科学家往动物园扔了一个键盘，6只猴子用它写了一本书
Scientists threw a keyboard into the zoo, and 6 monkeys used it to write a book
Length: • 1 min
Annotated by howie.serious
图片来源：New York Zoological Society - Public Domain
猴子进化成莎士比亚的可能性都比猴子打出《哈姆雷特》的可能性大。
The possibility of a monkey evolving into Shakespeare is greater than the possibility of a monkey typing out "Hamlet."
撰文 | 冬鸢 Written by | Dong Yuan
审校 | 王昱 Proofread by | Wang Yu
“钢琴只有88个琴键，但你却能用它创作出无限的音乐。”这是经典电影《海上钢琴师》中的一句台词。每次重温这部电影，都会被这句台词吸引，因为它阐述了我们可以在有限元素中创造出无限种可能。
"A piano has only 88 keys, but you can use it to create infinite music." This is a line from the classic film "The Legend of 1900." Every time I revisit this movie, I am drawn to this line because it explains how we can create infinite possibilities from finite elements.
以书籍为例，人类史上有数不胜数的诗歌、散文、戏剧、小说……如果把所有现存文学作品都翻译成英文，那你会发现它们都只是26个英文字母的不同排列组合而已。
Take books as an example. Throughout human history, there have been countless poems, essays, plays, novels... If you translate all existing literary works into English, you will find that they are merely different permutations of the 26 English letters.
如果你对科幻感兴趣，那你大概听说过一个很有名的理论——
If you are interested in science fiction, you have probably heard of a famous theory—the "infinite monkey theorem." This theory suggests that if you give a monkey infinite time to sit in front of a typewriter and type continuously, or if you have infinite monkeys typing randomly on infinite typewriters, then although the monkeys do not understand human language, they could eventually type out every possible combination of letters, including all of Shakespeare's works, such as "Hamlet."
图片来源：pixabay Image source: pixabay
一些人认为，“无限猴子理论”最早于1860年出现在英国牛津大学的一场辩论中，达尔文坚定的支持者托马斯·亨利·赫胥黎（Thomas Henry Huxley）在与进化论反对者激烈辩论时首次提出了这个理论。不过更多人认为“无限猴子理论”最早出现在数学家埃米尔·博雷尔（Émile Borel）1913年发表的论文中。
Some people believe that the "infinite monkey theorem" first appeared in a debate at Oxford University in 1860, when Thomas Henry Huxley, a staunch supporter of Darwin, proposed the theory during a heated debate with opponents of evolution. However, more people believe that the "infinite monkey theorem" first appeared in a paper published by mathematician Émile Borel in 1913.
其中的思想出现的时间更早，亚里士多德时期此类说法就出现了。古
The idea appeared even earlier, during the time of Aristotle. The Roman philosopher and politician Cicero once wrote, "If a large number of letters made of gold or other materials are randomly thrown on the ground, they could possibly arrange themselves into a classic epic."
看似不可能发生的事，只要它的概率不是绝对的0，那么只要尝试无限多次，它几乎一定会发生。
Events that seem impossible, as long as their probability is not absolutely zero, will almost certainly happen if attempted an infinite number of times.
一千亿次，几乎一定能得到香蕉 A hundred billion times, it's almost certain to get a banana
当一只猴子在打字机上随意打6个字母，那么它偶然打出“香蕉”（banana）一词的概率小到几乎为0。
When a monkey randomly types 6 letters on a typewriter, the probability of it accidentally typing the word "banana" is almost zero.
一台打字机通常有44到47个键不等，假如我们给猴子用的打字机键盘有44个键，那么猴子每随机按下去一个键，都有44种可能性。它打出第一个字母是“b”的可能性是1/44，假设每个字母之间不互相影响，那么它连续打出6个字母，刚好是“banana”的概率就是(1/44)6，结果大概是0.0000000001378，概率相当低，四舍五入约等于0。反过来，它没有打出“banana”的概率是1-(1/44)6，约为0.99999999986，十分接近于1。
A typewriter usually has between 44 to 47 keys. If we assume the typewriter keyboard used by the monkey has 44 keys, then each time the monkey randomly presses a key, there are 44 possibilities. The probability of it typing the first letter as "b" is 1/44. Assuming each letter is independent, the probability of it typing 6 letters in a row to form "banana" is (1/44)^6, which is approximately 0.0000000001378, a very low probability, rounding to about 0. Conversely, the probability of it not typing "banana" is 1-(1/44)^6, approximately 0.99999999986, very close to 1.
图片来源：unsplash+ Image source: unsplash+
但如果我们让这只猴子多尝试几次，情况好像就不一样了。我们假设猴子打字n次，每次打6个字，那么它没有打出“香蕉”这个词的概率是[1-(1/44)6]n。稍微有一点数学基础的朋友很快就会意识到，当n越来越大时，猴子没有打出“香蕉”概率就越来越接近0（打出“香蕉”的概率也越来越接近1）。比如，我们让猴子打6个字母，重复一千亿次，即n=1011，则它没有打出“香蕉”的概率约为0.000001035。在这种情况下，猴子打出至少一次“banana”几乎是必然发生的事。
But if we let the monkey try a few more times, the situation seems different. Let's assume the monkey types n times, typing 6 letters each time, then the probability of it not typing the word "banana" is [1-(1/44)^6]^n. Those with a bit of mathematical background will quickly realize that as n becomes larger, the probability of the monkey not typing "banana" gets closer to 0 (the probability of typing "banana" gets closer to 1). For example, if we let the monkey type 6 letters, repeating a hundred billion times, i.e., n=10^11, the probability of it not typing "banana" is about 0.000001035. In this case, the monkey typing "banana" at least once is almost inevitable.
