Thursday, October 18, 2007

10 Typing Monkeys to the exponent power of 700

I found this article from Catholic Educator's Resource and I think it is interesting.

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.
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. (Gerald Schoeder, When Pigs Fly and Monkeys Type)

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