Re: A question on Dawkins

Mark Phillips (mark@maths.flinders.edu.au)
Wed, 24 May 1995 13:23:42 +0930

>> "To 'tame' chance means to break down the very improbable into less
>> improbable small components arranged in series. No matter how
>> improbable it is that an X could have arisen from a Y in a single
>> step, it is always possible to conceive of a series of infinitesimally
>> graded intermediates between them. However improbable a large-scale
>> change may be, smaller changes are less improbable. And provided we
>> postulate a sufficiently large series of sufficiently finely graded
>> intermediates, we shall be able to derive anything from anything
>> else"*
>> (Dawkins R., "The Blind Watchmaker", 1991, Penguin, p317).
>
>Pardon my possible ignorance of the subtleties involved here, but I keep seeing
>this quote, and I keep thinking *it just ain't so* - perhaps someone can
>explain what I am missing (I assume Dawkins hasn't made the basic mistake I am
>about to accuse him of)
>
>If one takes 100 dice, rolls them all at once, the probability of getting 100 x
>sixes is pretty low (1/6 ^ 100). *Ah, but,* says Dawkins, *a SINGLE six is
>much more likely - only 1/6 - THUS if we roll a single dice 100 times we are
>more likely to get 100 x sixes.* Now, as I say, this just ain't so, but it
>appears to me that this is exaclty what Dawkins is saying. What am I missing,
>or is he indeed plain wrong?

The two scenarios are different. Perhaps a better illustration of what Dawkins
is saying is this:

Suppose you play a game where, in a single step you do the following:
1. throw 100 dice
2. take out all the dice that came up with a six
3. replace these dice with special new dice with the peculiar
feature that they have six dots on every side. (let's
call these special dice, "multi-six" dice)

Dawkins is saying that, though the probability of getting 100 sixes after a
single step is very small, it is far more probable that we will get 100 sixes
after lots of steps. Indeed, in the limit as the number of steps approches
infinity, the probability of getting all sixes approaches 1.

You won't get from 0 multi-six dice to 100 multi-six dice in one step, but if
we have a series of graded intermediates, eg:

0 multi-six dice -> 16 msd -> 21 msd -> ... -> 96 msd -> 96 msd -> 97 msd
-> 97 msd -> 97 msd -> ... -> 100 msd

then providing we have enough of these intermediates, then we can quite reasonably
go from 0 msd to 100 msd.

The question of course to be asked is, does the evolutionary framework work as
nicely as in this example? The answer is: no, it isn't quite as nice. However,
it may be nice enough. Certainly evolution has similarities with the above
example, but it is more complicated than this. In this case, the path by
which one would go from 0 msd to 100 msd is quite clear - it is also clear
that the random process would naturally tend in that direction. With evolution,
it is not so clear that a pathway for the evolutionary process to naturally
follow, exists. (Though they may well exist?)

Dawkins is right in saying that we can't rule out a transition from X to Y,
just because a one step transition is highly improbable, for it may be that
with gradual transitions between intermediates, the eventual transition
from X to Y becomes highly probable. However, it is one thing to argue
the ruling out of an X Y transition, it is much harder to argue that
gradual transitions will in fact get to the desired result.

I hope this helps,

Mark Phillips.