iMonkey

by Don Crouse
Copyright 2018 Don Crouse

We have the iMac, the iPod, the iPad and the iPhone. Now, I present to you, the iMonkey! It's still in beta testing, but it will work just fine for my purposes today.

So what exactly is the iMonkey? Well, I'm glad you asked (just pretend you actually care). The iMonkey is the smart monkey. I didn't invent it. But it's about time someone marketed it! You probably already have some familiarity with the smart monkey and you don't even know it. It's actually called the Infinite Monkey Theorem.[1] The Infinite Monkey Theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will type the complete works of William Shakespeare. Well, that is something, isn't it? Amazing - especially considering William Shakespeare didn't even do that! The typewriter wasn't invented until 1808. Shakespeare died in 1616. But that doesn't stop the iMonkey! The iMonkey isn't obligated to live by the normal constraints of time and physics. And it doesn't even have to work in reality. It just has to work in principle… because it's only a theory. Of course, in the real world, the iMonkey would never work; but in theory anything is possible, right? Well, maybe not.

Today we have vast amounts of amazing technology and monkeys at the ready. Yet those monkeys have yet to type even one line of Shakespeare - or anything else for that matter. What's the deal? You would have thought by now some researcher would have tried to test the iMonkey - or am I the only one who thinks it's worth a shot? [2] Hey, the United States Government spent $136,555 for some English lit students to go to England to retrace the trip described in Chaucer’s

Canterbury Tales

. So you'd think we'd have a few bucks to type up a few copies of Shakespeare. I mean, come on, how much would a monkey charge to sit at a typewriter for the rest of its life? Okay, technically we'd probably use a chimp, and they charge more than say, a Rhesus monkey would, but we could probably work out a deal where they'd work for bananas. Hey, here's a thought… let's pay them by the word. So for each word they type we give them, say, a banana. Better yet, we'll just give them whatever they type (hopefully the first word won't be Ferrari). But say they want a banana, how long could it take for a chimp to randomly come up with the word 'banana'? Well, I'm glad you asked, because I actually know the answer… well, sorta. It depends on how fast the chimp can type and how many keys there are on the typewriter. Doing some quick research I found out that really old, mechanical typewriters, had 47 keys, [3] including the space bar. My keyboard has considerably more - over 60 if you include function keys. But we want this to be as productive as possible for our chimp. So the fewer the keys the better. We'll go with 47. Those old time typewriters also had a return bar, a ribbon spool, a cylinder and a bunch of other parts for a chimp to mess with. And chimps do like to mess around. So the chance of them not (messing around, that is) is infinitesimally small. In addition, our chimp will need to change paper once a page has been filled with text, and replace the ribbon when it becomes unusable. They will also need to master the use of the return bar to add spacing between the lines of type, or we will be reading the mono-linear works of Shakespeare. If all that wasn't enough, I'm sure our monkey will be excited to try out other parts of our typewriter, resulting in the loss of work time or the destruction of the typewriter. In our example, I'm just avoiding adding any probabilities like those previously mentioned, and only focusing on the chimp hitting 47 keys. The relevant point I'm trying to make here is that typing the works of Shakespeare involves more than just hitting keys on a typewriter. I don't want to try and figure out the probability of having our chimp complete its task with all those variables. So, to make my life easy we're going to ignore all the variables that don't involve hitting one of those 47 keys. I'm also going to postulate that the space bar has an equal probability of being hit as any of the other keys. [4]

So back to our chimp getting a banana. As far as speed, I hit around 120 keys a minute when I'm actually trying to spell things, but a chimp just pounding on a keyboard would probably be faster. So let's do the math. Assuming (and we probably should never assume, because of that old metaphor about making you and me a certain farm animal), but assuming our chimp randomly hits one key at a time, there is one chance in 47 that they will hit the letter 'b' first. There is also a 1 in 47 chance that each of the following letters will be correctly struck. So the chance our chimp will hit all six letters to correctly spell the word 'banana' is (1/47) × (1/47) × (1/47) × (1/47) × (1/47) × (1/47) = 1 chance in 10,779,215,329 tries. ^[1] But how long will that take our typist? There are 31,536,000 seconds in a year. Assuming (and again, probably shouldn't) our chimp hits 4 keys every second, they should come up with 'banana' in about 85 years, give or take a few extras days for leap years. The math works like this: you multiply 60 seconds times 60 minutes to get 3,600 seconds in an hour, which you multiply by 24 hours to get 86,400 seconds in a day, which you multiply by 365 to get 31,536,000 seconds in a year. Then you multiply 31,536,000 by 4 (the number of keys the chimp hits per second) to get the number of letters our chimp will type in a year (given continuous typing and no dinner or potty breaks) - which is 126,144,000. Now divide 126,144,000 into 10,779,215,329, which should give you about 85.5 years. But sadly, our chimp will probably only live about 40 years. So even if we start the little tike typing at birth, they won't have enough time to randomly spell 'banana'. Okay, so we'll need to feed the chimp.

