# 機遇再生論 1.8

$P(A_{10,000,000})$
$\approx 1.2398 \times 10^{-61}$

$P(A_{20,000,000})$
$\approx 1.2398 \times 10^{-54}$

.

（問：那我不需要在「洗完一千萬次牌後，發現原本排列 A 還未重新出現時」，才問_另一個_問題，因為，事先透過運算，就已經知道，那機會十分之微。

」）

$P(A_{10,000,000^{10}}) = 0.9999999...$

.

（問：為什麼要「相對於現在的你而言」？）

.

$P(A_{10,000,000^{10}})$ 了，

$P(A_{10,000,000^{10} - 1})$

（問：你的意思是，即使我洗了（例如）一千萬牌，仍然得不回原本的排列 A，只要我洗多一千萬次，得回 A 的機會，就會大一點？）

.

.

.

「機遇再生論」在同情地理解下，可以有這個意思。

— Me@2018-03-20 02:26:35 PM

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# 機遇再生論 1.7

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

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

$1.239799930857148592 \times 10^{-61}$

.

「（在一次牌都未洗的時候問）洗牌 二千萬 次，起碼一次洗到原本排列 A 的機會率」

「（在一次牌都未洗的時候問）洗牌 一千萬 次，起碼一次洗到原本排列 A 的機會率」。

.

$P(A_m)$
$= 1 - (1 - \frac{1}{N})^m$
$= 1 - (1 - \frac{1}{52!})^{10,000,000 \times 2}$
$\approx 2.479599861714297185 \times 10^{-61}$,

$P(A_m)$
$= 1 - (1 - \frac{1}{52!})^{10,000,000 \times 10,000,000}$
$\approx 1.2397999308571485923950342 \times 10^{-54}$

$m = 10,000,000^3, P(A_m) = 1 - (1 - \frac{1}{52!})^{10,000,000^3} \approx 1.2398 \times 10^{-47}$

$m = 10,000,000^4, P(A_m) \approx 1.2398 \times 10^{-40}$

$m = 10,000,000^8, P(A_m) \approx 1.2398 \times 10^{-12}$

$m = 10,000,000^9, P(A_m) \approx 0.000012398$

$m = 10,000,000^{10}, P(A_m) = 0.9999999...$

.

$P(A_{10,000,000^{10}}) = 0.9999999...$

.

（問：你的意思是，即使我洗了（例如）一千萬牌，仍然得不回原本的排列 A，只要我洗多一千萬次，得回 A 的機會，就會大一點？）

.

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

$(N = 52! \approx 8.07 \times 10^{67})$

$P(A_{10,000,000})$
$\approx 1.2398 \times 10^{-61}$

$P(A_{10,000,000})$
$\approx 1.2398 \times 10^{-61}$

$P(A_{20,000,000})$
$\approx 1.2398 \times 10^{-54}$

— Me@2018-02-23 08:21:52 PM

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# 機遇再生論 1.6

.

（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）

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

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

.

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

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

.

(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

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

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

.

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

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

$1.239799930857148592 \times 10^{-61}$

— Me@2018-01-25 12:38:39 PM

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# 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

# 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

# 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

# 注定外傳 2.2

Can it be Otherwise? 2.2

「成績注定」和「主動溫習」，根本沒有矛盾。

— Me@2015-12-29 03:12:39 PM

# 注定外傳 2.1.2

Can it be Otherwise? 2.1.2 | The problem of induction 2.2

1. 當你的「相似事件」和「原本事件」的結果相同時，你只可以知道「原本事件」，可能是注定；你並不可以肯定「原本事件」，一定是注定，因為，你並不能保證，下一件「相似事件」的結果，會不會仍然和「原本事件」相同。

2. 當你的「相似事件」和「原本事件」的結果不同時，你亦不可以肯定「原本事件」，一定是偶然，因為，結果不同，可能只是由於「相似事件」和「原本事件」，不夠相似而已。

— Me@2015-11-17 02:02:03 PM

# 注定外傳 2.1.1

Can it be Otherwise? 2.1.1 | The problem of induction 2.1

（層次一的事件描述：）

（層次一的反證：）

（層次二 —— 準確一點的事件描述：）

（層次二 —— 詳細一點的反證：）

（層次三：）

（層次四：）

— Me@2015-11-17 02:02:03 PM

# 注定外傳 1.11

Can it be Otherwise? 1.11

— Me@2015-10-29 03:10:19 PM

Q: Can it be otherwise?

