The Infinite Monkey Theorem

The Infinite Monkey Theorem

Picture a monkey sitting in a chair with a typewriter. Now, imagine an infinite number of monkeys in the same position. Done? Okay. We’ve set the stage for the Infinite Monkey Theorem.

The Infinite Monkey Theorem states that, given an infinite amount of time, an infinite number of monkeys with an infinite quantity of typewriters will randomly hit the keys in such a way that they will write all the works of Shakespeare.

chimpanzee_seated_at_typewriter             shake

If you don’t understand or believe this, think about it. It’s a simple statistics problem. While the chance of the monkeys typing the works of Shakespeare is very, very, VERY low, it is still possible. And, given an infinite number of monkeys with an infinite amount of time, it is bound to happen eventually. It is called “accidental excellence.” There are proofs for this, but I won’t describe them here. If you want to see the proofs, you can click here. Unfortunately, it is impossible to test this theorem in real life, for obvious reasons.

Opponents of this theorem have their own arguments, however. Some state that literature is art, and monkeys cannot produce art because they are not intelligent animals like humans. Others say that even if the monkeys somehow type the works of Shakespeare, it will not count because they did not type it intentionally. Well, in response to this, I agree with Nelson Goodman:  “That the monkey may be supposed to have produced his entire copy randomly makes no difference. It is the same text, and it is open to all the same interpretations…”

This theorem does, of course, have its variants. The monkeys could type anything, not just the works of Shakespeare (although that is the target text most commonly used). So, you could say that the monkeys would eventually type the entire Harry Potter series, if you’re a Potterhead like me. And, in a simplified experiment, instead of having all 26 letters of the alphabet, the keyboard only has two keys – 1 and 0. Thus, the numbers that the monkey types can be part of an infinitely long string of binary, and can be decoded into words.

So, what’s the point of this theorem, anyway? Good question. Well, this theorem can be applied to many subjects (besides statistics). The first one that comes to mind is a random document generator. On the internet, there are many applications for choosing something randomly- a number, a name, etc. This theorem uses the same idea. Also, the theorem is a part of evolution. Scientists and evolutionary biologists, like Richard Dawkins, use this as an example to prove that natural selection can cause numerous, random mutations to occur and cause favorable traits in organisms.

Well, that’s all for this post. Thanks for reading, and I hope you learned something new!

monkeys-and-typewriters

Sources:

  • “Infinite Monkey Theorem.” Wikipedia. Wikimedia Foundation, 20 May 2017. Web. 23 May 2017.
  • “Proof of Infinite Monkey Theorem.” Probability – Proof of Infinite Monkey Theorem. – Mathematics Stack Exchange. N.p., n.d. Web. 23 May 2017.
  • Babu_Kurra. “This Is What the Infinite Monkey Theorem Looks Like in Real Life.” Wired. Conde Nast, 03 Dec. 2013. Web. 23 May 2017.
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15 thoughts on “The Infinite Monkey Theorem

  1. Your post made me smile! I think your blog is very interesting, and I like how you add your personal voice to each of your posts. I like the picture of the monkey at the top and the attached link explaining the statistics about the theory.

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    1. I’m glad my post made you smile! I thought this theorem was pretty cool (and weird) when I first read about it, and I wanted to share it with other people. I glad you learned something new. I try to add my humor to my posts. Thanks for reading!

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  2. I really liked this post and found it hilarious. For math geeks (or nerds, I am not quite sure which. I still need to read the Nerds vs Geeks post), like me, I found this post informational. I didn’t know that this theorem was basically the foundation for all sources of randomness. I had never heard of this theorem until now and think it’s cool, in a funny way. I can’t wait to see what you post next!

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    1. I’m glad you learned something while laughing! I try to add humor to my posts, because many people find math boring (I just hope I’m not too cringey). Yeah, when I learned about this, I couldn’t even believe it was an actual theorem! I thought it was the weirdest, coolest math concept ever. Anyway, thanks for reading, and I’ll see you in the next post!

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  3. At first when I read the title of your blog I was slightly amused but also curious. As I kept reading through your whole post I was able to understand the basic idea of the theorem itself and was interested as to why I had never come across this before. The way your writing explained the theorem in an easy to understand language amazed me. I hope to read more of your posts and opinions about these weird theorems out in the world wide web.

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    1. I’m glad you found my post enjoyable! If you learned something new, then my goal was accomplished. Thanks for commenting; I like to hear my readers’ opinions! I will (maybe, possibly, hopefully) see you in the next post!

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  4. I really enjoyed reading this post because I learned something new. This blog shows a new perspective on math and it is just really interesting to read, because I am able to learn things that I never knew before. The pictures you used were very interesting and they connected back to your post very well. I really enjoy your blog, and I hope you keep writing!

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    1. Yeah, I think that it’s really unfortunate that people don’t like math, because there are so many cool concepts like this. I’m really happy that you learned something new and found my blog interesting, because most people think math is boring. Thanks for commenting, and I hope to see you in my next post!

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  5. Ananya,
    This is super interesting. I have always been fascinated with theorems and rules that explain everything, and theoretically statistics are so cool to think about.

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    1. Yeah, I think statistics is a really fascinating subject too. Of course, this probably isn’t taught in statistics, but still, it’s cool to think about. Thanks for the comment, and I hope that you read my future posts!

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  6. This is a very strange idea about monkeys who type different stories. I wonder who originally thought of this and why they did. Though it’s not possible to test this theorem exactly, it would be interesting to see around 15-20 moneys each with a typewriter( or computer on docs so they can collaborate) and see what happens. Leave them in there for maybe just a few minutes of possible an hour or two.

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    1. Yeah, it is strange, isn’t it? Émile Borel originally mentioned something about this in one of his books. Then, it appeared in books/essays written Arthur Eddington, James Jean, and Jorge Luis Borges (in that order). Also, fun fact: in 2003, a study done in the University of Plymouth tested this theorem for a month. The monkeys wrote 5 pages, mainly with the letter “s.” They also hit the typewriter with a rock and urinated on it. The experiment pretty much failed (although the experimenters said that the monkeys looked as if they were typing with intention). However, in 2008, another experiment started, this time replacing monkeys with software that generated random letters. This one is actually [kind of] working, and it has managed to produce some famous works in literature (but not the works of Shakespeare – at least not yet, because parts of it have been produced).

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  7. Hey Ananya! I found this post very interesting, as I have never seen the Infinite Monkey Theorem. However, after thinking about it after a while, I do have to point out that it is not guaranteed, but only “almost surely”, as what if all the monkeys decide to just type “a” over and over again (The probability of this is 0, but there is still a chance (infinite things have fun paradoxes))? I liked how you tied this into subjects like statistics though, Keep up the good work!

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    1. Thanks, I plan to continue writing stuff like this. It’s amazing what there are theorems for, right? And even more amazing is that the sound crazy but they are completely supported by math/logic. In response to the thing you pointed out, it is guaranteed because there is infinite number of time. Therefore, it must happen eventually. Thanks again for the comment, and I hope yuo revisit my blog!

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