Disclaimers aside, you've asked an extremely good
question that has a surprising answer. Surprising,
that is, if you know too much probability theory. :)
A standard argument against the probability argument
goes like this. I've just flipped a coin 48 times with
this specific result. The probability that I would get
this specific result is 2^-48. Therefore its impossible
for me to do what I just did. Now, in your post I sensed
a little rebellion :) at the idea that such an example
is actually a refutation of the probability argument.
Its somewhat of an affront to one's sensibilities. But
the argument is entirely correct wrt probability theory.
What few people realize is that developments over the
last 30 years have over turned the argument and rescued
our common sense. This is not to say that we can always
trust common sense. Quite often it will lead us astray
in science and mathematics. Anyway, what I'm talking
about is the relatively new field of Algorithmic Information
Theory (AIT).
I've written extensively on this in the past so I'm going
to be brief here. More complete treatment can be
found in two posts I made almost 3 years ago:
http://asa.calvin.edu/archive/evolution/199601-02/0263.html
http://asa.calvin.edu/archive/evolution/199601-02/0264.html
Better yet, you can take a look at Gregory Chaitin's web
page (Chaitin is one of the founders of AIT).
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/
More specifically I would recommend Chaitin's 1975 SciAm
article "Randomness and Mathematical Proof", available
at:
http://www.cs.auckland.ac.nz/CDMTCS/chaitin/sciamer.html
For those who don't want to look these up, the idea is as
follows. One first introduces a new definition of randomness.
This definition has to do with compressibility. Random means
incompressible. I don't want to get into details so let me
just say that the basic idea of compressibility has to do with
patterns. If any sequence has a pattern, that pattern can be
utilized to compress the sequence. So random can also be
interpreted as patternless. Now, where this really differs
from probability theory is that one no longer has to look
at specific sequences (this is what got us into trouble above).
Instead one can put sequences into large groups defined by
their degree of compressibility. Now, the important result for
our discussion here is the finding that the vast majority of
all possible sequences ofa given length are random, i.e.
patternless.
Now let's apply this idea. Suppose that you are flipping a fair
coin and recording a 1 for heads and a 0 for tails. Now consider
the following two potential outcomes:
(A) 0101010101010101010101010101010101010101010101010101010101010101
(B) 1110101010010010101001010011000111100111100110011111000011010011
and try to imagine yourself flipping a coin and writing down the sequence
term by term. Would either of the two results be surprising in any way?
Common sense tells us that (A) should be really surprising while
probability theory says we shouldn't be surprised at either one
since they both have an equal probability (2^-64) of occurring.
AIT rescues us from the absurd in the following way. The vast
majority of all sequences of length 64 have no pattern. Therefore
we should be really surprised to observe *any* sequence that
has a pattern. Not just that particular sequence we wrote in (A),
*any* sequence with a pattern.
So, for the above reasons, I would never give the "any specific
sequence is improbable" as an answer to the probability argument.
Instead, its better to point out the inherent assumptions in
the probability argument and that these assumptions are
most often violated in the situations to which the argument is
applied. A common argument one sees is: "If it doesn't happen
by chance, it must be intelligent design." Well, this misses out
on one important alternative in scientific discussions, i.e.
natural law ;-). This has been discussed amply by others.
Here's an example I like to use. Of all the umptity gazillion
possible paths that a planet might follow about the sun,
what's the probability that it just happens to follow an
elliptical path?
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"It appears to me that this author is asking
much less than what you are refusing to answer"
-- Galileo (as Simplicio in _The Dialogue_)