# Creative constraints

Imagine you were asked to invent something new. It could be whatever you want, made from anything you choose, in any shape or size. That kind of creative freedom sounds so liberating, doesn’t it? Or … does it?

If you’re like most people you’d probably be paralyzed by this task. Why?

Brandon Rodriguez explains how creative constraints actually help drive discovery and innovation.

With each invention, the engineers demonstrated an essential habit of scientific thinking – that solutions must recognize the limitations of current technology in order to advance it.

Understanding constraints guides scientific progress, and what’s true in science is also true in many other fields.

Constraints aren’t the boundaries of creativity, but the foundation of it.

— The power of creative constraints

— Lesson by Brandon Rodriguez

— animation by CUB Animation

— TED-Ed

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We cannot change anything until we accept it. Condemnation does not liberate, it oppresses.

— Carl Jung

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# Twelve-step program

A twelve-step program is a set of guiding principles outlining a course of action for recovery from addiction, compulsion, or other behavioral problems. Originally proposed by Alcoholics Anonymous (AA) as a method of recovery from alcoholism, the Twelve Steps were first published in the 1939 book Alcoholics Anonymous: The Story of How More Than One Hundred Men Have Recovered from Alcoholism. The method was adapted and became the foundation of other twelve-step programs.

As summarized by the American Psychological Association, the process involves the following:

– recognizing a higher power that can give strength;

– examining past errors with the help of a sponsor (experienced member);

– making amends for these errors;

– learning to live a new life with a new code of behavior;

– helping others who suffer from the same alcoholism, addictions or compulsions.

— Wikipedia on Twelve-step program

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We cannot change anything until we accept it. Condemnation does not liberate, it oppresses.

— Carl Jung

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# 深淵 2

— 尼采

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As soon as men decide that all means are permitted to fight an evil, then their good becomes indistinguishable from the evil that they set out to destroy.

— Christopher Dawson

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2018.02.16 Friday ACHK

# 機遇再生論 1.6

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（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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$P(A) = \frac{1}{N}$

$P(\text{not} A) = 1 - \frac{1}{N}$

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(問：那樣，為什麼要問多一次呢？）

「如果洗牌兩次，起碼一次洗到原本排列 A 的機會率是多少？」

$A_2$ = 兩次洗牌的結果，起碼一次洗到原本排列 A

$A_2$ 的互補事件為「不是 $A_2$」：

= 兩次洗牌的結果，不是起碼一次洗到原本排列 A

= 兩次洗牌的結果，都不是排列 A

$P(\text{not} A_2) = (1 - \frac{1}{N})^2$

$P(A_2)$
$= 1 - P(\text{not} A_2)$
$= 1 - (1 - \frac{1}{N})^2$

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$P(A_m)= 1 - (1 - \frac{1}{N})^m$

$P(A_m)$
$= 1 - (1 - \frac{1}{N})^m$
$= 1 - (1 - \frac{1}{52!})^{10,000,000}$

$1.239799930857148592 \times 10^{-61}$

— Me@2018-01-25 12:38:39 PM

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# Riemann Surfaces

Imaginary Numbers Are Real [Part 1: Introduction]

Imaginary Numbers Are Real [Part 2: A Little History]

Imaginary Numbers Are Real [Part 3: Cardan’s Problem]

Imaginary Numbers Are Real [Part 4: Bombelli’s Solution]

Imaginary Numbers Are Real [Part 5: Numbers are Two Dimensional]

Imaginary Numbers Are Real [Part 6: The Complex Plane]

Imaginary Numbers Are Real [Part 7: Complex Multiplication]

Imaginary Numbers Are Real [Part 8: Math Wizardry]

Imaginary Numbers Are Real [Part 9: Closure]

Imaginary Numbers Are Real [Part 10: Complex Functions]

Imaginary Numbers Are Real [Part 11: Wandering in 4 Dimensions]

Imaginary Numbers Are Real [Part 12: Riemann’s Solution]

Imaginary Numbers Are Real [Part 13: Riemann Surfaces]

— Welch Labs

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In case the original videos are lost, please use the Internet Archive link:

— Me@2018-02-12 02:14:51 PM

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# Utopia

So why bother with all this pessimism?

