The language of Change

Posted on by

Energy conservation, 6 | Energy 5

.

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

.

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

.

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

.

.

2018.02.15 Thursday (c) All rights reserved by ACHK

機遇再生論 1.6

Posted on by

.

…

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 N = 52! \approx 8.07 \times 10^{67} 個，可能的排列。亦即是話，洗牌後仍然是排列 A 的機會率，只有 \frac{1}{N}。

由於分母 N 太大（相當於 8 之後，還有 67 個位），洗牌後，理應變成另外一個排列 B 。

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

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

洗了一次牌後，發覺排列是 B 不是 A 後，我們可以再問，如果再洗一次牌，「是 A」和「不是 A」的機會，分別是多少？

.

由於，機會率只是與未知的事情有關，或者說，已知的事件，發生的機會率必為 1；所以，如果發生了第一次洗牌，而你又知道其結果的情況下，問「如果再洗一次牌，『是 A』和『不是 A』的機會，分別是多少」，第二次洗牌各個可能結果，發生的機會率，與第一次洗牌的結果無關。

第二次洗牌結果為組合 A 的機會率，仍然是

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

—

不是組合 A 的機會率，仍然是

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

.

(問：那樣，為什麼要問多一次呢？）

我是想釐清，我真正想問的是，並不是這個問題，而是另一個：

如果在第一次洗牌之前，亦即是話，一次牌都未洗的話，問：

「如果洗牌兩次，起碼一次洗到原本排列 A 的機會率是多少？」

把該事件標示為 A_2：

A_2 = 兩次洗牌的結果，起碼一次洗到原本排列 A

再把該事件的機會率，標示為 P(A_2)。

由於 P(A_2) 相對麻煩，我們可以先行運算其「互補事件」的機會率。

A_2 的互補事件為「不是 A_2」：

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

其機會率為

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

那樣，我們就可推斷，

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

.

同理，在一次牌都未洗的時候，問：

如果洗牌 m 次，起碼一次洗到原本排列 A 的機會率是多少？

答案將會是

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

留意，N = 52! \approx 8.07 \times 10^{67}，非常之大，導致 (1 - \frac{1}{N}) 極端接近 1。在一般情況，m 的數值還是正常時， P(A_m) 會仍然極端接近 0。

例如，你將會連續洗一千萬次牌（m = 10,000,000），起碼有一次，回到原本排列 A 的機會是：

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

你用一般手提計算機的話，它會給你 0。你用電腦的話，它會給你

1.239799930857148592 \times 10^{-61}

…

— Me@2018-01-25 12:38:39 PM

.

.

2018.02.13 Tuesday (c) All rights reserved by ACHK

Riemann Surfaces

Posted on by

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

.

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

https://web.archive.org/web/20170714105446/https://www.youtube.com/watch?v=T647CGsuOVU

— Me@2018-02-12 02:14:51 PM

.

.

2018.02.12 Monday (c) All rights reserved by ACHK

Eyes on me

Posted on by

dziungles 14 days ago

Hey, this is really cool to see natural eyesight topic on the hacker news.
I practice this for more than 10 years. Each day I work with computer for ~10 h., drive a car and do other things, and never wear glasses, even though the traditional ophtalmologic measures clearly indicate that I need strong glasses and I shouldn’t see even the biggest letter on the Snellen chart, but I see not only the biggest, but sometimes even the 20/20.

Doctors can’t explain this, and only congrats me on my achievement. Of course, the eyesight is not perfect. I see clearly in the daytime, but in the nighttime or low light conditions it becomes much harder to distinguish faces.

The best book I found so far is “Relearning to See” by Thomas R. Quackenbush. The originator of this theory was William Bates.

Actually, there is no clear unified theory on how to achieve this. Everyone interprets it differently and the results are inconsistent. There is also a lot of criticism from the medical establishment.

Natural eyesight improvement really works. And the unified theory, in a form of an app, or a good book, maybe including findings from neuroplasticity, would be a great gift for humanity.

.

bsder 14 days ago

Natural eyesight improvement really works. And the unified theory, in a form of an app, or a good book, maybe including findings from neuroplasticity, would be a great gift for humanity.

It SORT OF works in stable and predictable situations.

