Thursday, October 11, 2007

When pigs fly and monkeys can type

~who can resist such a headline? Here's an excerpt from Gerald Schroeder via CERC on chance and sonnets:
Stephen Hawking in his A Brief History Of Time taught the world that given enough time, monkeys hammering away on typewriters could type out a Shakespeare sonnet.

It is a nice adage but totally off base, at least within the reality of our world. Having gone to MIT I don't know many sonnets. In fact when I thought about this I only knew the opening line of one, "Shall I compare thee to a summer's day." There are a bit fewer than 500 letters in that sonnet [All Shakespeare's sonnets are about the same length; all by definition 14 lines long.]

Let's consider a grab bag with the 26 letters of the English language in it. I reach into the bag blindfolded and pull out a letter. The likelihood that it will be 's' for the first letter of the sonnet is one chance in 26. The likelihood that in two draws I will get an 's' and then an 'h' is one chance in 26 times 26. And so on for the 500 letters. Neglecting spaces between the words, the chance of getting the entire sonnet by chance is 26 multiplied by itself 500 times. That number comes out to be a one with 700 zeroes after it. In conventional math terms, it is 10 to the exponent power of 700.

To give a sense of scale for reference, the known universe including dark matter and black energy weighs in the order of 10 to the power 56 grams; the number of basic particles [protons, neutrons, electrons, mesons] in the known universe is 10 to the power 80; the age of the universe from our perspective of time, 10 to the power 18 seconds. Convert all the universe into micro-computers each weighing a billionth of a gram and run each of those computers billions of times a second non-stop from the beginning of time and we still will need greater than 10 to the power 500 universes, or that much more time for even a remote probability of getting a sonnet; any meaningful sonnet. Chance does not produce intelligible text and certainly not a sonnet, not in our universe.

But so convincing is the Hawking argument that the students at the Plymouth University in England convinced the National Arts Council to put up 1500 Sterling, about $3000, to try monkey typing skills. They rented a monkey house for a month. Six monkeys hammered away on a computer key board and failed to produce a single English word. Surprised, since the shortest word in the English language is one letter long? Surely the monkeys must have hit an 'A' or an 'I' in all their efforts. But think about it. To a make an 'A' a word requires a space on each side of the 'A'. That means typing: space, 'A,' space. If there are about 100 keys on the computer key board, the probability is one chance in a 100 times 100 times 100 which comes out to be one chance in a million. Random guessing in a spelling bee is always a losing proposition. And that is for a single letter word.

But what about life? Could random mutations have actually produced the ordered complexity of life, or even a viable protein? Mutations that are to be passed on to the next generation must occur in the genetic material of the reproductive line, which is in the DNA of sperm or egg. That mutation results in a variant (mutated) protein which might produce a new more effective type of organ, say a better muscle or the beginning of a transition from fin to foot. That would be the neo-Darwinian concept. But let's look at that process rigorously. When we do we'll see it does not work if randomness is the only driving force.
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