Though there is a sense in which we can say that a stream of random numbers
has no pattern, this really is not so; it does have a pattern. But, the
pattern is nearly as complex as the string is long, so there is no general
way to find a simpler structure that is equivalent to the string of numbers.
In effect, the pattern of a string of random numbers is not reducible to a
shorter pattern, where as the pattern of a string of non-random numbers *is*
reducible to a shorter pattern. For example, one-third is representable as a
decimal number consisting of an infinite string of 3's following the decimal
point, but we can reduce this either to the specification I just gave
(repeating 3's) or to the representation 1/3 (with only an infinitesimal
loss in theoretical accuracy). If we had an infinite string of *random*
digits, we would not be able, even in principle, to get such a reduction
without losing a specific finite amount of accuracy. Thus, if we want to
encode and transmit a string of truly random numbers, we have to transmit a
message that is as long as or longer than this string of numbers, otherwise
the receiver will not get it all; there is no shortcut as there is with,
say, an algorithmically specified string ("Calculate a million digits of
one-half of pi").
Now, there is one other major point to be made here:
What if a number is algorithmically specifiable in a short algorithm, but
you don't *know* that? If I showed someone a billion digits of pi starting
from the million and first digit after the decimal point, it would be
extremely unlikely that he'd recognize that it was not a random number. Even
if he applied mathematical tests for randomness, this string would pass
those tests, even though it is strictly algorithmic.
What does this mean? It means that, when a string of numbers looks a certain
way, we treat it as random, even though it may not be.
What does *this* mean? It means that, in nature, causation assures that
nothing is random, but, because we do not have access to the details of the
"algorithm" that produces these results (i.e, the *exact* state of *every*
atom and subatomic particle and photon in the area at the time of
DNA-replication), we must treat genetic without reference not only to
purpose but to exact *causes* as well. When we say that something in nature
is random, this is usually what we mean, outside of a theological context.
This kind of randomness does not *strictly* imply non-design, because (as
the pi example shows) data can *appear* to us to be completely disorderly
even when it is strictly and mathematically precisely ordered.
On the other hand, it certainly does not imply *design*, either. So Brian is
right to suggest that the proper approach is to proceed simply without
*reference* to purpose.
Randomness as a mathematical term needs to be retained, but randomness as
denial of purpose is irrelevant.
However, there is simply no place for purpose in most of science (psychology
being one case where this does not apply), so, if anyone wants to bring
purpose into biology as such, it is up to him to support the burden of
proof. Otherwise, simply ignoring the possibility of purpose is the only way
to go; if there are patterns that *require* the conclusion of purpose, they
will be noticed *first* as mere *patterns*, not as purpose.
I have not been keeping up lately, so I want to end by asking about some
challenges I made some while back. Has anyone proposed a set of patterns or
other specific evidence that is claimed to support the design theory, or are
we still at the stage of saying, rather uselessly: "Well, it looks designed
to me."? Has anyone developed my suggestions for *why* living organisms
*look* designed?
--Chris