Name: 什麼是非隨機？ (What is NOT Random?)
Uploaded: 2021-01-14T06:42:08.000Z
Duration: 10 min

程度副詞

- What will happen tomorrow is not random. In other words, it's at least somewhat predictable.

明天會發生什麼事並不是完全隨機的 換句話說，至少有些事是可以預測的

I mean, not entirely to be sure, but some things will happen for certain, and other

我的意思至，並不是完全可以預測，但至少有些是必定會發生，而有些事

things definitely won't. For example, the sun will rise, water will still freeze at

絕對不會發生。舉例來說，太陽一定會升起，水仍然會在

- We know this because everything in the universe is made of 12 fundamental particles, and they

我們可以這麼確定是因為 宇宙中的萬物是由12種基本粒子組成

而且它們以4種可以預測的方式彼此互動

- What if I were able to determine the positions and velocities of every single one of these

假設我可以知道宇宙中每一個的粒子的特定位置以及速度

- Well, you would be the intelligence envisioned by Laplace, who thought if you could really

那麼，你就是拉普拉斯設想的全知者，只要你真的可以

figure out where everything is and how fast it's moving, you would know the entire future

知道每個東西的位置以及他們移動的速度，你就能夠預知宇宙的未來

of the universe, because you know how every particle interacts with every other particle.

因為你知道每一個粒子是如何和其他粒子互動 (皮爾．西蒙．拉普拉斯：在那個全知者的眼中，未來和過去一樣都被完整呈現)

- Wow, so nothing would be unpredictable, which means, nothing would be random.

哇，所以沒有什麼事是無法預測的 也就是說，沒有什麼事是隨機的

- Not even human behavior. Since we are made of the same fundamental particles as everything

甚至連人類的行為也不是隨機的 因為我們和宇宙萬物一樣

in the rest of the universe, everything we will ever do, or have ever done, would be

都是由這些基本粒子組成，我們即將做的每一件事，或者已經完成的事，都將被

determined by the information in the state of the universe at any one time.

宇宙任一時刻所蘊涵的資訊(information)決定

- But what is information? Well, it seems to be fundamentally about order. The order

但所謂的「資訊」是什麼？它似乎就是所謂的「排列/次序」(order)

of molecules in your DNA contain the information needed to make you. It is the order of zeros

你的DNA的分子排列包含了所有你的資訊

and ones streaming through the internet that contain all the information required to play

網路上0和1的排列順序蘊含了所有這部影片的資訊

this video. It is the order of letters that makes a word, and the order of words that

字母的排列組成一個單字，而單字的排列

makes a sentence that carries information. So fundamentally, information seems to be

組成一個蘊含資訊句子 所以基本上，資訊看起來

about order. Regularity. That is, until you really think about it. I mean, does every

就是「排列/次序」(order)、「規則」(regularity) 但你真的仔細思考似乎不是這麼一回事，我的意思是

letter of a word carry the same amount of information? No. I mean, after a "Q", you

每一個英文單字的字母所蘊含的資訊量是相同的嗎？ 不是，接在一個Q後面的下一個字母

know almost for certain that the next letter will be a "U". After a "Th", there will probably

你幾乎可以確定會是一個u，在Th後面非常有可能

be an "E". So these letters carry very little information, because you could predict them

會是一個e，所以這些字母事實上具備非常少的訊息 因為你可以預先預測它們

beforehand. They are redundant. In fact, the founder of information theory, Claude Shannon,

它們是冗餘的 事實上，資訊論的奠基者：克勞德．夏農

estimated the redundancy of English at about 75%, which is why we can make sense of things

估計英文中有75%是冗餘的，所以我們可以看得懂

like this. So English can be compressed, because it is not random. It has patterns. Similarly,

這樣子的東西。英文其實是可以被壓縮的，因為它不是完全隨機的，它有特定的形式(pattern)

this video is compressible because of its regularities. In each frame, the pixels of

同樣的，這部影片因為它有規律所以它是可以被壓縮的。每一幀數，相似顏色的

similar color cluster together. Plus, from frame to frame, most of the pixels don't change.

像素可以混在一起 而且大部分的像素並不會隨著幀數改變

So you only need to record the ones that do change.

所以你只需要記錄那些顏色有改變的像素就好了

- You can take advantage of this technique to create some trippy effects known as datamoshing.

運用這個技術你可以創造出奇幻的效果，稱作「資料混雜」(datamoshing)

It's the application of the movement data from one video, to the pixels of another.