So what about the claim that a monkey could, given enough time, type the entire works of Shakespeare? Well, we already know if they can't get a banana, they're not going to get the works of Shakespeare. So we're going to need an eternal monkey. Poof! There it is. Now that we have one of those, let's see how they do with our playwright’s scripts. The math gets a little harder with this example, so I used a really big scientific calculator I found online (because I have neither the proficiency or time to crunch numbers as big as the ones that are coming). ^[5] So let's do the math!

We’ll start with something easy, like Romeo and Juliet. Romeo and Juliet has about 24,545 words in it (I Googled it). ^[6] And since there are lots of different words, of lots of different lengths, we'll make this easy and just say that each word is 3 letters long to make our monkey's work as simple as possible. I think that's being charitable in regards to helping out our monkey, because I'm guessing that the average word length is longer than that. But I like monkeys, so I'm going with the average word length being three letters. So we multiply 24,545 words by 3, which gives us only 73,635 letters for our monkey to type in the correct sequence. And we'll need to add spaces between our words, or we'll be running all our Montagues and Capulets together, which would make a terrible mess. So adding the spacing would give us about 24,544 more keys that will need to be hit in the correct order, to keep our warring families apart and avoid further bloodshed. So, in total, our monkey will need to hit 98,179 keys in the correct order to give us our first primate rendering of Romeo and Juliet. Remember, we have 47 keys on our typewriter, so that means our monkey has 1 chance in 47 of getting each letter correct, and they're going to have to correctly type 98,179 letters (and spaces). So the chance of our monkey successfully typing Romeo and Juliet is one chance in 47, multiplied by itself, 98,179 times, or 47 to the 98,179 power (47 ^98,179). Another way we could do that is multiply (1/47) x (1/47), until we've done that 98,179 times. I don't want to do that. But using my handy dandy online scientific calculator, I determined the resultant odds of our monkey typing Romeo and Juliet is approximately 1 chance in 7.86 x 10 < ^164,164. ^[5]

Or, if we rounded and wrote that number out, it would be 8 followed by 164,164 zeros! I don't want to do that either. Let's just say it's a very big number. So the chance of our monkey writing our play is a very, very, very small number.

Now let's try to put that number (7.86 x 10^164,164) into some sort of perspective. Not sure if that's possible, but I'll try.

The universe is only about 13.8 billion years old, based on the Lambda-CDM concordance model (and I'm assuming that's correct, because I don't know what the Lambda-CDM concordance model is!). [7] That means the universe is only 434,196,800,000,000,000 seconds old (which is 434 quadrillion, 196 trillion, 800 billion seconds).[8] That's roughly 4.3 x 10 ¹⁷ seconds.

The universe is just a baby, at least compared to the amount of time needed for iMonkey to type Romeo and Juliet. And now it's time for more math (did I mention I hate math). So we'll multiply the amount of time the universe has been in existence by the number of letters our monkey types per second (which we'll increase to 10 letters per second - to make the odds better for the monkey and the math easier for me). So the hated math is 4.3 x 10 ¹⁷ seconds x 10 letters per second = 4.3 x 10 ¹⁸ letters. That means our monkey would have typed 4.3 x 10 ¹⁸ letters over 13.8 billion years. And what that means is that if we had an iMonkey that typed 10 letters a second for 13.8 billion years (without potty breaks), our little primate friend would still need to type about 8 x 10 ^164,164 more letters to randomly get a copy of Romeo and Juliet … and they'd also have a super full bladder! And that's a big deal. Let's see you go 13.8 billion years without a potty break! But what's the deal with the number of letters not changing, even after our monkey typed for 13.8 billion years. Well it has to do with the relative size of the two numbers used in the equation. 8 x 10 ^164,164 is astronomically larger than 4.3 x 10 ¹⁸. To see the difference (which is the mathematical term for the result of subtracting one number from another) of these two numbers we'd have to write out at least 164,146 of the numbers in the difference before we'd see the numerical change between the minuend (the number from which another number is subtracted) and the subtrahend (the number which is subtracted). And I don't have the time to write down 164,146 numbers so you can see I'm right. But say I do two smaller numbers. I'll subtract 10 ² from 1.01 x 10 ¹² . That would be 1,010,000,000,000 - 100 = 1,009,999,999,900. When rounded to the closest two digits and expressed as a power of 10 ¹² , the difference is still 10 ¹² . So listen to me now and believe me later. Or just use the big scientific calculator I found for you online and see what you get. ^[5]