Because at their heart, dystopias
are cautionary tales,

or technology,

but the very idea that humanity can be
molded into an ideal shape.

Think back to the perfect world
you imagined.

Did you also imagine what it would
take to achieve?

How would you make people cooperate?

And how would you make sure it lasted?

Now take another look.

Does that world still seem perfect?

— How to recognize a dystopia

— Alex Gendler

— animation by TED-Ed

The road to hell is paved with good intentions.

2018.01.23 Tuesday ACHK

# Then and Now

The most distant a memory, the blurrier it is.

If a memory was completely vivid, you would not be able to distinguish between then and now.

— Westworld (TV series)

— paraphrased

— Me@2018-01-13 10:43:04 AM

# 機遇再生論 1.5

（請參閱本網誌，有關「重言句」、「經驗句」和「印證原則」的文章。）

「同情地理解」的意思是，有些理論，雖然在第一層次的分析之後，有明顯的漏洞，但是，我們可以試試，代入作者發表該理論時的，心理狀態和時空情境；研究作者發表該理論的，緣起和動機；從而看看，該理論不行的原因，會不會只是因為，作者的語文或思考不夠清晰，表達不佳而已？

（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

$P(A) = \frac{1}{N}$

$P($not $A) = 1 - \frac{1}{N}$

— Me@2017-12-18 02:51:11 PM

# Mathematics

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

A possible explanation of the physicist’s use of mathematics to formulate his laws of nature is that he is a somewhat irresponsible person. As a result, when he finds a connection between two quantities which resembles a connection well-known from mathematics, he will jump at the conclusion that the connection is that discussed in mathematics simply because he does not know of any other similar connection.

— The Unreasonable Effectiveness of Mathematics in the Natural Sciences

— E. P. Wigner

2017.10.07 Saturday ACHK

# Determined by what?

If you say “an event is determined”, in order to be meaningful, you have to specify, explicitly or by context, that the event is determined by whom.

Similarly, if you say something is free, you have to specify “free from what” or “free with respect to what”.

free ~ independent of

Without a grammatical object, the phrase “independent of” is meaningless, unless the context has implied what that grammatical object is.

— Me@2015-05-23

free [without an object] ~ free from everything

is meaningless, because the word “everything” is meaningful only if it has a context.

— Me@2017-07-20

# The meanings of ONE

One bag of apples, one apple, one slice of apple — which of these is one unit? Explore the basic unit of math (explained by a trip to the grocery store!) and discover the many meanings of one.

— Lesson by Christopher Danielson, animation by TED-Ed.

A unit ~ a definition of one

(cf. One is one … or is it? — TED-Ed)

— Me@2017-02-13 8:48 AM

One is not a number, in the following sense:

Primality of one

Most early Greeks did not even consider 1 to be a number, so they could not consider it to be a prime. By the Middle Ages and Renaissance many mathematicians included 1 as the first prime number. In the mid-18th century Christian Goldbach listed 1 as the first prime in his famous correspondence with Leonhard Euler; however, Euler himself did not consider 1 to be a prime number. In the 19th century many mathematicians still considered the number 1 to be a prime. For example, Derrick Norman Lehmer’s list of primes up to 10,006,721, reprinted as late as 1956, started with 1 as its first prime. Henri Lebesgue is said to be the last professional mathematician to call 1 prime. By the early 20th century, mathematicians began to arrive at the consensus that 1 is not a prime number, but rather forms its own special category as a “unit”.

A large body of mathematical work would still be valid when calling 1 a prime, but Euclid’s fundamental theorem of arithmetic (mentioned above) would not hold as stated. For example, the number 15 can be factored as 3 · 5 and 1 · 3 · 5; if 1 were admitted as a prime, these two presentations would be considered different factorizations of 15 into prime numbers, so the statement of that theorem would have to be modified. Similarly, the sieve of Eratosthenes would not work correctly if 1 were considered a prime: a modified version of the sieve that considers 1 as prime would eliminate all multiples of 1 (that is, all other numbers) and produce as output only the single number 1. Furthermore, the prime numbers have several properties that the number 1 lacks, such as the relationship of the number to its corresponding value of Euler’s totient function or the sum of divisors function.