它是一種把一部影片的資料 混雜到另一部影片的像素的應用技術

- It also means that an average video can be compressed to just one thousandth of its

這也說明一部影片可以被壓縮到原本大小的

- But what is the most you can compress something?

但一個東西可以被壓縮的極限是什麼？

- Well, anything that is not random, any patters or regularities, can be reduced, because they

只要不是隨機的東西、任何的形式或規律、都是可以被壓縮的，因為他們

are predictable. So you can continue shrinking a file down until what you're left with is

可以被預測。所以你可以不斷壓縮一個檔案，直到剩下的東西是

- And that will contain all of the information of the original item but distilled. Pure information.

而那就是蘊含所有原始檔案資訊的濃縮版本 純粹的資訊

- So pure information is randomness. If you want to know how much information something

所以純粹的資訊竟然是「隨機」 如果你想知道某個東西蘊含多少資訊

contains, you need to know how random it is. And randomness is disorder... What we also

你需要知道它有多麼隨機 而隨機的意思是「混亂/無序」(disorder)，我們又稱作

- So information, fundamentally, is entropy. This makes sense if you consider a string

所以「資訊」根本上指的就是「熵」 這非常合理，以一連串的二進制位碼來說

of binary digits. For example, this string is perfectly ordered. It has very low entropy,

這一串數字非常有秩序的排列，它所蘊含的熵非常少

and it contains no information. That's the state of an erased hard drive. Now, this string

它沒有透露任何資訊，這也是被抹除資訊的硬碟狀態。現在這一串

contains slightly more information, but again, the regularities allow it to be easily compressed.

數字蘊含稍微多一點的資訊，但是它的規律讓它變得容易壓縮

So the string that contains the maximum amount of information is just-- a random set of zeros

因此具有最海量資訊的二進制數字就是0和1的隨機排列

and ones. It has maximum entropy because it's totally disordered. You could not predict

它蘊含最大量的熵 因為它是完全混亂無序的，你無法預測

any of those digits by looking at any of the other digits. And if you wanted to send this

任何位碼，如果你想要把這個資訊

information to someone, you would have no other option but to send the whole string

寄給其他人，你別無選擇的只能把一整串位碼寄給他

of digits. There's no way to compress it. But here's the thing about any object that

沒有任何方法可以壓縮 但是任何具有最大量資訊的東西

contains maximum information. For us as human beings, they carry no meaning. For example,

對於人類來說，它們毫無意義，舉例而言

a video containing maximum information would look like this. It is just white noise. The

一個具有最大量資訊的影片看起來會像這樣 它就是白雜訊

color of each pixel is independent of all the other pixels, and they all change randomly.

每個像素的顏色和其他像素之間毫無關聯 並且隨機轉換顏色

This video could not be compressed, because it's already totally random. Now a random

這段影片無法被壓縮，因為他是完全隨機的 (有注意到影片的畫質變差嗎)

sequence of DNA would not make an organism. And a random string of letters does not generally

一段隨機排序的DNA序列無法構成生命 字母的隨機排列也沒辦法產生一個單字

make a word. We are drawn to things that are neither perfectly ordered, containing no information,

我們感興趣的事 並不是完全的規律/秩序(沒有透露任何資訊)

nor are they perfectly disordered, containing maximum information. Somewhere in the middle,

也不是完全的混亂無序(具有最大量資訊) 而是介於兩者之間

we can recognize complex patterns, and that is where we derive meaning. In music, poetry,

我們可以辨識複雜的形式，而這也是意義的導源 音樂、詩歌

and ideas. It is this search for meaning that leads us to propose scientific theories, which

以及思想 對於意義的探求使我們提出科學理論

if you think about it, are really our way of compressing the universe. For example,

如果你仔細思考，科學理論就是我們壓縮宇宙的方式 舉例而言

general relativity, our current theory of gravity, compresses into one short equation.

廣義相對論(目前關於重力的主流理論)，將重力壓縮成一個簡短的方程式

Everything from how an apple falls to the earth, to how the moon orbits the earth, how

它解釋了蘋果是如何掉落到地面 月亮如何繞著地球轉動

all the planets orbit the sun, how the sun orbits a supermassive blackhole at the center

行星如何繞著太陽運行 太陽如何繞著銀河系中心超巨大黑洞運行

of our galaxy, how blackholes form and behave, and how the whole universe expands out from

黑洞如何形成、有什麼樣的表現 整個宇宙如何從大霹靂後不斷擴張

the Big Bang. Now that we have this theory, the future is more predictable. I mean, we

現在我們有廣義相對論，使得未來變得更可以預測 舉例來說，我們可以

can predict eclipses thousands of years into the future. So, with all of our scientific