2011年，一位叫做杰西·安德森（Jesse Anderson）的软件工程师通过JAVA代码模拟了这个过程，他让电脑中的100万只虚拟“猴子”每次随机敲出9个字母，如果这9个字母能对得上莎士比亚文章里的词，就保留，如果对不上，就抛弃。这些虚拟“猴子”花了不到两个月的时间，就打出了莎士比亚所有作品中的所有文字。
In 2011, a software engineer named Jesse Anderson simulated this process using JAVA code. He had 1 million virtual "monkeys" on a computer randomly type 9 letters at a time. If these 9 letters matched words in Shakespeare's works, they were kept; if not, they were discarded. These virtual "monkeys" took less than two months to type out all the words in all of Shakespeare's works.
直到宇宙的尽头，猴子也打不出莎士比亚 Until the end of the universe, monkeys will not be able to type out Shakespeare.
“无限猴子理论”蕴含的核心思想可以归纳为：当我们尝试无限多次，就算一件事只存在那么一丝丝的可能性，也必然会发生。
The core idea contained in the "infinite monkey theorem" can be summarized as: if we try infinitely many times, even if there is only a tiny possibility of something happening, it will inevitably occur.
但是，我们真的可以尝试无限次吗？ However, can we really try infinitely many times?
上述探讨的情况，仅仅是让猴子一次性打出6个或9个字母的情况，那如果要让猴子一口气打出整部《哈姆雷特》呢？《哈姆雷特》全文大概有130000个字母，这次我们降低难度，假设打字机上只有26个英文字母，不去管标点、空格之类的。那么猴子随机打130000个字母，恰好打出完整的《哈姆雷特》的概率是26130000，换句话说，大概每3.4×10183946次，猴子才能成功打出1次《哈姆雷特》。
The situation discussed above is merely about monkeys typing 6 or 9 letters at a time. But what if we want the monkeys to type out the entire "Hamlet" in one go? The full text of "Hamlet" contains about 130,000 letters. This time, we lower the difficulty by assuming there are only 26 English letters on the typewriter, ignoring punctuation, spaces, and the like. The probability of monkeys randomly typing 130,000 letters and coincidentally typing the complete "Hamlet" is 26^130000. In other words, monkeys would succeed in typing "Hamlet" once every approximately 3.4×10^183,946 times.
我难以向你们描述3.4×10183946这个数字到底有多大，因为在我们可观测的宇宙中，原子总数才只有1080的量级。
I find it difficult to describe to you how large the number 3.4×10 183946 really is, because the total number of atoms in our observable universe is only on the order of 10 80 .
因此，尽管“无限猴子”理论描述了一种关于无限的浪漫思想实验，但许多科学家仍然在思考一个问题，在宇宙终结之前，猴子到底能不能“创作”出打出莎士比亚的所有作品？
Therefore, although the "infinite monkey" theorem describes a romantic thought experiment about infinity, many scientists are still pondering a question: before the end of the universe, can the monkeys "create" and type out all of Shakespeare's works?
图片来源：pixabay Image source: pixabay
关于我们的宇宙何时、会以何种方式终结，有理论认为宇宙膨胀速度会因引力而减慢和逆转，最终坍缩回致密状态；也有理论认为暗能量可能随着时间的推移变得愈加强烈，最终甚至会撕裂宇宙中的所有原子。
Regarding when and how our universe will end, some theories suggest that the expansion of the universe will slow down and reverse due to gravity, eventually collapsing back into a dense state; other theories propose that dark energy may become increasingly intense over time, eventually tearing apart all atoms in the universe.
最广为接受的是宇宙热寂说（heat death of the Universe），即如果暗能量继续加速宇宙膨胀，星系、恒星和黑洞最终将被隔离在冰冷、黑暗的宇宙中。在数万亿年的时间里，恒星会燃烧殆尽，甚至黑洞也会通过霍金辐射蒸发掉，只剩下稀薄的粒子汤。
The most widely accepted theory is the heat death of the Universe, which suggests that if dark energy continues to accelerate the expansion of the universe, galaxies, stars, and black holes will eventually be isolated in a cold, dark universe. Over trillions of years, stars will burn out, and even black holes will evaporate through Hawking radiation, leaving only a thin soup of particles.
