Anon.  wrote or quoted:
> Tim Tyler wrote:
> > Anon.  wrote or quoted:
> >>Jim McGinn wrote:
> >>>jason{at}kalavinka.freeserve.co.uk (friend) wrote in message
news:...

> >>>>Pardon my ignorance, but I have only just discovered this law.
> > 
> > [...]
> > 
> >>>Many of the more popular myths of the current paradigm 
> >>>of evolutionary biology pivot off a kind of rhetorical 
> >>>trick.  Specifically the trick involves employing a 
> >>>word that has more than one meaning in an argument (or 
> >>>special case) to achieve the illusion of scientific 
> >>>validity.  This is *all* that's going on with the 
> >>>Hardy-Weinberg, socalled, Law.  And you hit the nail on 
> >>>the head with respect to which word is the "pivot" with 
> >>>respect to how this rhetorical trick is manifested in 
> >>>Hardy-Weinberg: randomness.  
> >>
> >>Wierd.  The Hardy-Weinberg law is deterimistic: there is no randomness 
> >>in it.
> > 
> > The Hardy-Weinberg law is normally stated in a form that refers to
> > a large population where mating is random.
> 
> The theorem was derived for an infinite population.
> 
> > E.g. see: 
> > 
> >   http://library.thinkquest.org/19926/java/tour/06.htm?tqskip1=1
> > 
> > Alas, this page expresses the law in terms of an infinite population :-(
> > 
> > A disasterous error - IMO - since talking about gene frequencies in an 
> > infinite population is a sign of mathematical ignorance.
> 
> No, it's a simplifying assumption.  I think to accuse Hardy in 
> particular of mathematical ignorance deserves, well, a 
> non-mathematician's apology.

I never said the problem was at Hardy's end.

> > Popularisers should make explicit the behaviour is what happens as
> > the population size tends towards infinity - and not attempt to pass
> > it off as an effect in an infinite population.
> 
> But it is - in finite populations, you get an excess of homozygotes, as 
> any student of population genetics should know.

Any mention of gene frequencies in an infinite population is nonsense -
as I stated originally.

You can't talk about a fraction of an infinite population having
a trait.  You would get different results for that fraction depending
on how you enumerated through the population.

It's like claiming that half the integers are even.

Such statements are total mathematical gibberish.

What *can* be said is that the fraction of the set of integers from
0 to N that are even tends to 0.5 - as N => oo.

No serious mathematician can talk about fractions of infinite sets and 
expect to be taken seriously.
-- 
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