纽约时报2025年1月3日文章
原文标题：Could Monkeys Really Type All of Shakespeare? Not in this universe, a new study concludes.
作者：Alexander Nazaryan
这篇文章讨论了无限猴子定理，该定理假设给无限数量的猴子无限的时间，每只猴子随机在打字机上敲击，最终可能会偶然间完成威廉·莎士比亚的全部作品。这个想法最早由法国数学家埃米尔·博雷尔在1913年提出。多年来，进行了各种实验和模拟来测试这一理论，包括2003年英国科学家在猴子笼中放置一台电脑，结果是五页主要由字母“S”组成的文本。
最近，悉尼科技大学的数学家斯蒂芬·伍德科克进行的一项研究得出结论，即使给定宇宙的时间也不足以让有限数量的猴子完成哪怕是《好奇的乔治》这样短的作品，更不用说莎士比亚的全部作品了。
研究要点
•The long-established result of the Infinite Monkeys Theorem is correct, but misleading.
无限猴子定理的长期既定结论虽然正确，但具有误导性
•Non-trivial text generation during the lifespan of our universe is almost certainly impossible.
在我们宇宙的寿命内，生成非平凡文本几乎肯定是不可能的
•The Finite Monkeys case shows there will never be sufficient resources to generate Shakespeare.
有限猴子案例表明，永远不会有足够的资源来生成莎士比亚的作品
[Abstract]
The Infinite Monkeys Theorem has long-established the eventual certainty of the complete works of William Shakespeare being reproduced by a monkey randomly pressing keys on a typewriter. This only considers the infinite limit, with either an infinite number of monkeys and/or an infinite time period of monkey labour. Here, we consider the Finite Monkeys Theorem and look at the probability of a given string being typed by one of a finite number of monkeys within a finite time allocation consistent with estimates for the lifespan of our universe. We also calculate the expected number of keystrokes until a target string would first be produced. Given the expected time until the heat death of the universe, we demonstrate that the widely-accepted conclusion from the Infinite Monkeys Theorem is, in fact, misleading in our finite universe. As such, this places the theorem in a class of probabilistic problems or paradoxes, including the St. Petersburg paradox, Zeno’s dichotomy paradox and the Ross–Littlewood paradox wherein the infinite-resource conclusions directly contradict those obtained when considering limited resources, however sizeable.
【原文摘要】无限猴子定理长期以来确立了通过猴子随机按键最终能够重现莎士比亚的全部作品的必然性。这只考虑了无限的情况，即无限数量的猴子和/或无限的时间。然而，本文考虑了有限猴子定理，并研究了在有限数量的猴子和有限的时间内，给定字符串被打出的概率。我们还计算了直到目标字符串首次出现所需的预期按键次数。考虑到宇宙热寂的预期时间，我们证明了无限猴子定理在我们有限的宇宙中实际上是误导性的。因此，这将该定理置于一类概率问题或悖论中，包括圣彼得堡悖论、芝诺二分法悖论和罗斯-利特尔伍德悖论，其中无限资源的结论与考虑有限资源时得到的结论直接矛盾。
了解更多：
原文：A numerical evaluation of the Finite Monkeys Theorem
原文链接https://www.sciencedirect.com/science/article/pii/S2773186324001014?via%3Dihub