預測千年後的日蝕現象 所以，有了這些科學理論

theories, does that mean that the universe is completely not random? That it is perfectly

是不是代表整個宇宙完全不是隨機的呢？ 是不是代表整個宇宙完全可以

predictable? Well, let's assume for a second that Laplace was right, and that knowing the

預測呢？我們先假設拉普拉斯是對的 只要知道

state of the universe at any one time, means you also know its state at every other time

宇宙任一時間也的狀態，你就可以知道其他時間的狀態

as well. Well, that would mean that the information in our universe would be constant. But if

這也代表了宇宙的資訊量是固定的

information is entropy, that would mean the entropy of the universe is also constant.

但如果資訊是熵，那也代表了宇宙中的熵是恆定的

And that does not appear to be the universe that we live in. The second law of thermodynamics

但這不是我們所觀測到的宇宙 熱力學第二運動定律告訴我們

states that entropy in the universe increases with time. Or in other words, things don't

宇宙中的熵隨著時間的過去會不斷增加 換句話說，攪拌一杯水的時候

stir themselves apart. But if entropy is going up, that means the information in our universe

物質不會因攪拌而分開 如果熵只會越來越大，那表示我們宇宙的資訊

is constantly increasing. That makes sense, because it would take more information to

是不斷增加的，這其實非常合理 因為要釐清宇宙現在的狀態

specify the state of the universe now, than right after the Big Bang. So, where is this

會比大霹靂之後沒多久的狀態需要更多資訊 那麼這些新資訊

new information coming from? My best bet is quantum mechanics. Quantum mechanics describes

是從哪來的呢？我想應該是量子力學 量子力學描述

how the 12 fundamental particles behave. And as spectacularly successful as it is, it is

12種基本粒子如何表現 而最令人驚豔的是：它是一個

only a probabilistic theory. Meaning that you cannot predict with absolute certainty

機率性的理論，也就是說你無法準確 預測一個電子

where an electron, say, will be at some later time. You can only calculate probabilities

在確切時間會出現在哪個確切的位置 你只能計算你最可能在哪裡

of where you are likely to find it. So when you do interact with it, and locate the electron

找到那個電子的機率 所以當你和它有接觸而確認電子的位置時

at a particular point, you have gained information. You now know something that you couldn't have

你就獲得了全新的資訊，你知道了一些你本來

predicted with certainty beforehand. This drove Einstein crazy. He said, "God does not

絕對無法預先預測的資訊 這令愛因斯坦非常抓狂，他曾經說過

play dice," referring to this. I mean, he wished that we could compress our theory of

「上帝不擲骰子」，就是在說這件事 他希望我們可以再把量子力學

quantum mechanics further, so that we could really figure out where these particles were

的理論更加壓縮，這麼一來我們就可以真正知道這些粒子到底會出現在哪裡

going to be. But maybe the reason why we haven't been able to compress quantum mechanics further,

但或許我們無法繼續壓縮量子力學理論的原因是

is because fundamentally, it's random. Fundamentally, new information is being generated every time

量子力學根本上是隨機的 基本上，只要量子事件發生

a quantum event like that occurs. In that case, it could be these quantum measurements

新的資訊就會不斷的產生，在這種想法之下 量子測量就是

which are driving up the entropy of the universe. They are creating new information all of the

導致宇宙中的熵增加的原因 他們不斷製造宇宙中新的資訊

time, and that means the disorder in our universe must go up. This is what we observe as the

這也意味著宇宙中的混亂與無序一定會增加 這也是我們所觀察到的

second law of thermodynamics. You know, we often think about the second law as a curse.

熱力學第二定律 我們常常以為第二定律是一個詛咒

As though everything which is ordered is going towards disorder. But maybe, I mean, it's

因為所有井然有序的事物都註定走向混亂 但或許，只有在遵守第二定律

only in a universe where this law is obeyed, that the truly unexpected can occur. That

的宇宙，才有辦法發生那些無法預期的事情

the future can be actually undetermined. For us really to have free will, we need the second

未來無法完全被預測 如果人類要擁有決定未來的自由意志，那麼我們

law of thermodynamics. Now, you might think that these quantum events are too small to

就會需要熱力學第二定律 你可能會以為這些量子事件太過微小

have any meaningful impact on the evolution of the universe, but that is not true. And

以至於對於宇宙的演化沒有辦法產生深遠的影響 但這並不是真的

that's because, there are physical systems which are so dependent, so sensitive to the

因為有些物理系統對於初始狀態非常敏感