Suppose there are C cups of water in the ocean and each cup has M molecules of water. Then there are CM molecules of water in the ocean. One cupful, or M molecules, are marked, so M out of MC, or 1 out C, molecules in the ocean are marked. In a cup of water taken at random (i.e. from a well-stirred ocean) there would still be about 1 out of C marked molecules so about M/C molecules per cup.
In the case at hand, M/C is 1000 so each random cup has about 1000 marked molecules. If we examined a large number of such cups they would have a mean of 1000 marked molecules wit a standard deviation of the square root of 1000 (between 31 and 32). Their distribution would be (for all practical purposes) normal. a cup with no marked molecules would be 31 standard deviations from the mean and such events essentially don't happen. Even a cup with only 100 marked molecules would be (almost) 28 standard deviations from the mean. So virtually all cups of water drawn at random will have at least 100 molecules ________________________________________ From: [email protected] [[email protected]] On Behalf Of Nicholas Thompson [[email protected]] Sent: Monday, April 26, 2010 11:50 PM To: [email protected] Subject: [FRIAM] Schroedinger's "What is Life?" All, I am working my way through this book, and, rather than write one huge email that nobody reads, I thought I would write some short ones that somebody might read. It's a splendid little book, very cleanly and economically written. S. is not beset with jargonophilia. The basic idea of the book (correct if wrong, please) is that living systems are orderly systems that fight off disorder with order. Although written many years before the double helix, he is struck by the fact that the elemental particles of genetic inheritance are so very small that their absense of vulnerability to quantum processes is next to miraculous. Right now I just have questions, so I will start with a question. S. writes, channelling Lord Kelvin: Suppose that you could mark the molecules in a glass of water; then pour the contents of the glass into the ocean and stir the latter thoroughly so as to distrubute the marked molecules uniformly through out the seven seqs; if then you took a glass of water anywhere out ot the ocean, you wound find in it about a hundred of your marked molecules. I am sorry this HAS to be wrong. However many molecules there are in a glass, there are a gazillion glasses of water in the ocean, and isnt the probability of coming up with any part of any one of them, vanishingly small. Ok, work it out, thompson: There are, apparently, 8x 10^21 cups of water in the ocean. and 8 x 10^24 molecules in each cup. Which means to this former english major that there are a thousand times as many molecules of water in the glass as there are glasses of water in the ocean in the ocean. So, my chance of drawing any one of the hundred marked molecules by chance is one in a thousand, right? Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([email protected]<mailto:[email protected]>) http://home.earthlink.net/~nickthompson/naturaldesigns/ http://www.cusf.org [City University of Santa Fe] ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
