When asked how random events can lead to the synthesis of a complex biological molecule like an enzyme, evolutionists like to bring up the "Infinite Monkey Theorem" which goes something like this: If you give a monkey a typewriter, and he types random keys for an infinitely long time, eventually he'll type a Shakespearean sonnet.
This is right up my alley because it involves two areas in which I have some expertise: Enzymes, and statistics.
OK, let's break that down.
Shakespearean Sonnet #106 has 582 characters, including punctuation. The total number of different characters is 31, which includes the alphabet plus comma, period, space, semicolon, and apostrophe.
Alpha-amylase, an enzyme I worked with, has 496 amino acids. There are 21 different amino acids. In order for an enzyme to fold correctly, the amino acids have to be in exactly the correct order. So the "Infinite Monkey Theorem" is roughly appropriate.
Amino acids come in two flavors: Levorotatory (L), and Dextrorotatory (D)
Letters of the alphabet come in two flavors: lower case, and upper case.
Enzymes are composed of almost all levorotatory amino acids. This corresponds to a sonnet needed to have the correct case for each letter. In the analysis we'll ignore this aspect however, just to make the math a little easier.
Now, we obviously need more than one monkey with a typewriter if we want to approximate enzyme synthesis which can't just be allowed to occur in one spot, but everywhere there are amino acids that can combine.
So let's cover the surface of the earth with monkeys and typewriters. One monkey and typewriter for each square foot of the surface of the earth. That's 5,490,000,000,000,000 monkeys with typewriters. (5.49 quadrillion)
And let's say they can each type one letter per second.
With 31 different characters, the possible number of 582 character sequences of 31 unique characters is 31^582, or approximately 9.39x10^867
For a single monkey, the probability of typing Sonnet #106 in a single try is 1 in 9.39x10^867
It takes 582 seconds to type 582 characters, which is 9.7 minutes. So if we let the monkey type for an infinite amount of time, he will, on average, type Sonnet #106 once every 6.93x10^862 years.
But we don't just have one monkey, we have 5.49 quadrillion monkeys. So if we put them all to work, we can get Sonnet #106 once every 1.26x10^847 years.
The oldest estimate of the age of the universe is 13.8 billion years. That's 1.38x10^10 years.
So the probability of our 5.49 quadrillion monkeys typing Sonnet #106
JUST ONCE during the entire age of the universe is one in 4.7x10^828
Or, to put that in perspective: One chance in 470,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
In other words...
*Somebody* didn't do the math...