But seriously folks, 8 x 10 ^164,164 is an insanely big number! So is there a way we can get an idea of how big that number is? No. No, there really isn't. There are only estimated to be between 10 ⁷⁸ to 10 ⁸² atoms in the entire universe. [9] And that's a pretty big range. We're talking about a size difference of 10,000 universes between a universe containing 10 ⁷⁸ atoms and a universe containing 10 ⁸² atoms. With the addition of each zero we increase the size by 10 fold! The number we're trying to grasp (8 x 10 ^164,164 ) is massively bigger than 10 ⁸² . We still need to add 164,082 more zeros to 10 ⁸² to get to 10 ^164,164 … with the addition of each zero increasing the previous number by ten fold! So forget the entire works of Shakespeare. We can’t even get Romeo and Juliet

! Even if our monkey types a thousand letters a second, for trillions and trillions of years, there is still no chance for success. [10] Even if we had all the monkeys that have ever lived, and will ever live, typing over that time, we still won't get a primate copy of Romeo and Juliet . Bad news for our iMonkey and the

Infinite Monkey Theorem . And my hopes were so high for my first primate addition of

Romeo and Juliet . So give the iMonkey a banana, be happy Shakespeare was around to write Romeo and Juliet , and stop tormenting those poor animals.

When I first heard about the iMonkey I thought to myself, "Self, they've really got something there! Given enough time a monkey could randomly type the entire works of Shakespeare!" But upon closer examination, I discovered there was one fatal flaw with the iMonkey. There hasn't been enough time. Not even close. So iMonkey is a total bust. No 'entire works of Shakespeare', no Romeo and Juliet, not even a soliloquy from Hamlet. And if we wait for our chimp to type 'banana' before we feed it, it'll die in 3 weeks.

So what can we take away from the example of the iMonkey? Well, first, apparently nobody bothered to factor the math into the theorem. Second, monkeys are not good at typing. Third, in theory, anything could happen. However, in the real world, a theory may have no chance of actually occurring. It may just be an impossible idea someone dreamt up to convince us other impossible things could also happen. The iMonkey is pure fiction. Not fact. In the real world it can't happen - ever!

Bottom line? Any cotton-headed ninnymuggins can come up with a theory. But no matter how many ninnymuggins believe it, or how strong their conviction, it's still not fact. Until we can verify a theory scientifically, it's just supposition. The iMonkey is a great theory, but in the real world it will never happen. The math says so. And numbers don't lie (a mathematician said that - no one knows which one, but one of them). My point? There are a lot of theories floating around the ether. Many are accepted as scientific truth, when nothing could be farther from it. The only things giving those theories credibility are the ninnymuggins that espouse them. It's a case where science doesn't back up the theory. Yet we accept these baseless claims, without facts, because someone of prominence said they're true. Why? Sometimes we just don't like the truth, so we conveniently dismiss it. Sometimes we don't think we're smart enough to disagree with Professor Ninnymuggins... and sometimes we're not. Sometimes we just believe whatever load of tripe is placed in front of us (and I've got to be honest, I've never liked the idea of eating a digestive organ of another animal). Whatever the reason, a faulty theorem is still wrong. Don't believe everything you hear… or read… unless you read it on the internet, because everything on the internet is true (which is false, because that’s sarcasm). Take a little time to learn the science and see if it proves the theory... or refutes it. You do the math, because I hate math! See if you get the same result I did.

One final thought. Why is it that we are so quick to believe any impossible, unproven theory the scientific community throws at us, but the idea of God is thrown out? If any theory has the possibility of being true, then why not God? I propose the theory of Jesus Christ. My theory is that He came to make all our lives better and restore us to our natural, intended state.

"I am come that they might have life, and that they might have it more abundantly." (John 10:10b KJV)

We work hard to remove God from the equation. Maybe He's the solution to it.

Workin' the numbers,

Don

Disclaimer: I still hate math. I have done my best to get the math for this article correctly calculated. If you find a mistake feel free to let me know. It won't matter, because a monkey will NEVER type the complete works of Shakespeare. But if it makes you feel better to let me know I messed up, great!