Life, 3

生命 3

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We exist in time because time is change.

Growing is part of the definition of life. Growing is a kind of change.

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Also, without time/change, there would be no thinking and no thoughts.

— Me@2017-12-26 11:42 am

— Me@2018-05-23 10:05:03 PM

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time ~ change

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Time is logically necessary if change is necessary.

— Me@2018-02-04 09:07:48 PM

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2018.05.23 Wednesday (c) All rights reserved by ACHK

The language of Change 1.2

Energy conservation, 6.2 | Energy 5.2

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time ~ change

energy ~ the ability of _keeping_ changing

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constant velocity ~ the amount of an object’s change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}

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kinetic energy ~ the amount of the ability of keeping changing an object’s position

\frac{1}{2} m v^2 ~ the square of (the amount of change of position, relative to the observer’s unit of change)

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Energy difference is _not_ exactly a measurement of the amount of change, time interval is.

— Me@2018-02-20 09:39:30 AM

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2018.02.20 Tuesday (c) All rights reserved by ACHK

The language of Change

Energy conservation, 6 | Energy 5

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time ~ change

energy ~ the ability of causing change

Assuming

1. a system of one single particle

2. has only kinetic energy

3. and that kinetic energy is conserved.

conservation of energy ~ an object’s potential amount of change of position, measured with respect to its observer’s unit of change, is constant

s = \Delta x

v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}

— Me@2018-02-15 02:21:20 PM

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Note:

The above argument has a bug:

If the mass m is constant, the kinetic energy E_K should be proportional to velocity squared v^2, instead of velocity v.

E_K = \frac{1}{2} m v^2

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However, the above argument is still technically correct:

When E_K is constant, v^2 is constant. In turn, the magnitude of v also remains unchanged.

— Me@2018-02-19 09:37:24 PM

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2018.02.15 Thursday (c) All rights reserved by ACHK

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
 
 
 
2016.06.08 Wednesday (c) All rights reserved by ACHK

注定外傳 2.6

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

還有,「宇宙」這個詞語,其實分析下去,是不合法的,因為「宇宙」的意思,就是「所有事物」。

而「所有」這個詞語的意思,是相對的,因為「所有」,即是「百分之一百」。

在沒有一個基數時,講「百分之一百」,其實不會知道,是指多少數量。同理,在沒有上文下理時,講「所有」,其實不太知道,是指什麼意思。例如,「所有人」即是有「多少人」呢?

沒有明確的上文下理,「所有人」自然沒有明確的意思。

詳情請參閱,我以往有關「所有」的文章,例如:

相反,如果有明確的上文下理,就自然有明確的意思。例如,『三十元中的百分之一百』,就很明顯是指,那三十元。

又例如,『這間屋的所有人』,都有明確的意思,因為有明確的範圍;有範圍,就可點人數:

凡是在這間屋內遇到的人,包括你自己,你都記下名字,直到在這間屋,再不找到新的人為止。那樣,你就可以得到,有齊『這間屋所有人』的名單。

『所有』,就是『場所之有』。

沒有明確的場所,就不知所「有」何物。

— Me@2016-05-18 11:40:31 AM

2016.05.18 Wednesday (c) All rights reserved by ACHK

Quantum Indeterminacy

注定外外傳 1

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

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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

2015.09.15 Tuesday (c) All rights reserved by ACHK

機遇再生論 1.3

『機遇再生論』的大概意思是,所有可能發生的事情,例如重生,在無限長的未來時間中,必會發生。

機遇再生論原始版本,有問題的字眼中,除了「所有」之外,還有「無限」。「無限」通常都是一個違法詞語。「無限」引起的問題,以前論述過,現不再詳談。請參閱「無限」系列的文章。

你可以嘗試移除「無限」這個詞語,只把「無限」的意思中,有意義的部分保留:

『機遇再生論』的大概意思是,所有可能發生的事情,例如重生,只要等足夠長的時間,總會發生。

但是,即使避開了「無限」,用了「足夠長」,仍然會有其他問題。「足夠長」這個詞語雖然不算違法,但是十分空泛,空泛到近乎沒有意義。

試想想,怎樣才為之「足夠長」呢?

— Me@2015.04.08

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2015.04.09 Thursday (c) All rights reserved by ACHK

Tactics and Strategy

What’s the difference between the adjectives “strategic” and “tactical”?

Tactics is knowing what to do when there is something to do. Strategy is knowing what to do when there is nothing to do.

— Savielly Tartakower

2013.10.28 Monday ACHK

A good speaker

Definition of a good speaker:

His overrunning does not annoy you.

— Me@2011.04.27

If you do not mind if a speaker overruns a speech, he must be a good speaker.

想知道一個演講者功力,你就觀察一下,如果他的演講超時,聽眾有什麼反應。

如果他超時,你會感到煩擾還是高興呢?

— Me@2013.09.12

2013.09.12 Thursday (c) All rights reserved by ACHK

量子力學 1.6

因果律 1.11 | Verification principle, 5.11

這段改編自 2010 年 4 月 3 日的對話。

其實,理論上,至少有一個物理系統,可以在完全不受外在環境的因素下,自然演化。那就是「整個宇宙」。因為「宇宙」的意思是「所有東西」,所以根據這定義的話,「宇宙」並沒有所謂的「外面」,或者「外在環境」。

(安:無錯。但是,如果在其他情況,我們考慮的物理系統,都不會是「整個宇宙」。那樣,那個物理系統,就一定有「外面」。而我的講法,就有可能是正確的。)

正確。「隨機」這個詞語中的「機」字,在「經典物理學」中,正正是可以用來指「未知」。某一些物理實驗,例如擲錢幣,結果是「隨機」的;意思就是指,那結果受該個物理系統之中,一些「未知」的因素所決定。而這些「未知」的數據,例如錢幣被擲時的角度方向、轉動速度 和 離地高度 等,雖然可以量度得到,但是物學家會故意忽略,為的是要大大簡化運算。總括而言,「經典物理學」中的「隨機」,可以詳寫成「跟隨未知因素」。

至於在「量子物理學」中,剛才提過,即使在理論上,我們知道了一個「量子物理系統」的全部狀態數據,再加以調校,令到每一次實驗的設置都是百分百相同的,導致我們可以肯定,每一次實驗所面對的,都是「同一個物理系統」;那個「同一個物理系統」,仍然會產生超過一個可能的結果。

簡而言之,即使掌握了一個「量子物理系統」,運作時的所有資料,「隨機性」仍然存在。所以,「量子隨機性」中的「機」字,如果解作「未知」,那些未知因素一定不會是指,該個物理系統的內在設定;「未知」可以指的,就唯有是「外在因素」,即是「環境狀態」。總而言之,「量子物理學」中的「隨機」,可以翻譯成「跟隨環境因素」。

無論是「經典隨機性」,還是「量子隨機性」中的「機」,都可以是指「知識範圍以外」,或者「控制範圍以外」。那符合「機」這個字,在日常生活的用法。

「機」字在日常生活中,廣義是指「因素」,即是「原因元素」,或者「先決條件之一」;而狹義是指「未知因素」,或者「控制範圍以外的因素」。例如,「機會」就是「數個因素的會合」;「機遇」就會「多個因素的相遇」。當你說「有機會」時,你的意思是:

一堆不受你控制的因素,終於會合起來,令你可以完成,主觀期望(已久)的事情。

— Me@2013.08.30

2013.08.31 Saturday (c) All rights reserved by ACHK