« Creative Commons Search on Google | Main | Tulane Students Back In School »
January 8, 2006
A Probabilistic Definition of Never
In the style of a Fermi problem 'never' can be defined by comparing something's half-life to the life of the universe. Examples (somebody check my math: in the spirit of a Fermi problem I rounded a lot):
If a protein of 100 amino acid residues had to assume every possible conformation at the theoretically fastest rate (the period of a molecular vibration is about 10^-13 seconds) then it would take 10^85 seconds or 10^77 years to have a 50% chance of finding its native, biologically active conformation. (paraphrased from Lehninger's Principles of Biochemistry, 3rd Ed.)
How long would a 1000 monkeys have to type to have a 50% chance of punching out Hamlet? There are about 167,000 characters in unique sequence, 96 characters on the keyboard, and a good typist can type 100 words a minute, or about 8 characters per second. The monkeys will be there (96^167)/8 or about 10^320 seconds.
How long would one have to watch an empty room at standard temperature and pressure for a 50% chance of observing every molecule of air in the room spontaneously aggregrate in one half of the room? Assuming air is one, pure, ideal gas, the average speed of these air molecules at 20 degrees C is 300 m/s; there are 6.022x10^23 molecules in a mole of any gas; 1 mole of gas occupies 22.4 liters. Let the room be 5mx5mx3m: all the particles would appear on the left side of the room once in 10^300000000000000000000000 seconds.
Compare those times to the predicted lifespan of the universe, when the last black hole is expected to disintegrate: about 10^80 seconds. Is this a long time? The age of the universe to date is about 4x10^17 seconds.
Posted by Niels Olson at January 8, 2006 7:03 PM
Comments
Post a comment
Thanks for signing in, . Now you can comment. (sign out)
(If you haven't left a comment here before, you may need to be approved by the site owner before your comment will appear. Until then, it won't appear on the entry. Thanks for waiting.)