we are infinite monkeys
(originally posted 11/26/2012)
For those not in the mood to do some intellectual heavy lifting I’d advise you to skip this story for I’d like to ramble a bit on the topics of infinity and probability. In particular I’d like to look at the old expression “given an infinite number of monkeys sitting at an infinite number of typewriters they would eventually rewrite every book ever published.” Quite a claim and one that no doubt most people don’t really believe in their heart of hearts.
Let’s change the rules ever so slightly and say that we give these monkeys special keyboards that only have letters, punctuation and a space bar and we do not hold our hairy friends responsible for proper capitalization. Given these parameters they only have a 1 in 34 of starting off Joao Magueijo’s Faster Than the Speed of Light with the correct letter I. Chances that this same monkey would then hit the space bar and follow it up with the letters A and M are only 1 in 1,336,336. You can imagine the frustration of watching the monkey go ahead and correctly hit the next 263 pages of words only to end with “univerce.” So close.
Probability of a monkey correctly tapping out a complete work is indeed daunting so let’s meet our monkeys.
Obviously an infinite number of monkeys is sizable but I’d like to at least try to get a handle on it. Let’s say we have a large building. Large enough where each floor is able to house 100 billion billion up-and-coming primate writers. Each building has 1000 floors and I am able to get 100,000 of these building placed in each city.
Don’t worry about food, I have a reliable vendor who can deliver an infinite amount of bananas on a daily basis. Sanitation, on the other hand, is a bit more dicey as I have another vendor that has promised an infinite amount of ape port-a-potties but has to date only delivered fourteen.
But I digress.
Let’s assume that I can place 6 trillion cities full of these building on every planet I have access to and it turns out that I have access to over 900 billion billion billion planets. This amount of monkeys makes up less that .0000000000000001% of the monkeys I would need to even make a reasonable run at infinity.
I realize I am assuming that I could control all these monkeys and have them feverishly typing away for at least 12 hours a day. I’d hate for you to think I would become some sort of evil monkey-tyrant lording over all these hapless chimps and gibbons but these books aren’t going to write themselves you know!
It really is amazing to think about. Probability is an awe-inspiring force, whether it be when you’re clutching your lottery ticket as the balls bounce around on TV or looking over the shoulder of a Mandrill that is two paragraphs away from finishing Scott Aaronson’s Who Can Name the Bigger Number?. I suppose it is somewhat comforting that the smart money is on you winning the big bucks and Mandrillus sphinx botching the very next sentence if the likelihood of the two events are put to the ol’ either/or scenario. Do I need bother to mention who would win if Mr. Lighting Striking You is added to the mix?
So there we have it. If you actually tried to think this through then your brain should be throbbing and your vision swimming. Interestingly enough, to me anyway, the largest number that the human brain can actually entertain (quantified by the number of separate thoughts it is capable of) was for the longest time thought to be only slightly over 3 billion. Then Mike Holderness came along and suggested that our brains contain about 10 billion neurons, each of which sends out feelers, or axons, to link it to about one thousand others. He suggested that one way of estimating the number of possible thoughts that a brain could conceive is to count all those connections. Scientists today put the Holderness Number at 10^70,000,000,000,000.
The irony that your brain is now almost shut down trying to get a handle on just how many thoughts your brain can hold is probably completely lost on you. Before you get too full of yourself be aware that the largest number the human brain can comprehend without counting or guessing is four. Five elements can be quickly counted but everything after that can only be guessed at unless you have the time to count. Proving that despite our enormous capacity to process data our ability to grasp the number of objects in a group is quite limited. Remember that humility if you ever come before me interested in one of my many monkey-wrangler positions (I’m eternally hiring).
Just imagine the disappointment of the monkey who was lucky enough to complete Dialogues of Plato only to feel the sting of the critic’s pen when his follow up jmscfl sh cjfvlkcahwfb was not received as warmly. If you think that observation was stupid… I’ve apparently got 10^70,000,000,000,000 more where that came from.
For instance… “given an infinite number of monkeys sitting at an infinite number of typewriters they would eventually write a much better story than this”.
No argument here. This one got away from me undoubtedly.
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