Sometimes, life doesn’t give you what you want.
Not because you don’t deserve it, but because you deserve more.
—
.
.
2017.11.18 Saturday ACHK
機遇再生論 1.5
…
例如，
「
甲在過身之後，一千億年內會重生。
」
是句「科學句」（經驗句），因為你知道在什麼情境下，可以否證到它 —— 如果你在甲過身後，等了一千億年，甲還未重生的話，那句就為之錯。
但是，
「
甲在過身之後，只要等足夠長的時間，必會重生。
」
則沒有任何科學意義，只是一句「重言句」；因為，沒有人可以講得出，它在什麼情況下，為之錯。
如果你等了一千億年，甲還未重生的話，這個「機遇再生論」，仍然不算錯；因為，那只代表了，那一千億年，還未「足夠長」。
把「重言句」假扮成「經驗句」，就為之「空廢命題」。
（請參閱本網誌，有關「重言句」、「經驗句」和「印證原則」的文章。）
但是，那不代表我們，應該立刻放棄，機遇再生論。反而，我們可以試行「同情地理解」。
「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？
其實，該理論的「真身」，可能充滿著新知洞見。那樣的話，我們就有機會把「機遇再生論」，翻譯成有意義，不空廢的版本。
所以，「同情地理解」亦可稱為「意念淘金術」。
—
機遇再生論，可以同情地理解為，有以下的意思：
（而這個意思，亦在「機遇再生論」的原文中，用作其理據。）
假設，你現在手中，有一副樸克牌，存在於某一個排列 A 。洗牌一次之後，排列仍然是 A 的機會極微。
一副完整的撲克牌，共有 
由於分母 N 太大（相當於 2 之後，還有 71 個位），洗牌後，理應變成另外一個排列 B 。
…
— Me@2017-12-18 02:51:11 PM
2017.12.18 Monday (c) All rights reserved by ACHK
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
2017.07.29 Saturday (c) All rights reserved by ACHK
PhD
Holodny: Yeah, I noticed you don’t have a Ph.D. Are you not into the Ph.D. system?
Dyson: Oh, very much against it. I’ve been fighting it unsuccessfully all my life.
Holodny: Any reason in particular?
Dyson: Well, I think it actually is very destructive. I’m now retired, but when I was a professor here, my real job was to be a psychiatric nurse. There were all these young people who came to the institute, and my job was to be there so they could cry on my shoulder and tell me what a hard time they were having. And it was a very tough situation for these young people. They come here. They have one or two years and they’re supposed to do something brilliant. They’re under terrible pressure – not from us, but from them.
So, actually, I’ve had three of them who I would say were just casualties who I’m responsible for. One of them killed himself, and two of them ended up in mental institutions. And I should’ve been able to take care of them, but I didn’t. I blame the Ph.D. system for these tragedies. And it really does destroy people. If they weren’t under that kind of pressure, they could all have been happy people doing useful stuff. Anyhow, so that’s my diatribe. But I really have seen that happen.
— Legendary physicist Freeman Dyson talks about math, nuclear rockets, and astounding things about the universe
— Elena Holodny Sep. 9, 2016, 9:15 AM
— Business Insider
當年「大導修課」時，李生講過：
「
我有好多朋友，當年去（外國／美國）讀博士，摧毁了他們自己一生。
（當然，在他們面前，我就不好意思，直接那樣説啦。）
他們本來性格好好，但是，回來之後，思想變得古靈精怪。試問世間上，有多少事情，比損失良好性格，更加悲慘呢？
」
所以，李生向阿熹提議：
「
你可以考慮一下，在香港，先完成了碩士。然後，才去外國升博士。
那時，事隔兩年，你個人成熟一點，『出事』的機會，自然細一點。
還有，剛才同你傾計，發覺你思想都幾周到；會顧慮很多東西，才下一個決定。
反而，讀博士的過程中，有時，你必須有一種『即管試，錯就錯啦』的心態。
」
— Me@2016.02.24
— Me@2016.06.12
— Me@2017.06.19
2017.07.05 Wednesday (c) All rights reserved by ACHK
The meanings of ONE
鑽石棉花 2
.
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
.
there are 2 units of apple == there are 2 apples
— Me@2021-08-22 07:13:46 AM
.
2 units = 2
— Me@2021-08-22 10:27:52 AM
.
You define one in a context.
But you cannot define two without defining one.
— Me@2017-02-14 07:10:51 AM
.
