《那些古怪又让人忧心的问题》第100期:论Twitter的无穷性(2)

文章目录

Twitter would look like this:

那么Twitter上看起来会是这个样子的:

The messages are relatively long, but there 8217;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 8217;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.

这些消息看上去很长,但其中每一条的信息量只有一点——你所得知的只是某人选择发那条关于马的消息还是关于房子的消息。这本质上就是要么1要么0。虽然字母有许多,但对于一个看懂了语言模式的读者来说,这个语言的每一句话只含有1比特的信息。

This example hints at a very deep idea, which is that information is fundamentally tied to the recipient 8217;s uncertainty about the message 8217;s content and his or her ability to predict it in advance.

这个例子蕴含了一个十分深刻的思想,那就是:信息,是与接收者对于信息内容的不确定性以及他们提前预测的能力息息相关的。

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.

克劳德•香农——他几乎是以一己之力发明了现代信息理论——对于衡量一种语言的信息量有一个十分巧妙的方法。他给一组一组的受试者看普通的英语句子,只不过这些句子被随机在一个地方切断,然后他要求受试者猜出下一个出现的字母是什么。

It 8217;s threatening to flood our town with information!

它威胁用信息把我们村子淹没!

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 .txt ebook, that 8217;s about what you 8217;ll find.

根据猜对的频率——以及严谨的数学分析——香农发现普通的写下来的英语句子的信息量是每个字母1~1.2比特。这意味着一个好的压缩算法能够把ASCII格式的英语文本——这种文本每一个字符占8比特——压缩到原来大小的八分之一。事实上,如果你用一款不错的压缩软件压缩一本txt电子书,你会发现结果基本上就是如此。

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 8217;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.

如果一段文本包含了n比特的信息,那么某种意义上来说这意味着它可以传达2n种不同的信息。这里用到了一些数学技巧(譬如,信息的长度以及“唯一解距离”这个概念),但我们至少可以知道所有有意义的推文的数量级在2(140×1.1)≈2×1046附近,而非之前所说的10200或10800。

Now, how long would it take the world to read them all out?

那么全世界的人把这些都读出来要花多长时间呢?

Reading 2 × 1046 tweets would take a person nearly 1047 seconds. It 8217;s such a staggeringly large number of tweets that it hardly matters whether it 8217;s one person reading or a billion-they won 8217;t be able to make a meaningful dent in the list in the lifetime of the Earth.

朗读2×1046条推文大概需要一个人1047秒的时间,因而朗读完所有推文所需的时间大得惊人,以至于你可以不用纠结是让一个人去读还是让十亿人去读——因为不管是前者还是后者,在地球的有生之年里都不可能读完。

Instead, let 8217;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 8217;ll just go with it.)

所以还是让我们回到那个鸟儿在石头上磨喙的故事吧。假设这只鸟每一千年都会磨掉一小片石头,在它离去的时候会把磨下来的这点儿尘埃颗粒带走。(一只正常的鸟儿磨掉的喙的量恐怕要比它能带走的石头量要多的,不过在现在这种情形下没有什么东西能用正常的思维来衡量,所以就先不管它,接着往下看吧。)

Let 8217;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.

我们不妨假设你每天有16小时在大声朗读推文,而在你身后每一千年都有一只小鸟前来磨掉100英里长的山的微不足道的一小块尘埃。

When the mountain is worn flat to the ground, that 8217;s the first day of eternity.

当最终山被磨平时,永恒才刚过了第一天。

The mountain reappears and the cycle starts again for another eternal day: 365 eternal days-each one 1032 years long-makes an eternal year.

然后这座山又再次出现,然后这个循环继续进行,然后过了永恒的第二天。如此往复365个永恒日——每一个都有1032年这么长——然后一个永恒年才过去。

A hundred eternal years, in which the bird grinds away 36,500 mountains, make an eternal century.

那只小鸟在100个永恒年里磨掉了36500座山,然后一个永恒世纪过去了。

But a century isn 8217;t enough. Nor a millennium.

但一个世纪还不够呢,一个千年还是不够。

Reading all the tweets takes you ten thousand eternal years.

读完所有的推文要花掉你一万个永恒年。

That 8217;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.

这段时间足够你旁观一遍从书写的发明一直到现在的人类的全史了,并且那只小鸟每磨掉一座山,你这里才刚过了一天。

While 140 characters may not seem like a lot, we will never run out of things to say.

140个字符看起来不是很多,不过我们是永远不会无话可说的。

1 It also hints at a very shallow idea about there being a horse in aisle five.

1. 同时也隐约地暗示出五号通道有一匹马。

标签:   发布日期:2024-02-29 05:02:00  投稿会员:Aucao