The Infinite Monkey Theorem & biology

Today in my logic class we discussed probability calculations as a way of illustrating inductive arguments.  I amused my students and myself by discussing the infinite monkey theorem and, better yet, actually calculating the odds.  It occurs to me tonight that this has some bearing on one of the big questions in biology. 

The IMT is a famous thought problem in philosophy.  If you had a number of monkeys randomly typing on keyboards, could they eventually produce a copy of one of Shakespeare’s plays?  The IMT is a good test of rationality.  Some students simply refuse to agree that it would be possible, even given infinite numbers of monkeys and time.  That suggests a mental block.  Given those assumptions, the outcome is not only possible but inevitable.  It is also a good illustration of the difference between logical possibility (which the IMT demonstrates) and causal possibility (which the IMT demonstrably fails). 

The monkeys in the theorem are, of course, metaphors for random signal generators.  They are also cute.  To explain my test, I’ll employ metaphorical chimpanzees (they’re easier to train).  I stipulate the following:

a constant team of 100 chimps;

each has a keyboard with twenty-six letters (no other symbols or spaces);

each chimpanzee has an equal chance of hitting any of the twenty-six keys on each keystroke;

each chimpanzee types exactly twenty-six characters per minute;

a full team of 100 primates is working at the stipulated speed twenty-four hours a day;

all the keystrokes are entered in a single line that we test for results;

there is no time limit on how long I can keep the experiment going. 

If you think that these stipulations are unrealistic, you think correctly; it’s a thought problem. 

Now: forget about a whole play; let’s just ask our simian team to produce

Now is the winter of our discontent made glorious summer by this son of York. 

One of my favorite lines, opening Richard III if memory serves.  That doesn’t look so hard.  If my apes are following the above stated rules, each will produce an “n” about once every minute.  To get the first and second letters in the right order, we have to multiply the probability of each: 26 x 26.  So, each 676 keystrokes will produce “no” and our team will produce about four examples every minute.  That’s pretty good.  We’ll be done by lunch.  Bananas all around!

The team will produce the first word in the line about every seven minutes.  Unfortunately, the wonders of geometrical progressions slow us down precipitously.  To get the first two words will require three full days.  Better alert the[KB1]  caterer. 

It gets worse fast.  Given our stipulations, the first three words “nowisthe” are going to appear in order, somewhere in our line, about once every 153 years.  Just to get the next three letters of the fourth word in order will require our team to work for about three million years. 

So how long will it take to get the first four words out?  Forty-seven billion, two hundred and six million, one hundred and four thousand, eight hundred and ninety-four years.  We are going to need a lot of chimpanzees and a lot of bananas.  Unfortunately, the Kosmos is only fourteen billion years old. 

I submit that our thought problem demonstrates two things.  One is that it is logically possible for our chimpanzees to produce Richard III.  Given enough animals, bananas, and time, they could produce the entire corpus.  The other is that it is causally impossible.  Vast stretches of time beyond calculation are necessary even to get going. 

There have been two recent attempts to play out the scenario.  One involved a number of macaque monkeys.  After two months, they failed to produce a single English word (they did have an inexplicable fondness for “s”); they broke the computer and pissed on the keyboard. 

The other was actually interesting.  Someone created a very large number of virtual monkeys, using the cloud to borrow computer time.   He claims to have produced almost the entire Shakespearean corpus by this method.  However…he cheated.  Whenever his virtual monkeys produced nine letters that appeared consecutively anywhere in the corpus, the program took them out and put them in their place.  The monkeys would not have to produce that string again. 

That is cheating because it means that our monkeys can produce Shakespeare only if they begin with Shakespeare as a forced sorting device, even with vast resources.  One might argue that it is analogous to divine intervention. 

It occurs to me that this is analogous to natural selection.  Instead of monkeys we have random changes in DNA.  Very large numbers of organisms constantly reproducing result in very large strings of genetic characters.  Natural selection saves the ones that code for viable traits.  That is how natural selection eventually builds a Shakespeare. 

But what about the UR organism, the first genuine replicator?  Is the simplest such organism that science can yet imagine more or less complex than the Bard’s Dickey Three?  Allow me to suggest that the answer is “more”.  How do you get from inorganic processes to even the simplest organic processes without some kind of preordained sorting? 

I don’t know and neither do you.  No one knows.  I have previously blogged on one attempt to answer that question.  Andreas Wagner argues that evolution worked because nature had a preexisting library of Platonic forms.  As a Platonist, I like that idea and I am pretty sure he is right.  I am just wondering who, precisely, was the librarian? 

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 [KB1]