有科学家估计，在宇宙热寂说下，宇宙的寿命还剩10100年。于是，在上个月发表在Franklin Open上的一片论文中，数学家斯蒂芬·伍德科克（Stephen Woodcock）和杰伊·法利塔（Jay Falletta）就计算了一下，实际情况中，猴子是否真的可以在我们的宇宙10100的寿命中，通过不断地次敲击键盘，随机打出莎士比亚的作品。
Some scientists estimate that under the heat death theory of the universe, the universe has 10 100 years left. Thus, in a paper published last month in Franklin Open, mathematicians Stephen Woodcock and Jay Falletta calculated whether, in reality, monkeys could indeed randomly type out Shakespeare's works by continuously hitting keys on a keyboard during the 10 100 lifespan of our universe.
他们假设打字机有30个键，包括了所有的英文字母和必要的标点符号。他们假设地球上现存所有的黑猩猩以每秒敲击一次键盘的速度一刻不停地打字。那么，它们打出全部莎士比亚作品（大概总共884647字）大约需要敲击键盘107448366次，在宇宙热寂之前完成的概率只有约6.4×10-7448254。就算研究者增加黑猩猩的数量和它们打字的速度，当它们成功打出莎士比亚的作品时，我们的宇宙也早就不知道灭亡多少次了。
They assumed the typewriter has 30 keys, including all the English letters and necessary punctuation marks. They assumed that all the chimpanzees currently existing on Earth type continuously at a speed of one keystroke per second. To type out all of Shakespeare's works (approximately 884,647 words) would require about 10 7448366 keystrokes, and the probability of completing this before the heat death of the universe is only about 6.4×10 -7448254 . Even if researchers increase the number of chimpanzees and their typing speed, by the time they successfully type out Shakespeare's works, our universe would have perished countless times.
横坐标表示对应作品的文字数的对数，纵坐标表示宇宙寿命的对数的对数（图片来源：Woodcock & Falletta, 2024）。
The horizontal axis represents the logarithm of the number of words in the corresponding works, and the vertical axis represents the logarithm of the logarithm of the universe's lifespan (Image source: Woodcock & Falletta, 2024).
现实终究不是无限的 Reality is ultimately not infinite.
在现实生活中，也有研究者曾试图通过真实的实验来验证“无限猴子理论”。2002年，英国普利茅斯大学的几位研究者在一家动物园中生活了6只猴子的圈舍中放置了一个电脑键盘，让这6只猴子自由敲击键盘，看最终会得到什么有趣的结果。实验从当年的5月1日开始，但在大多数时间里，这些猴子貌似只把这个键盘当作公共厕所，不断在上面撒尿，偶尔会敲击一下键盘。实验只持续了7周，6月22日，键盘被一只猴子暴力破坏，实验被迫结束。
In real life, there have been researchers who attempted to verify the "infinite monkey theorem" through actual experiments. In 2002, several researchers from the University of Plymouth in the UK placed a computer keyboard in the enclosure of six monkeys living in a zoo, allowing these monkeys to freely hit the keys to see what interesting results might be obtained. The experiment began on May 1st of that year, but for most of the time, the monkeys seemed to treat the keyboard as a public toilet, urinating on it continuously and occasionally hitting the keys. The experiment lasted only 7 weeks, and on June 22nd, the keyboard was violently destroyed by one of the monkeys, forcing the experiment to end.
猴子们一共打出了5页纸，其中大部分都是字母“S”，掺杂着些许其他字母。研究者最终将这5页纸内容装订成册，做成一本书出版了，作者一栏写上了6只猴子的名字。
The monkeys typed a total of 5 pages, most of which were the letter "S", interspersed with a few other letters. The researchers eventually bound the contents of these 5 pages into a book and published it, listing the names of the 6 monkeys as the authors.
当你拥有无限多的时间，一切几乎不可能都能成为几乎必然。然而宇宙的寿命很可能不是无限的，猴子不可能在打字机前打字到永远，我们的时间也都是有限的。人生太短，来不及去体验所有种随机可能，错过的东西或许永远无法再找回，所以只能倍加珍惜眼前的人和事，享受每一刻仍然拥有的光阴。
When you have an infinite amount of time, almost anything impossible can become almost inevitable. However, the lifespan of the universe is likely not infinite, and monkeys cannot type at a typewriter forever, and our time is also limited. Life is too short to experience all kinds of random possibilities, and what is missed may never be found again, so we can only cherish the people and things in front of us and enjoy every moment of the time we still have.
参考链接： Reference link:
https://www.sciencedirect.com/science/article/pii/S2773186324001014?via%3Dihub#bib0014
https://www.scientificamerican.com/article/the-mathematical-case-for-monkeys-producing-shakespeare-eventually/
https://rss.onlinelibrary.wiley.com/doi/full/10.1111/j.1740-9713.2011.00533.x
https://www.scientificamerican.com/article/does-pi-contain-all-of-shakespeare/
https://arxiv.org/pdf/2402.16253
http://news.bbc.co.uk/1/hi/3013959.stm
https://web.archive.org/web/20090318143423/http:/www.vivaria.net/experiments/notes/publication/NOTES_EN.pdf
https://arxiv.org/pdf/2402.16253
https://en.wikipedia.org/wiki/Infinite_monkey_theorem
https://iopscience.iop.org/article/10.1086/308434#skip-to-content-link-target
https://en.wikipedia.org/wiki/Ultimate_fate_of_the_universe
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