A: What is “it”?

— Me@2015-10-29 03:10:14 PM

# 注定外傳 1.10

Can it be Otherwise? 1.10

（問：如果只是「類似」，當然可以有不同結果。你應該直接問：

』）

（問：不是呀。在量子力學中，即使有兩組百分百一樣的物理系統，即使它們獲得完全相同的輸入，都可能有不同的輸出。）

「相同」的意思，並不是指「沒有可能找到任何分別」。

「相同」的意思是「分別小到不易察覺」。

」，

— Me@2015-10-29 10:12:16 PM

# 注定外傳 1.9

Can it be Otherwise? 1.9

（這裡的「東西」，是指宏觀的物理系統。至於兩粒微觀粒子，則有可能「全同」。但那是另一個話題，容後再談。）

（問：那如果連位置都相同呢？）

— Me@2015-10-07 02:52:21 PM

# 注定外傳 1.8

Can it be Otherwise? 1.8

（問：那如果是數數目（使用整體）的情況呢？

（問：那為什麼不可以說「絕對相同」？）

「絕對」，應該用作「相對」的相反。而「近似」的相反，則應該用「確切」。

（這裡的「東西」，是指宏觀的物理系統。至於兩粒微觀粒子，則有可能「全同」。但那是另一個話題，不宜在這裡詳述。）

— Me@2015-10-04 07:32:32 AM

# 注定外傳 1.7

Can it be Otherwise? 1.7

3.1415926

3.1415927

（問：如果 3.1 和 3.1 呢？它們不是完全（絕對）相同嗎？）

（問：怎樣為之「有實際因素考慮，真的要應用」？）

3.1 厘米 和

3.1 厘米。

（問：那如果是數數目（使用整體）的情況呢？

— Me@2015-09-30 04:26:45 AM

# 注定外傳 1.6

Can it be Otherwise? 1.6

… 因為，如果真的是「百份百相同」的情境，又怎可能有不同的結果呢？

（問：不是呀。在量子力學中，即使有兩組百分百一樣的物理系統，即使它們獲得完全相同的輸入，都可能有不同的輸出。）

— Me@2015-09-25 10:40:58 AM

# Quantum Indeterminacy

Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, that has become one of the characteristics of the standard description of quantum physics.

Indeterminacy in measurement was not an innovation of quantum mechanics, since it had been established early on by experimentalists that errors in measurement may lead to indeterminate outcomes. However, by the later half of the eighteenth century, measurement errors were well understood and it was known that they could either be reduced by better equipment or accounted for by statistical error models. In quantum mechanics, however, indeterminacy is of a much more fundamental nature, having nothing to do with errors or disturbance.

— Wikipedia on Quantum indeterminacy

Quantum indeterminacy is the inability to predict the behaviour of the system with 100% accuracy, even in principle.

If everything is connected , quantum indeterminacy is due to the logical fact that, by definition, a “part” cannot contain (all the information of) the “whole”.

An observer (A) cannot separate itself from the system (B) that it wants to observe, because an observation is an interaction between the observer and the observed .

In order to get a perfect prediction of a measurement result, observer (A) must have all the information of the present state of the whole system (A+B). However, there are two logical difficulties.

First, observer A cannot have all the information about (A+B).

Second, observer A cannot observe itself to get (all of) its present state information, since an observation is an interaction between two entities. Logically, it is impossible for something to interact with itself directly. Just as logically, it is impossible for your right hand to hold your right hand itself.

So the information observer A can get (to the greatest extent) is all the information about B, which is only part of the system (A+B) it (A) needs to know in order to get a prefect prediction for the evolution of the system B.

— Me@2015-09-14 08:12:32 PM

# 注定外傳 1.4

（問：你不是說理論的成本較低嗎？）

— Me@2015-09-07 08:59:31 PM