PROBABILITY and EVOLUTION

Most people have heard of the mathematician Bertrand Russel’s suggested analogy to demonstrate how evolution operates. He proposed that if a million chimpanzees were to type randomly on a million typewriters for a million years there would be a good chance one of them would produce one of Shakespeare’s classics. Have you ever given that a little thought? Consider –

A million chimps (I’ll use the notation 10^6 as 10 to the sixth power ) typing randomly on a million typewriters.

A novel would be a pretty big challenge, so let’s just see if they can type the first verse of Genesis:

IN THE BEGINNING GOD CREATED THE HEAVENS AND THE EARTH.

By using only capitals this verse contains 14 unique letters plus a space and a period –

—  I N T H E B G O D C R A V S  sp  .  —

If we give the chimps typewriters with only these keys, they have a much better chance of reaching their goal.

Since the verse has 55 print positions this means that the number of possible Permutations that must be typed in order to have an even chance of typing Gen. 1:1 is

16^55   (1.6^55   X   10^55   =   1.68499   X   10^66)

This number is a little messy to work with so let’s give the chimps another break and reduce the Permutations to

10^66 (that is a “1” followed by 66 zeros)

Let’s also say that the chimps are as fast as a good Secretary and can type (randomly, of course) 120 words/minute. This is 2 words/Second and since the average word has 5 characters then the chimps will be typing 10 characters/SEC. Not only that, but as soon as they’ve typed their first 55 characters, they’ll then be creating 10 new PERM./SEC.

Since you’ve got a million chimps, each creating 10 PERM./SEC., this means they’re creating –

10^6   X   10   =   10^7 PERM./SEC.

OK, so that means that to have an even chance of hitting Gen. 1:1, they’ll need –

10^66 PERM.
———————-              =            10^59 SEC
10^7 PERM./SEC.

That’s kind of big so let’s convert to years.

One year has 60   X   60   X   24   X   365 SEC.   =   31,536,000 SEC./YR.

We’ll give your chimps another break and round up to make calculations easier. (they can create more PERM./YR. This way.)

we’ll say 1 year = 100,000,000 SEC   =   10^8 SEC/YR

So the number of years to break even is-

10^59 SEC
——————                    =               10^51 years
10^8 SEC/YR

Well, since the accepted age of the universe is only 10^10 years, I think we better put some more chimps to work.

Let’s put a billion chimps (10^9) to work. And, we’ll hire faster ones that can type, oh, about 12000 words/min.

That’s 1000 characters/SEC   =   10^3 PERM/SEC

That’s 10^9   X   10^3   =   10^12 PERM/SEC

OK, so now to have an even chance of producing Gen. 1:1, they’ll need –

10^66 PERM.
———————            =         10^54 SEC.
10^12 PERM./SEC.               —————–        =         10^46 years
. . . . . . . . . . . . . . . . . . . . . . .     10^8 SEC/YR

Looks like we’re going to need more and faster chimps.

How about if we put 1 chimp on every square foot of the earth’s surface
(we’ll assume that the oceans have been paved over). How many square feet will that be?

Surface area of a sphere   =   pi   X   r^2   X   4

= 3.14   X   (7800 miles / 2   X   5280 ft/mile)^2   X   4

= 3.14    X   4.23   X   10^14   X   4

= 5.3   X   10^15 sq. Ft.

We’ll round up to get more chimps to work and say that the number of square feet = 10^16 sq.ft   =   10^16 chimps

Also, we’ll make them typing maniacs and say they can type a billion characters/SEC. This gives us

10^16   X   10^9   =   10^25 PERM/SEC

So 10^66 PERM.
——————-            =           10^41 SEC
10^25 PERM/SEC                 —————               =                   10^33 years
. . . . . . . . . . . . . . . . . . . . . . . .  10^8 SEC/YR

I don’t know, we’ve quite a way to go. How about this –

Instead of one chimp on each square foot of earth we’ll stack them up. (we’ll assume that it doesn’t affect their typing to have another chimp on their shoulders.) In fact we’ll stack a billion chimps on each sq. Ft. Of the surface of the earth.

this will take down the time to only – 10^24 years.

So there you go, the chimps have an even shot at typing the first verse of Genesis and it will only take them 100,000,000,000,000 times the accepted age of the universe. Unfortunately, each stack of chimps (each 3 feet tall) would reach out twice the distance to the moon so we would have to remove it before doing this experiment to avoid an unpleasant meeting between chimps and same.

Now, rumor has it that scientists actually tried to perform this experiment. Of course, it was not practical to get a million chimps for a million years so they settled for a thousand chimps trained to randomly punch keys for a few hours each day for a year. Obviously, they didn’t get any works of Shakespeare or even Gen 1:1. They did get three copies of Valley of the Dolls and one near hit with the character string “to be or not to be, that is the burgelmitz.”

Advertisements