” means “all the time“, not “an infinite length of time“, for “infinity” is not a number.

— Me@2013-02-21 11:14:53 AM

# 無理數 2.1

2.4 cm = 24 mm

 This is a file from the Wikimedia Commons.

「開方 2」就為之「無理數」（irrational number）。表達成小數的話，它會「無盡不循環」。

（安：那如果用對角線作為單位呢？

— Me@2013.02.20

# Feeling time

Time as other things

.

“Feeling the existence of time” means that you stop but other things keep going. That’s why “feeling time” is not a good thing.

— Me@2011.05.24

.

Time is not valuable anymore if all you have is only time.

.

.

# Rediscovery

I hold with the Swiss psychologist Jean Piaget that the process of learning mathematics is itself a process of rediscovery. A similar view was expressed by the logician Ludwig Witgenstein, asserting in the preface to his famous Tractatus Logico-Philosophicus that he would probably not be understood except by those who had already had similar thoughts themselves.

— A Unified Language for Mathematics and Physics

— David Hestenes

— Clifford Algebras and their Applications in Mathematical Physics

2013.02.18 Monday ACHK

# 無限蘋果 1.4

lim_{x -> infinity} x^2/(x^3 + 6)

= lim_{x -> infinity} (1/x)/(1 + 6/x^3)

= (0)/(1 + 0)

= 0

( lim_{x -> infinity} 1/x ) = 0

lim_{x -> infinity} x^2/(x^3 + 6)

= （無限）^2/（（無限）^3 + 6）

= 0

— Me@2013.02.17

# The Heisenberg picture, 2

As I suggested in the article about the solution of the Hydrogen atom using the SO(4) symmetry, one of the reasons why almost no people properly learn the “foundations of quantum mechanics” is the textbooks’ and teachers’ excessive focus on the Schrödinger picture (and the wave functions) and their disrespect for the Heisenberg picture (and the operators) even though operators – the observables – is what quantum mechanics is all about.

— Celebrating the Heisenberg picture

— Lubos Motl

2013.02.17 Sunday ACHK

# Panaceas

Health care providers often call exercise the “miracle” or “wonder” drug — alluding to the wide variety of proven benefits that it provides.

— Wikipedia on Physical exercise

Doing physics (for my mind) and doing physical exercises (for my body) are my panaceas (for health).

— Me@2011.10.10

— Me@2013.02.16

# 乘法意思 4.3

(a^3) a^2 = (a^3) a a = a^5

(a^3) a^{-2} = a a a = a

(a^3) a^{-2} = a a a (but cancel two a’s) = a

a a a (?) (?) = a

(a^3) a^{-2} = a a a (1/a) (1/a) = a

a^{-2} = 1/a^2

— Me@2013.02.15