You define a unit in a context.
But you cannot define a number without defining a unit.
— Me@2021-08-21 10:08:58 PM
.
.
2017.03.26 Sunday (c) All rights reserved by ACHK
The Dunning–Kruger effect
想不出來 1.2.2
The Dunning–Kruger effect is a cognitive bias in which low-ability individuals suffer from illusory superiority, mistakenly assessing their ability as much higher than it really is. Dunning and Kruger attributed this bias to a metacognitive incapacity, on the part of those with low ability, to recognize their ineptitude and evaluate their competence accurately. Their research also suggests corollaries: high-ability individuals may underestimate their relative competence and may erroneously assume that tasks which are easy for them are also easy for others.
Dunning and Kruger have postulated that the effect is the result of internal illusion in those of low ability, and external misperception in those of high ability: “The miscalibration of the incompetent stems from an error about the self, whereas the miscalibration of the highly competent stems from an error about others.”
— Wikipedia on Dunning–Kruger effect
I’ve found that people who are great at something are not so much convinced of their own greatness as mystified at why everyone else seems so incompetent.
— Paul Graham
2017.02.17 Friday ACHK
馬後炮
注定外傳 2.3.4 | Can it be Otherwise? 2.3.4
或者說，到頭來，你也是要根據「有沒有道理」這個原則，去判別一個想法，是不是「神的旨意」。
如果沒有「神的旨意」，你就要靠自己，判斷是非明白，決定行事策略。如果有「神的旨意」，你也要靠自己，判斷哪些意念想法，真的是「神的旨意」，應該跟隨執行。
換言之，即使有「神的旨意」，你並不會在一件事發生之前，（在毋須自己判斷的情況下，）就知道那是不是「神的旨意」。
你至多只可以在，該件事件發生後，根據它的結果好壞，把它歸類為「神的旨意」或否。
但是，那又會令我們回到，今天討論的起點：
「
以往的事是注定的；未來之事不完全注定。
即使有些未來之事是注定的，你也不會在事前，百分之百肯定地知道，那注定的結果是，眾多可能性的哪一個。
」
既然就算有注定，你也不知注定為何；事情注定與否，對你又怎會有影響呢？
— Me@2017-02-03 04:15:54 PM
2017.02.03 Friday (c) All rights reserved by ACHK
Uncertainty Principle 8
EPR paradox for entangled particles
Bohr was compelled to modify his understanding of the uncertainty principle after another thought experiment by Einstein. In 1935, Einstein, Podolsky and Rosen (see EPR paradox) published an analysis of widely separated entangled particles. Measuring one particle, Einstein realized, would alter the probability distribution of the other, yet here the other particle could not possibly be disturbed. This example led Bohr to revise his understanding of the principle, concluding that the uncertainty was not caused by a direct interaction.
But Einstein came to much more far-reaching conclusions from the same thought experiment. He believed the “natural basic assumption” that a complete description of reality, would have to predict the results of experiments from “locally changing deterministic quantities”, and therefore, would have to include more information than the maximum possible allowed by the uncertainty principle.
In 1964, John Bell showed that this assumption can be falsified, since it would imply a certain inequality between the probabilities of different experiments. Experimental results confirm the predictions of quantum mechanics, ruling out Einstein’s basic assumption that led him to the suggestion of his hidden variables. Ironically this fact is one of the best pieces of evidence supporting Karl Popper’s philosophy of invalidation of a theory by falsification-experiments. That is to say, here Einstein’s “basic assumption” became falsified by experiments based on Bell’s inequalities.
While it is possible to assume that quantum mechanical predictions are due to nonlocal, hidden variables, and in fact David Bohm invented such a formulation, this resolution is not satisfactory to the vast majority of physicists. The question of whether a random outcome is predetermined by a nonlocal theory can be philosophical, and it can be potentially intractable. If the hidden variables are not constrained, they could just be a list of random digits that are used to produce the measurement outcomes.
— Wikipedia on Uncertainty principle
2017.01.18 Wednesday ACHK
Zooming out
In this morning’s dream, I had seen an ultra zooming out of the universe, where in the end the universe became a particle of a super-universe.
Perhaps the afterlife (or near-death experience) is like this kind of bizarre feeling.
— Me@2011.08.17
It is a fractal.
— Me@2011.08.22
Note: This kind of feeling is unhealthy, since it is induced by eating too little food.
