The Law of Large Numbers Meets an Infinite Number of Monkeys

In my last post, I talked about the weak responses of evolutionists when addressing the statistical improbability of abiogenesis. Basically, they say that the first living cell evolved from simple, self-replicating molecules. It's funny for two reasons: first, because they usually say that abiogenesis isn't part of evolution. Why then do they use evolution to explain abiogenesis? Secondly, they really have no idea how the first living cell formed so from where do they have grounds to assert a gradual, molecule-to-cell story of evolution? There is no scientific theory of abiogenesis.

In this post, I'd like to explore another tactic sometimes employed by evolutionists in their effort to climb “mount improbable.” Even though the odds of amino acids combining to form even one, simple protein are astonishingly small, evolutionists place their hope in a near infinite number of trials. After all, even the most improbable combination – even a seemingly impossible combination – will be accomplished if all possible combinations are tried. In a universe as large as ours, there are chemical processes occurring everywhere. If you have billions of years of trial and error, even something as unlikely as abiogenesis becomes almost a certainty.

There's an old analogy used to demonstrate this principle: if there were an infinite number of monkeys typing randomly on typewriters, eventually they will type all of Shakespeare's plays. Now, I'm not a math wizard but even I can understand that books are merely combinations of words and words are merely combinations of letters. If someone could attempt every possible combination of letters, then of course he will chance upon the same combination of letters found in a Shakespeare play. If I may be so bold, I might even correct the analogy: in an infinite number of attempts, the correct combination would immediately be reached, not eventually.

However, there's something that's always nagged me about the monkey analogy (besides evolutionists' seeming obsession with monkeys – he he). Like I said, I'm not a math genius but I do have a degree in business and have worked in financial services for nearly 30 years so I'm not a stranger to math. There's a widely understood principle in the business world known as the law of large numbers. The law is used in many different ways but basically the law predicts that the larger a sample is, the more typical it will be. Let me explain how it works, If I tossed a coin 10 times, I should theoretically get 5 heads and 5 tails. However, 10 trials is not a large sample so my results are not easily predicted. I could get 7 heads and 3 tails. 10 is just too small to be representative. If I next tossed the coin 100 times, I still might not get exactly 50 heads, but it will likely be closer to 50/50 than 70/30. If I tossed the coin 1,000,000,000 times, I can almost guarantee that approximately 50% of the tosses will be heads. As a matter of fact, if I got 70% heads after 1 billion tosses, I would suspect that the coin is not truly random.

The difference between the law of large numbers and the theoretical monkeys is that the law of large numbers has been tested many times over. Casinos, insurance companies, lotteries, and many other businesses rely on this principle in their business models. For example, an insurance company with 5,000,000 customers can predict with uncanny accuracy how many 45 year old, insured men will die this year. If slot machines are truly random (which they are), I could theoretically win 100 jackpots with 100 pulls. The odds of doing that may be remote but they exist in theory. Yet by using the law of large numbers, casinos know almost to the penny how much they will pay out in winnings for every 1,000,000 pulls of a slot machine.

The law of large numbers puts a kink in the infinite monkey analogy. I'm not sure how many words typically make up a play but let's say it's 200,000. We'll further assume an average word length of 5 letters. Therefore, a typical Shakespeare play is 1,000,000 characters long (we'll also assume that includes spaces). There are 26 letters in the alphabet plus a space so each peck of the typewriter could yield 27 possible outcomes. 1 million pecks is a reasonably large enough sample that the law of large numbers should apply so we know that 1/27^th of the letters will be “A,” 1/27^th will be “B,” 1/27^th will be “C,” etc. In other words, after 1 million pecks, you will have about the same number of “X” as “A.” Don't forget too that there are punctuation marks are the keyboard so you will actually have as many $, @, and % as you have A, B, or C. In English, the letter A occurs far more frequently than the letter X so I don't care how the letters are arranged, you can never have a Shakespeare play when there are as many X's and #'s as A's!

Even in an infinite number of trials, the letters typed out by each monkey should be distributed evenly if each trial is truly random. In each 1 million letters, any 1,000,000 long string of characters will look approximately the same as any other 1,000,000 long string. There will roughly be equal numbers of A's, Q's, X's, spaces, and punctuation marks. An infinite number of monkeys will yield an infinite number of manuscripts that will all resemble each other and will all be gibberish.

Time is not a magic formula that suddenly makes the improbable likely. Amino acids combining over and over could be likened to letters being spit out by the monkeys. In a large number of trials, they will randomly combine in similar sequences over and over. There's no certainty or even likelihood that they will ever combine in that fortunate sequence that creates life. Some things are truly impossible.