From: throopw@sheol.UUCP (Wayne Throop)
Newsgroups: talk.origins
Subject: Holden and probability
Summary: it seems very improbable that Ted can justify the 1/64 odds
Date: 29 Sep 92 02:01:13 GMT

::: 1.  That the continents were all clumped into a single mass in the first
::: place.  No force exists at present which might ever draw them all
::: together, and the odds of them all merely drifting together for no
::: reason are greater than 64 - 1, which would be the odds against them
::: ever merely appearing in the same hemisphere for no real reason.
:       It amazes me that you repeat this unbelievably stupid probability
:       argument.
: It amazes me that you, PHD degree and all, cannot comprehend it.  

It is perfectly clear that Bill Hyde *does* understand it, and that
Ted Holden does *not*.  But Ted goes on, with a marvelous example of
"argument from irrelevance" that really deserves to be repeated:

: The odds
: against all continents ending up in one place are certainly a good deal
: greater than the 64/1 figure I noted.  This would not ever happen by chance.
: I think that by most serious mathematicians agree that no number of chimps
: with tyewriters would ever write even one of the great novels, much
: less all of them...

Ted refuses to discuss the assumptions and reasoning behind the 1/64
figure for "ever in same hemisphere", but let us speculate.  It seems
likely that Ted supposes that there are seven continents (europe, asia,
africa, australia, antarctica, north america, south america) each one of
which is either in a given hemisphere or "the other" one, with equal
probability.  Out of the 128 ways these situations can combine, we get 2
where all seven fall the same, one case of all heads-hemisphere, one
case of all tails-hemisphere.  Which is, of course, 1/64. 

There are, of course, several problems with this.  For one, it overlooks
cases that would satisfy the "same hemisphere" for a different choice of
hemisphere.  For example, if we kept track of four quarter-spheres, that
would be 16384 possible outcomes, and 128*4-4 cases where all seven are
in two adjacent quadrant, or just a tad more than 1/32.  Making this
continuous I won't bother with...  but you see the point. 

For another, it is modeling things as one-shot, and there would be
sufficient time, even at 2-4 cm/year, for at least two throws of the
continental dice, perhaps 4.  Perhaps more.  This gives a figure more
like 1/16 or 1/8 (but only something like... remember actual rules for
adding probabilities).  Given enough time, it'd be arbitrarily close to a
sure bet, so the "odds of ever being in one hemisphere" is quite clearly
wrong on this ground alone. 

Finally and most importantly, plate tectonics does NOT suppose that the
continents drift at random.  They follow rather constant courses for
long periods of time.  In such a situation, something like the
supercontinent cycle would *have* to occur...  plotting seven continents
traversing great-circle routes doesn't leave much room for anything
*but* a consolidation into a supercontinent. 

To sum up, Ted's (via Rose's) model of continental drift from which
the bogus 1/64 probability is derived is inaccurate for several
reasons, because

      - it doesn't seem to take into account arbitrary 
        hemisphere orientation
      - it doesn't take into account repeated trials
      - it treats the course of drift as random, and it is known
        not to be random
      - it models the continents as points, and ignores their size

( My statistics is rusty... I'd appreciate any corrections or
  refinements to the above points by other t.o. denizens.   Certainly
  I'd love to see Ted support the 1/64 figure with the assumptions and
  calculations he (Rose) uses to arrive at it.  )
--
Wayne Throop  ...!mcnc!dg-rtp!sheol!throopw
Newsgroups: talk.origins