— Me@2017.01.09
Several months ago, I had another this kind of super-feeling dream, in which I could get a time traveling feeling.
— Me@2011.08.17
2017.01.14 Saturday (c) All rights reserved by ACHK
注定外傳 2.3.3
Can it be Otherwise? 2.3.3
對於未來之事，究竟注定與否，並不會指引到你，如何做決定。世事「必然」與否，對你的日常生活，不會構成影響。
彷彿是「神的旨意」一樣 — 即使有「神的旨意」，它並不能指引你，去做最佳的決定。
（問：為什麼呢？
如果知道「神的旨意」，而我又跟著「神的旨意」去行事的話，那不就是「最佳的決定」嗎？）
你試想想，你怎樣可以知道，「神的旨意」是什麼呢？
（問：如果有神明存在，神明可能透過我的靈感，去指引我。）
那樣，當你有靈機一觸的感覺時，你怎樣可能知道，那是真正的靈感（神的指示）、魔鬼的誤導、自己的創意，還是隨機的幻覺呢？
（問：如果有道理的，那就可能是「神的旨意」。
如果那些道理十分深刻，深刻到在自己在一般狀態下，也很難想到的，那就極有可能是「神的旨意」。
相反，那個所謂「靈感」，其實指示著我去做壞事，那就應視為「魔鬼的誤導」。）
在靈感有道理時，你怎樣知道，那是來自「神的指示」，還是「自己創意」呢？
—
依照你的講法，你是根據那個靈感想法，有沒有道理，去決定是否附諸實行，而不是那個靈感想法本身，是不是「神的旨意」；因為，你並不會在毋須任何判斷的情況下，就知道那個靈感，是不是「神的旨意」。
或者說，到頭來，你也是要根據「有沒有道理」這個原則，去判別一個想法，是不是「神的旨意」。
如果沒有「神的旨意」，你就要靠自己，判斷是非明白，決定行事策略。如果有「神的旨意」，你也要靠自己，判斷哪些意念想法，真的是「神的旨意」，應該跟隨執行。
— Me@2016-12-30 03:37:35 PM
2017.01.01 Sunday (c) All rights reserved by ACHK
Superposition always exists
A Non-classical Feature, 2
.
superposition
~ linear overlapping
~ f(ax + by) = a f(x) + b f(y)
.
Reality is a linear overlapping of potential realities, although different components may have different weightings.
Superposition always exists, if it exists at the beginning of a process.
So the expression “the wave function collapses and the superposition ceases to exist” does not make sense.
.
Superposition always exists; interference (pattern) does not.
For a superposition to have an interference pattern, the two (for example) component eigenstates need to have a constant phase difference.
In other words, they have to be coherent.
.
superposition without an interference pattern
~ microscopically decoherent component states
~ macroscopically a classical state
— Me@2016-09-01 4:42 AM
.
The above is not correct.
A quantum superposition is not just an overlapping of classical states, because if it is, for example, there would be no interference patterns formed in the double-slit experiment. If a quantum superposition is just an overlapping of classical worlds, how can you explain the destructive interference part?
— Me@2020-12-19 07:19:08 PM
.
.
2016.11.27 Sunday (c) All rights reserved by ACHK
Pixar
Toy Story
1995
1995
A Bug’s Life
1998
Toy Story 2
1999
Monsters, Inc.
2001
Finding Nemo
2003
The Incredibles
2004
Ratatouille
2007
WALL-E
2008
Up
2009
Toy Story 3
2010
Inside Out
2015
— Me@2016-10-21 03:11:28 PM
2016.10.21 Friday ACHK
注定外傳 2.3.2
Can it be Otherwise? 2.3.2
在討論「自由決定」這問題時，必須先行釐清「有沒有自由意志」，究竟是什麼意思。「沒有自由意志」的意思，起碼有兩個可能。
其中一個版本是，針對外在因素 — 有時，你想選擇一條路，但是，因為受制於外在因素，唯有違反原本意圖，改為選擇另一選項。多數人也會把這個情況，歸類為「沒有自由意志」。少數人會把這個情況，標籤為「仍然有自由意志」，因為你仍然可以思考，有自己的意向；你只是「沒有自由行動」，而不是「沒有自由意志」。
另一個版本，則針對內在因素 — 有時，連你那個選擇想法本身，根本也沒有自由；換句話說，你的原本意圖是什麼，其實也是受制於各項因素。 這個情況是，絕對的「沒有自由意志」。
如果在討論「自由決定」這問題時，沒有共識「沒有自由意志」是，用眾多可能意思的哪一個的話，討論不會有進展。
— Me@2016-10-15 06:10:12 AM
2016.10.15 Saturday (c) All rights reserved by ACHK
A Non-classical Feature
What makes the interference pattern of electrons in the double-slit experiment a non-classical feature?
