《那些古怪又讓人憂心的問題》第100期:論Twitter的無窮性(2)
Twitter would look like this:
The messages are relatively long, but there's not a lot of information in each one-All they tell you is whether the person decided to send the trap message or the horse message. It's effectively a 1 or a 0. Although there are a lot of letters, for a reader who knows the pattern of the language, each tweet carries only one bit of information per sentence.
這些訊息看上去很長，但其中每一條的資訊量只有一點——你所得知的只是某人選擇發那條關於馬的訊息還是關於房子的訊息。這本質上就是要麼1要麼0。雖然字母有許多，但對於一個看懂了語言模式的讀者來說，這個語言的每一句話只含有1位元的資訊。This example hints at a very deep idea, which is that information is fundamentally tied to the recipient's uncertainty about the message's content and his or her ability to predict it in advance.
這個例子蘊含了一個十分深刻的思想，那就是：資訊，是與接收者對於資訊內容的不確定性以及他們提前預測的能力息息相關的。
Claude Shannon-who almost singlehandedly invented modern information theory-had a clever method for measuring the information content of a language. He showed groups of people samples of typical written English that were cut off at a random point, then asked them to guess which letter came next.
克勞德•夏農——他幾乎是以一己之力發明了現代資訊理論——對於衡量一種語言的資訊量有一個十分巧妙的方法。他給一組一組的受試者看普通的英語句子，只不過這些句子被隨機在一個地方切斷，然後他要求受試者猜出下一個出現的字母是什麼。It's threatening to flood our town with information!
它威脅用資訊把我們村子淹沒！Based on the rates of correct guesses-and rigorous mathematical analysis-Shannon determined that the information content of typical written English was 1.0 to 1.2 bits per letter. This means that a good compression algorithm should be able to compress ASCII English text-which is 8 bits per letter-to about ⅛th of its original size. Indeed, if you use a good file compressor on a ebook, that's about what you'll find.
根據猜對的頻率——以及嚴謹的數學分析——夏農發現普通的寫下來的英語句子的資訊量是每個字母1～1.2位元。這意味著一個好的壓縮演算法能夠把ASCII格式的英語文字——這種文字每一個字元佔8位元——壓縮到原來大小的八分之一。事實上，如果你用一款不錯的壓縮軟體壓縮一本txt電子書，你會發現結果基本上就是如此。If a piece of text contains n bits of information, in a sense it means that there are 2n different messages it can convey. There's a bit of mathematical juggling here (involving, among other things, the length of the message and something called “unicity distance”), but the bottom line is that it suggests there are on the order of about 2140 × 1.1 ≈ 2 × 1046 meaningfully different English tweets, rather than 10200 or 10800.
如果一段文字包含了n位元的資訊，那麼某種意義上來說這意味著它可以傳達2n種不同的資訊。這裡用到了一些數學技巧（譬如，資訊的長度以及“唯一解距離”這個概念），但我們至少可以知道所有有意義的推文的數量級在2（140×1.1）≈2×1046附近，而非之前所說的10200或10800。Now, how long would it take the world to read them all out?
那麼全世界的人把這些都讀出來要花多長時間呢？Reading 2 × 1046 tweets would take a person nearly 1047 seconds. It's such a staggeringly large number of tweets that it hardly matters whether it's one person reading or a billion-they won't be able to make a meaningful dent in the list in the lifetime of the Earth.
朗讀2×1046條推文大概需要一個人1047秒的時間，因而朗讀完所有推文所需的時間大得驚人，以至於你可以不用糾結是讓一個人去讀還是讓十億人去讀——因為不管是前者還是後者，在地球的有生之年裡都不可能讀完。Instead, let's think back to that bird sharpening its beak on the mountaintop. Suppose that the bird scrapes off a tiny bit of rock from the mountain when it visits every thousand years, and it carries away those few dozen dust particles when it leaves. (A normal bird would probably deposit more beak material on the mountaintop than it would wear away, but virtually nothing else about this scenario is normal either, so we'll just go with it.)
所以還是讓我們回到那個鳥兒在石頭上磨喙的故事吧。假設這隻鳥每一千年都會磨掉一小片石頭，在它離去的時候會把磨下來的這點兒塵埃顆粒帶走。（一隻正常的鳥兒磨掉的喙的量恐怕要比它能帶走的石頭量要多的，不過在現在這種情形下沒有什麼東西能用正常的思維來衡量，所以就先不管它，接著往下看吧。）Let's say you read tweets aloud for 16 hours a day, every day. And behind you, every thousand years, the bird arrives and scrapes off a few invisible specks of dust from the top of the hundred-mile mountain with its beak.
我們不妨假設你每天有16小時在大聲朗讀推文，而在你身後每一千年都有一隻小鳥前來磨掉100英里長的山的微不足道的一小塊塵埃。When the mountain is worn flat to the ground, that's the first day of eternity.
當最終山被磨平時，永恆才剛過了第一天。The mountain reappears and the cycle starts again for another eternal day: 365 eternal days-each one 1032 years long-makes an eternal year.
然後這座山又再次出現，然後這個迴圈繼續進行，然後過了永恆的第二天。如此往復365個永恆日——每一個都有1032年這麼長——然後一個永恆年才過去。A hundred eternal years, in which the bird grinds away 36,500 mountains, make an eternal century.
那隻小鳥在100個永恆年裡磨掉了36500座山，然後一個永恆世紀過去了。But a century isn't enough. Nor a millennium.
但一個世紀還不夠呢，一個千年還是不夠。Reading all the tweets takes you ten thousand eternal years.
讀完所有的推文要花掉你一萬個永恆年。That's enough time to watch all of human history unfold, from the invention of writing to the present, with each day lasting as long as it takes for the bird to wear down a mountain.
這段時間足夠你旁觀一遍從書寫的發明一直到現在的人類的全史了，並且那隻小鳥每磨掉一座山，你這裡才剛過了一天。While 140 characters may not seem like a lot, we will never run out of things to say.
140個字元看起來不是很多，不過我們是永遠不會無話可說的。1 It also hints at a very shallow idea about there being a horse in aisle five.
1． 同時也隱約地暗示出五號通道有一匹馬。
