googlef87758e9b6df9bec.html A Sure Word: The Law of Large Numbers Meets an Infinite Number of Monkeys

Wednesday, October 17, 2012

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 1/27th of the letters will be “A,” 1/27th will be “B,” 1/27th 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.


Steven J. said...

There is another point to consider: most such calculations try to estimate the odds of getting some particular, specified protein. This is the wrong question, the inverse of the "Texas sharpshooter fallacy" (in which you draw the target on the wall after you hit the broad side of the barn. The odds of hitting that particular target are tiny; the odds of hitting the wall, large.

With proteins, we have an intermediate case: any particular protein is a nigh-infintesimally small "target" to hit by chance, but we need to consider the entire range of possible proteins with some useful function. We know that many variations on a protein can perform the same functions (given that many variations on the same protein exist between different species); we don't know how many proteins total can perform a given function, though surely it is larger than the variety actually observed.

Your point about the very unequal frequency of letters in English prose is not obviously relevant. On the one hand, the relevant comparison is the relative frequency of different amino acids in proteins. On the other, while a random selection process ought to throw up all English letters with equal probability, this is probably not true of random selection of amino acids in proteins, since amino acids don't have identical chemical properties.

Anonymous said...

Hey! Im CH from Brazil. Found your blog a little while, and have been reading ever since. Keep up the good work and Gob Bless!

P.S: Sorry (Bad english, trying to improve my writing, your blog is helping with that too -hahaha.)

RKBentley said...


Thanks for visiting and for your words of encouragement.

Let me say that your English is much better than my Portuguese. I love hearing that my blog is being read in other countries. Christ commanded His church to take the gospel into all the world. I don't have the means to travel much but the internet helps me do my small part in the Great Commission.

Please keep visiting. God bless!!


Anonymous said...

CH here(again.)

Theres no problem, portuguese is a difficult language. Believe me, there's a lot of brazilians that don't know speak (or write) correctly. I sure will continue visiting. I share your observations on creationism and atheism very interesting.

God Bless

RKBentley said...


The infinite monkey analogy isn't mine originally. Comparing it to the impossibility of abiogenesis is more a habit of your side than mine. Let me try to nail down my problem with it.

Statistics are a funny thing. For example, any particular arrangement of a deck of cards is no more likely than any other arrangement of the deck. To randomly shuffle the deck and discover they are ordered ace through King of each of the four suits seems impossible. However, it's really no more unlikely than arriving at any other particular order. The key consideration is if you are looking for only one particular order.

Suppose that order of the deck is a “magical” sequence. There are only 52 cards in a deck and if I had the means to shuffle a deck infinitely, the odds are that I will eventually shuffle them into that seemingly impossible order. However, my odds for success totally evaporate if I have an open pool of cards. Imagine a world filled with cards and monkeys pick up cards at random and stack them. Each stack might not have exactly 52 cards. Even in those stacks with 52, I might get 20 spades, 18 hearts, 10 clubs, and 4 diamonds. It could be that no stack has exactly 13 of each suit and exactly 4 of each card. In this case, a too large pool of cards – when exactly 52 specific cards are needed – actually works against my chances of success.

Suppose a protein is made up of only 20 amino acids. If I combined the same 20 over and over randomly, eventually I will happen upon the successful combination to make a protein. However, if I dumped an infinite number of molecules together, some conducive to life and others not, the molecules not conducive to life will combine just as often as those necessary for life. In this scenario, left handed amino acids will combine just as often as right handed amino acids. Luck would make some combinations longer than 20 and some less. The unnecessary elements would constantly intrude upon the formula and ruin the recipe just like the unnecessary X's, Q's, and punctuation marks would constantly intrude and ruin the play.

I'm sorry if the analogy wasn't immediately obvious. I hope this clears it up a little.

God bless!!


Anonymous said...

You conclude:

"Time is not a magic formula that suddenly makes the improbable likely"

Um, yes, yes it is.

If the probability of an event happening in 1 second is 1 in 1,000,000

Then the probability of it happening in 10,000,000 seconds is 99.6% i.e. almost certain.

All you are doing is showing that you do not understand probabilities.

RKBentley said...

If you tossed a coin 10,000,000, I can say with confidence that approximately 1/2 of your tosses will yield heads. If you drew 10,000,000 cards from a deck at random, I can say with confidence that approximately 1/13th of the cards you chose will have been aces. The more times you draw, the closer to the statistical average will your result be. I could theoretically toss 1 billion heads in a row - but in reality I won't.

It's the law of large numbers. I didn't make it up. It works everytime.