The probability pattern of every electron being a particle and that of being a wave are different.
For the particle pattern, the left-slit part and the right-slit part of the probability wave do not overlap. The quantum superposition does not cause a (interference) pattern.
This is why the interference pattern is a non-classical feature of the electron double-slit experiment.
— Me@2016-10-06 09:53:07 AM
2016.10.07 Friday (c) All rights reserved by ACHK
Illness 2
Illness is due to lack of problems.
Illness is due to lack of challenges.
— Me@2010.12.05
2016.08.31 Wednesday (c) All rights reserved by ACHK
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
你可以根據自己的意願來決定和行動；但是，你不可以控制自己的意願。即使可以，你也不可以控制，自己意願的意願。
— 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
2016.08.22 Monday (c) All rights reserved by ACHK
Black hole complementarity 3
Raphael nicely avoids many of the confusions by introducing a refined version of the complementarity principle, the so-called observer complementarity… If I add some “foundations of quantum mechanics” flavor to the principle, it says:
Quantum mechanics is a set of rules that allows an observer to predict, explain, and/or verify observations (and especially their mutual relationships) that he has access to.
An observer has access to a causal diamond – the intersection of the future light cone of the initial moment of his world line and the past light cone of the final moment of his world line (the latter, the final moment before which one must be able to collect the data, is more important in this discussion).
No observer can detect inconsistencies within the causal diamonds. However, inconsistencies between “stories” as told by different observers with different causal diamonds are allowed (and mildly encouraged) in general (as long as there is no observer who could incorporate all the data needed to see an inconsistency).
…
Bohr has said that physics is about the right things we can say about the real world, not about objective reality, and it has to be internally consistent. However, in the context of general relativity, the internal consistency doesn’t imply that there has to be a “global viewpoint” or “objective reality” that is valid for everyone.
— Raphael Bousso is right about firewalls
— Lubos Motl
2016.07.27 Wednesday ACHK
A Difficult Exam
Life is the most difficult exam.
Many people fail because they try to copy others,
not realizing that everyone has a different question paper.
—
2016.07.10 Sunday ACHK
注定外傳 3.0
Can it be Otherwise? 3.0
現在不如沿著另一個方向研究：
第一個可能，是「人有自由」。
第二和第三個可能，也是「人沒有自由」，只是原因不同（完全相反）。
有沒有自由，對你的生活有什麼影響？
還是，無論有沒有自由，你的生活其實沒有差別？
簡單起見，三個可能之中，我們暫時只討論頭兩個：
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？
如果我有自由，我就有機會透過自己的努力，去改善生活。那樣，我自然會積極一點。）
有很多人懶惰，並不是因為他們覺得，人沒有自由；而只是因為，（例如）他們不喜歡努力。
如果人有自由，自然有一部分人會利用其自由，選擇不努力。
留意，「覺得自己有自由」和「自己有自由」是兩回事。但是，無論是哪一回，都不一定會導致自己積極。
「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？
如果一切皆注定，我就沒有機會，改變任何事情的結果。那樣，我自然不會選擇，積極去做事，因為，積極來也沒有用。例不如，消極一點，以免浪費心機。）
既然一切皆注定，你又如何可以「選擇」消極呢？
如果一切皆注定，你積極還是消極，不在你控制。
如果一切皆注定，自然有些人注定積極，有些人注定消極。
無論你有什麼行動，或者有什麼態度 ，你既可以解釋成，因為「自己有自由」；亦可以解釋成，因為「一切皆注定」。
例如，當別人問你，為什麼做事那麼積極時，你可以答：「因為我有自由，我要提升我的人生」；你亦可以答：「命中注定我那麼積極，我也沒有辦法改變。」
又例如，當別人問你，為什麼做事那麼消極時，你可以答：「因為我有自由，那是我的選擇」；你亦可以答：「一切皆為注定，我沒有辦法改變，努力來也沒有意思。」
— Me@2016-07-04 11:21:49 PM
2016.07.04 Monday (c) All rights reserved by ACHK
Physics Town 
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