[...]
>>And if some are more probable than others,
>>how could we know which ones and how could we know
>>whether the specific one we're interested in is one of
>>the more probable ones or one of the less probable.
>>Given this uncertainty, isn't the fairest thing just to
>>assume they're all equally probable?
>
Bill H:===
>But we should be concerned with correct modeling, not "fairness".
For some reason this reminded me of a line in a Clint Eastwood
movie, can't remember the name. Clint is a bounty hunter. At
the end of the movie he's finally tracked down his man (Gene
Hackman) and it turns out that the guy has changed his ways.
He's now a respected member of the community. After the final
gun battle wherein Clint manages to get off 100 shots from
his 6-shooter without reloading ;-), Hackman is lying on the
floor helpless, looking up the barrel of Clint's gun. Hackman
says something like, "look how I've changed, I have a wife and
kids, I'm a respected member of the community. I don't deserve
to die this way, it's not fair". And then Clint says "fair ain't got
nuthin' to do with it" BANG.
As I think about it, it may have been "deserve ain't got nuthin'
to do with it". In any event I kind of imagined Bill with his
cowboy hat and boots and with his 6 gun drawn saying
"fair ain't got nuthin' to do with it" ;-).
And Bill is absolutely right of course, I'm just glad he's an engineer
and not a bounty hunter.
I think there is one thing I probably didn't make very clear in my last
post. What I was trying to do is put myself in the other guys shoes,
so to speak, and figure out how they came to the conclusion that
equi-probability of events is a good assumption. I don't think
the assumption is good myself and I don't think the various
lines of reasoning I was throwing out are particularly good
either, I was just trying to understand how the mistake came
about. What really bugs me about it is that the mistake is so
common. Previously I mentioned that its not a mistake that one
can pass off on those "ignorant creationists" since one finds the
mistake being made in the main stream literature. I had also mentioned
that it was the "old" literature. Well, looking through some of my
papers I found the assumption still occurs and is made by reputable
folks like Gerald Joyce:
=================================================
Regardless of what type of macromolecule one chooses
to use in a directed evolution experiment, the initial
step is the construction of a heterogeneous molecular
population. There are three basic strategies for
achieving this aim. The first is to prepare all the
possible sequences of a given length. If a proposed
macromolecule is to be 15 sub-units long and there
are four different types of subunits, the number of
possible arrangements is four raised to the 15th
power, or more than a billion. A starting population
of 10^13 molecules would therefore contain about
10,000 copies of each sequence. ...
-- Gerald Joyce, "Directed Molecular Evolution,"
SciAm, December 1992, pp.90-97, qt on pg 95.
=================================================
Of course, its entirely possible that Joyce's equi-probable assumption
in the above is not a mistake since the sequences were made under
controlled laboratory conditions in which the addition of all four bases
may be equally probable at all stages of the experiment. I don't know
enough about the chemistry to hazard a guess.
However, I think Bill's criticism is well founded if one is talking about
the hypothetical warm little pond. It seems to me a very poor assumption
to suppose the bases appear in equal concentrations in this case,
especially if one takes into consideration that there never was a warm
little pond (apologies to Erasmus Darwin ;-).
[...]
Brian Harper
Associate Professor
Applied Mechanics
Ohio State University