Friam - FW: molecules in a cup [was DON"T READ]

Friam

FW: molecules in a cup [was DON"T READ]

Posted by Eric Charles on Apr 28, 2010; 2:16am
URL: http://friam.383.s1.nabble.com/PLEASE-DON-T-READ-Nick-s-post-Schroedinger-s-What-is-Life-tp4966453p4972281.html

Ack, wrote this right before John sent his email.....

Sarbajit, et al,
Technically it would be a binomial distribution of some ugly sort. There would be some skew, or at least a tail cut off in one direction earlier than the other, but for many purposes a normal distribution approximates the binomial distribution.

The probability of getting a glass with 0 molecules in it, if there was random distribution, would be quite small. Based on the numbers given, the change of drawing any given molecule, if drawing one at a time, would be 1/8x10^21. However, you are drawing 8x10^24 molecules at a time. So, on average you should have 1000 molecules per glass. However, the probability of getting any specific number of molecules per glass is quite small. If we use the approximation of the normal curve, and this is just the type of situation in which that is ungodly helpful, the standard deviation of the number of molecules in any glass is (I hope) 31.6 molecules. So 99% of the glasses you draw will have between 918 and 1082 molecules from the original glass. 99.99% of the sample glasses will have between 877 and 1123 molecules from the original glass.

I really hope that is right, I think it is,

Eric

P.S. The standard deviation of the binomial distribution = the square root of (the number of trials x the probability of a success x the probability of failure). In this case we have (8*10^24) trials, with a probability of success = (1/8x10^21), and a probability of failure = (1-the prob of success). The z-scores marking off 99% of the distribution are plus and minus 2.58, for 99.99%, z=3.90.

P.P.S. I might be horribly off because of how low the probability of a success is. I think the ridiculously high number of trials mitigates that, but I'm not sure how much.

On Tue, Apr 27, 2010 02:22 PM, sarbajit roy <[hidden email]> wrote:

Hi Steve

" The chances of drawing a glass without any marked molecules is 1/1000, supporting ES's claim."

I don't think the maths works quite that way. Some glasses would have exactly 1000 molecules, some would have 1000 -/+ 1, or 2 .. -/+999. Presuming that the distribution is a "normal" distribution, there would be an exceedingly small probability of getting a glass with zero marked molecules.

Furthermore since there is the equally remote probability that a single glass would contain all the marked molecules (just like we started out with), the distribution would be skewed away from a normal one..

This is just an off the cuff observation. I could brush up my prob-stats if reqd (and eat humble pie if wrong).

On Tue, Apr 27, 2010 at 9:35 AM, Steve Smith <sasmyth@...> wrote:

Nick -

I read it through before seeing your retraction. As you may recognize by now, your fallacy is probably not a consequence of your being an English (Psychology?) Major but actually just not reading the statement of the problem carefully enough. The 10^24 (molecules) vs the 10^21 glasses (cups?) might be about right and your math is good (1000 molecules per glass on average)... but the conclusion (1/1000 chance of drawing a glass with a marked molecule) is reversed. The chances of drawing a glass without any marked molecules is 1/1000, supporting ES's claim.

I'd say you did good (right up to that premature send thingy) for an English Major.

I read ES's "What is Life" years ago and was deeply inspired by it's directness and simplicity (and lack of jargon) and timeliness (1949?) well before much was done to tie life to information theory. I look forward to your continued "book reports".

- Steve
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Eric Charles

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Penn State University
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