Posted by
Steve Smith on
Apr 27, 2010; 6:50pm
URL: http://friam.383.s1.nabble.com/PLEASE-DON-T-READ-Nick-s-post-Schroedinger-s-What-is-Life-tp4966453p4970269.html
sarbajit roy 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).
I'm not that confident in my own stats without careful review. My
number was just a rough revision of Nick's computation to put it back
in perspective (from his minor but significant error in what is in the
numerator and what is in the denominator). I'm not confident in this
myself (without some study/review that I'm not willing to do at the
moment) to support or refute your estimations.
In any case, we all seem to agree (including Erwin Schrodinger) that
when we wash our humble pie down with that glass of water, it is likely
to have some of those marked molecules in them (if the Nazi scientists
at Vemork, Norway spilled any of their heavy water down the river, we
would be assured of drinking some of that as well, right?)
How about whale piss from Moby Dick? Any of that in the glass of
water (a little harder to detect)? As for the heavy water (deuterium
oxide), I believe the natural concentration in water in the wild is
something like 10^-7 by mole (rather than mass), making it 14 orders of
magnitude more likely to be in your glass than ES's postulated glass.
Don't the "laws of large (and small) numbers" lead one down strange
passages. How do we think about these "laws" in the light of the "why
theorems?" thread.
I must be avoiding some kind of important work.
- Steve
On Tue, Apr 27, 2010 at 9:35 AM, Steve Smith
<[hidden email]> 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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============================================================
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