— Wikipedia on Prime number

As long as something exists, it is possible to define one.

One as the basis for counting (number); one itself is not a number, in the sense that one is for existence, not for counting.

When counting, we have to know count with respect to what. That “what” is a “unit”, aka one.

That is why

x times 1 = x

— Me@2017-02-13 8:48 AM

# 馬後炮

— Me@2017-02-03 04:15:54 PM

# 注定外傳 2.3.3

Can it be Otherwise? 2.3.3

（問：為什麼呢？

（問：如果有神明存在，神明可能透過我的靈感，去指引我。）

（問：如果有道理的，那就可能是「神的旨意」。

— Me@2016-12-30 03:37:35 PM

# 注定外傳 2.3.2

Can it be Otherwise? 2.3.2

— Me@2016-10-15 06:10:12 AM

# 注定外傳 4.0

Can it be Otherwise? 4.0

One of the major difficulties of free-will-VS-determinism problem is its “always-meta” nature.

— Me@2016-08-19 09:00:14 AM

You can will to act, but not will to will.

Man can do what he wants, but he cannot will what he wants.

You can do what you will, but in any given moment of your life you can will only one definite thing and absolutely nothing other than that one thing.

— Schopenhauer

— Me@2016-01-06 06:50:56 PM

By definition, will is a first cause. So you cannot control it.

— Me@2016-01-06 06:55:13 PM

# 注定外傳 3.0

Can it be Otherwise? 3.0

1. 人有自由；

2. 因為一切皆注定，人沒有自由。

（問：應該有差別吧？

「積不積極」主要取決於性格和際遇；與「自己有沒有自由」，或者「覺得自己有沒有自由」，沒有什麼大關係。

（問：如果「人沒有自由」呢？那大概不可能積極吧？

— Me@2016-07-04 11:21:49 PM

# Euler Formula

Exponential, 2

$a^x$

general exponential increase ~ the effects are cumulative

$e^x$

natural exponential increase ~ every step has immediate and cumulative effects

— Me@2014-10-29 04:44:51 PM

exponent growth

$e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$

~ compound interest effects with infinitesimal time intervals

multiply -1

~ rotate to the opposite direction

(rotate the position vector of a number on the real number line to the opposite direction)

~ rotate 180 degrees

multiply i

~ rotate to the perpendicular direction

~ rotate 90 degrees

For example, the complex number (3, 0) times i equals (0, 3):

$3 \times i = 3 i$
$(3, 0) (0, 1) = (0, 3)$

multiplying i

~ change the direction to the one perpendicular to the current moving direction

(current moving direction ~ the direction of a number’s position vector)

exponential growth with an imaginary amount

$e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n$

~ change the direction to the one perpendicular to the current moving direction continuously

~ rotate $\theta$ radians

— Me@2016-06-05 04:04:13 PM

# 注定外傳 2.6

Can it be Otherwise? 2.6 | The Beginning of Time, 7.3

『所有』，就是『場所之有』。

— Me@2016-05-18 11:40:31 AM

# 注定外傳 2.5

Can it be Otherwise? 2.5 | The Beginning of Time, 7.2

4. 即使可以追溯到「時間的起點」（第一因），所謂的「可以」，只是宏觀而言，決不會細節到可以推斷到，你有沒有自由，明天七時起牀。

（問：如果因果環環緊扣，即使細節不完全知道，至少理論上，我們可以知道，如果「第一因」本身有自由，那其他個別事件，就有可能有（來自「第一因」的）自由；如果連「第一因」也沒有自由，那其他個別事件，都一律沒有自由。

「第一因有自由。」

「第一因」根據定義，是沒有原因的。亦即是話，「時間的起點」，再沒有「之前」。而「有自由」，就即是「有其他可能性」。所以，「第一因有自由」的意思是，

「第一因還有其他的可能性。」

（問：如果有「造物主」，祂不就是那個誰，可以從宇宙之初的不同可能性中，選擇一個去實現嗎？）

「因果是否真的『環環緊扣』，有沒有可能，有『同因不同果』的情況？」

— Me@2016-03-15 08:43:58 AM

# 注定外傳 2.3

Can it be Otherwise? 2.3

— Me@2016-01-06 03:17:54 PM