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Re: Mass Extinction Statistics



> On Thu, 24 May 2001, David Marjanovic wrote:
>
> > > I put up 500,000 black dots and 500,000 red dots on my board.  I have
a
> > > cannon that fires 500,000 bullets at once.
> >
> > I'd rather say you have a big bomb rather than exactly 500,000
individual
> > bullets. You let the bomb detonate, and then you look if you find a
pattern
> > among the unhit dots.
>
> Well, whatever the delivery mechanism, it should have a random
> effect--perhaps more diffuse than a bomb--after all, the placentals are
> not all living together in one happy bunker, nor the marsupials.  There
> are millions (probably) of organisms in many niches.

AFAIK there were few niches occupied by meta- & eutherians in LK NA, just
everything between shrew, opossum and Tasmanian Devil.

> > > Given our assumption of equal population number, equal
> > > susceptibility, etc., is this not a fair analogy?  And isn't it true
that
> > > the more dots I have, the greater my chance of reaching 50/50?
> >
> > The more times you fire the cannon, not the more dots you have.

Sorry -- only if you average over the times you fire the cannon, of course.

If you, say, double the number of dots, each single dot still has a 50/50
probability of being hit, but the probability that 500,000 particular dots
will be hit is, if I'm correct, 0.5^500,000, whereas the probability that
1,000,000 particular dots will be hit is a mere 0.5^1,000,000 -- far, far,
far LESS.

> Several have said this.  Why?  What's the difference whether I increase
> the population or the number of bolide strikes?  Flipping a
> flippin' coin a hundred times is the same as flipping 100 flippin' coins
> once.

But flipping coins is not analogous to the above approximation to an impact.
0.5^500,000^2 (hitting 500,000 particular dots in two tries -- not
necessarily the same dots in both tries) is not the same as 0.5^1,000,000
(hitting 1,000,000 particular dots in one try)!