What seems to be happening is that your brain, in all of its neuroplastic glory, is learning to make better inferences from the broken information it receives.

The issue is that this works as long as the inferences are correct. That’s fine when you are reading a newspaper, using the computer, etc. as the situation is stable and predictable.

The problem is that when you are suddenly confronted by a situation where the inferences are NOT correct–such as a nighttime emergency situation while driving. Now you are relying on the “uninferenced” data coming in from your eyes and that data is subpar with all the resultant problems.

The best solution is both: fix the data coming in with corrective lenses for unpredictable situations, and train your brain to make better inferences so you can deal with predictable situations better.

.

dziungles 14 days ago

Before, I also had this theory in my mind for a year or so.
But for example, right now I’m in Thailand, traveling here for the first time. Everything is new, unfamiliar and unpredictable, daytime, nightime. I have no problems seeing things, everything is almost perfectly clear and sharp. I needed some time to adapt to a smaller screen of my laptop (I was using 24 inch before), but now I’m doing fine.

Actually, the more you look, the better you see. Like in Aaron Swartz blog post, if you want to retrain your weak legs, you need to walk more. Same with eyes.

https://web.archive.org/web/20180204094207/https://news.ycombinator.com/item?id=16194580

.

.

2018.02.09 Friday ACHK

Logical arrow of time, 6.2

Posted on by

Source of time asymmetry in macroscopic physical systems

Second law of thermodynamics

.

.

Physics is not about reality, but about what one can say about reality.

— Bohr

— paraphrased

.

.

Physics should deduce what an observer would observe,

not what it really is, for that would be impossible.

— Me@2018-02-02 12:15:38 AM

.

.

1. Physics is about what an observer can observe about reality.

2. Whatever an observer can observe is a consistent history.

observer ~ a consistent story

observing ~ gathering a consistent story from the quantum reality

3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.

4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.

Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.

5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.

— Me@2018-02-02 10:25:05 PM

.

.

.

2018.02.03 Saturday (c) All rights reserved by ACHK

War and Peace

Posted on by

Is peace better than war?

…

Peace is acceptance of the status quo

You cannot answer the question of whether peace is better than war without reference to the status quo. Preserve peace is another way of saying accept the status quo. Accepting the status quo is OK only if the status quo is acceptable. Sometimes, it is not.

Diplomacy is meaningless unless it is backed by potential use of force.

…

Nations negotiate diplomatically to prevent war. Were there no threat of war behind international negotiations, each side could just say “No” to the other forever …

…

Objecting to all wars is not an option for anyone unless the objector is protected by someone who does not object to all wars. No one should be willing to risk his life for such people.

https://web.archive.org/web/20180130120844/https://johntreed.com/blogs/john-t-reed-s-blog-about-military-matters/68514755-is-peace-better-than-war

— Is peace better than war?

— John Reed

.

.

.

2018.01.30 Tuesday ACHK

Slow down

Posted on by

You need to slow down, in order to enjoy NOW-HERE.

— Me@2018-01-24 08:15:35 PM
 
 
 
2018.01.25 Thursday (c) All rights reserved by ACHK

Utopia

Posted on by

何有之鄉
 
 
d_2018_01_23__21_48_52_PM_

So why bother with all this pessimism?

Because at their heart, dystopias
are cautionary tales,

not about some particular government
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

I AM

Posted on by

無額外論 5
 
 
“God” is your self at the farthest future.

That’s why we are all becoming gods.

— Me@2018-01-12 7:08 PM
 
 
Cooper : Did it work?

TARS : I think it might have.

Cooper : How do you know?

TARS : Because, the bulk beings are closing the tesseract.

Cooper : Don’t you get it yet, TARS? They’re not *beings*… they’re us! What I’ve been doing for Murph, they’re doing for me, for all of us.

TARS : Cooper, people couldn’t build this.

Cooper : No. No, not yet. But one day. Not you and me, but a people, a civilization that’s evolved beyond the four dimensions we know.

[the tesseract closes around him in a brilliant flash of light]

Cooper : What happens now?

[he sees the Endurance on its flight through the wormhole, touches Brand’s hand through the space-time distortion]

— Interstellar (film)
 
 
 
2018.01.14 Sunday (c) All rights reserved by ACHK