Most of us have at some point heard the saying that “if you place a million monkeys in front of a million typewriters, they will eventually write the entire works of Shakespeare.”  It’s used to illustrate that randomness can be expected to eventually, and quite accidentally, produce significant complexity and order.  It’s often used by those supporting evolution as an illustration that given enough time, the right materials swimming in the ‘primordial soup’ of earth’s oceans ‘hundreds of millions of years ago’ could have organized in just the right way to produce simple life.  Thus the godless origin of life should even be expected, rather than considered impossible.

Analyzing the ‘typing monkeys’ statement doesn’t necessarily say anything directly about the origin of life, but it is very interesting what one finds.

Instead of typing the entire works of Shakespeare, let’s start with something short and easy, like the 23^rd Pslam (KJV):

The LORD is my shepherd; I shall not want. He maketh me to lie down in green pastures: he leadeth me beside the still waters. He restoreth my soul: he leadeth me in the paths of righteousness for his name's sake. Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me; thy rod and thy staff they comfort me. Thou preparest a table before me in the presence of mine enemies: thou anointest my head with oil; my cup runneth over. Surely goodness and mercy shall follow me all the days of my life: and I will dwell in the house of the LORD for ever.

I’ve counted the number of characters (just letters and spaces – no punctuation) twice.  I got 568 the first time and 577 the second.  I’m not counting them again, so let’s say there are an even 570 characters that have to be typed in a precise order to produce the 23^rd Psalm.

Say we use a typewriter that only has 27 keys – 26 letters and a space bar (we’ll ignore proper capitalization too).

That means that on a given (completely random) key stroke, the chances are 1 in 27 of it producing the letter we want first, the ‘t’ in ‘The’.  The chances of typing a ‘t’ followed by an ‘h’ followed by an ‘e’ to properly start our random generation of the Psalm with ‘The’ is:

1 in 27 times 27 times 27 = 1 in 19,683

There are 19,683 possible combinations when we randomly type three characters.

This means that if we randomly type three characters in succession… ‘iem’  ‘i d’  ‘pqm’  ‘duf’ and so on, once we have done this 19,683 times, the laws of probability state that one of those 19,683 letter triplets can be expected to be ‘the’.

To randomly type the 23^rd Psalm, we need an exact succession of 570 random characters.

When it comes to a 570-character sequence, there are:

27 times 27 times 27 times 27…  566 more times = 27⁵⁷⁰ = 754 x 10⁸¹³ possible combinations.  That’s 754 followed by 813 zeros.  That’s

754,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,

000,000,000,000,000,000,000,000 possible combinations.

Extremely large numbers are often described as being ‘astronomical’.  The number we have here is WAY beyond astronomical.  This number can’t even be spoken because such a large number has never even been named.  There is simply no way for the human mind to understand the magnitude of it.  The best I can do to help put this number into perspective is to point out that the estimated number of ATOMS in the entire UNIVERSE is 1 followed by 80 zeros.

So, the odds of typing the 23^rd Psalm is then 1 in 754 x 10⁸¹³

That means that if we type random sequences of 570 characters 754 x 10⁸¹³ times, we should expect to produce a single occurrence of the 23^rd Psalm.  Let’s say luck is on our side and we produce the 23^rd Psalm after just 1% of those attempts (The equivalent of rolling a 100-sided die and getting ‘100’ on the first roll.  Anyone want to gamble in Vegas with those odds?).  That means we should produce the Psalm after only 754 x 10⁸¹¹ attempts.  In 754 x 10⁸¹¹ attempts, there are:

570 x 754 x 10⁸¹¹    =   430 x 10⁸¹⁴ characters that must be typed.

Let’s say we place a single 12 word-per-minute typing-monkey at a typewriter.  He types one random character a second (1 word = 5 characters), indefinitely.  At this rate, it will take him 430x 10⁸¹⁴ seconds, or 136 x 10⁸⁰⁷ years.  Well, actually, we have to make one adjustment to this number.  We haven’t accounted for a situation in which the Psalm spans two attempts.  In other words, we have to account for the possibility that the monkey starts a 570-character attempt by typing a nonsense letter such as ‘z’, followed by the first 569 characters of the 23^rd Psalm, then starts the next 570-character attempt by typing the ‘r’ at the end of the final word ‘ever’.  This is straightforward.  We simply need to divide 136 x 10⁸⁰⁷ by the number of characters in the Psalm.  This leaves us with a final answer of 239 x 10⁸⁰⁴ years.

Now the secular portion of the scientific community tells us that the earth is 4.5 billion years old.  They claim that the universe is 15 billion years old.  We’ll assume that our typing monkey came into being the instant the universe was born, and that he got his hands on a typewriter and went to work right away.  15 billion years have supposedly passed, yet he still has to work 159x10⁷⁹⁴ times that number of years before we can expect him to type the 23^rd Psalm.

OK, that’s one monkey, and a slow typist at that.  How long will we have to wait to read the 23^rd Psalm if we put a million monkeys to work?  These monkeys are more experienced typists, cranking out 60 words per minute (5 characters a second).  Rerunning the numbers under these improved circumstances (more monkeys, faster typists) means that we only have to wait…  478x10⁷⁹⁷ years, or 319x10⁷⁸⁷ times the hypothetical age of the universe, to read the 23^rd Psalm.  That’s a little better, but I’m still not that patient.

Let’s throw in 10 billion monkeys – more than the human population of earth.  These are a batch of super-typists.  They can crank out random text at 120 billion words per minute (10 billion characters per second).  Will any of us live to see them type our 23^rd Psalm now?  Nope.  It will still take them 239x10⁷⁸⁴ years. 

Again, there are an estimated 10⁸⁰ ATOMS in the UNIVERSE.  (Yes, the same group of people who claim this are telling us the universe is 15 billion rather than 6,000 years old, but let’s assume for the sake of argument that they manage to get within the ballpark, or at least the area code, at times.)

Back to the ‘million monkeys with a million typewriters’ argument.  We’ve given them 10 billion rather than 1 million monkeys.  They’re supernaturally fast typists.  They and their typewriters have existed since the instant the universe was supposedly born.  They will get lucky and produce their goal after only 1 percent of the expected number of attempts.  And yet they still have a LONG time to go before they will manage to write a Psalm with only six verses.  The entire works of Shakespeare?  I hope you brought something else to read while you wait!

So, the next time you hear this ‘million monkeys’ statement from someone as they try to argue their point, respectfully suggest that they actually work out the math and then get back to you.

Incidentally, this was actually tried once.  A computer keyboard was placed in a pen holding six monkeys.  The result?  The lead male grabbed a stone and started bashing the computer.  The rest took turns treating it as a latrine.  (Adam, D., ‘Give six monkeys a computer, and what do you get? Certainly not the Bard’, The Guardian, 9 May 2003, p. 3.)