Evolution in One Dimension
As odd as it may seem, evolution is possible, in an
abstract sense, in a one dimensional "world." That is,
if we start with a number-line and a zero-point and
any other point marked, and then replicate the marked
value while allowing for small random variations,
then, to any finite degree of accuracy, any number on
the number line can be reached in a finite number of
evolutionary steps (i.e., replications with occasional
variations, but with no selection, no exclusion of any
values).
What is even more interesting is that we can map
numbers on the line to numbers in a three-dimensional
"world" in such a way that any point in 3-space that
we might mark relative to X-Y-Z axes will also be
reached, with whatever finite degree of accuracy we
wish. This principle can be extended to *any* finite
number of dimensions, thus allowing us to represent,
solely by numbers on a line, any finite-length genome,
no matter how complex. This mapping can be
achieved in almost any number of ways, with different
results in 3-space depending on the mapping used
(and what happens in 1-space, of course).
What about selection? Yes, we can prevent some
values that appear on the number line from
replicating, thus excluding them and any values that
would depend on them. Thus, if the maximum size of
a random variation is, let us say, .5 of a unit of length,
and we block off a 1-unit length, the evolutionary
process will never get from one side of that blockage
to the other side.
What this means is that, in a 1-dimensional "universe"
with these kinds of restrictions, *if* a "species"
appears on the other side of the blockage, it got there
by some outside intervention of some sort. Could it be
design? Yes, in principle.
Further, since blocks to evolution can be of various
sizes, and since we could move them around, and
since selective mechanisms could be of weird types
(excluding only values close to prime numbers, etc.),
we can produce, even in this impoverished "world," a
number of bizarre and counter-intuitive results, some
of which might *look* like design (at least to Jones
and Bertvan), but which in fact could be the result of
randomly generated numeric variations starting from
an initial randomly chosen small number.
Since the blockages can come and go (depending on
how *they* are determined), we lose one key method
of determining design. We can no longer say that a
"species" that is *now* "too far" from other "species"
to have evolved from them or any of their ancestors
was *always* too far. The blockage may have
occurred *after* its ancestors were already on that
side of the area where the blockage is now placed. In
this case, in order to exclude random generation, we
have to have a fairly good knowledge of the *history*
of at least significant local span from this "world." If
the history is long and the data is sparse, we may be
*stuck* with presuming that the "species" arose
"naturalistically" (i.e., via the random variation and
repetition process).
In three or more dimensions, the problem becomes
even more nearly intractable.
Since most genomes can only be reasonably
represented in thousands or *millions* of dimensions
(without "folding" them into arbitrary numbering
schemes that use fewer dimensions), the process of
tracing a current genome back and ensuring that at
*some* time there was a sufficiently large genetic
"gap" and/or spatial-temporal gap between its first
ancestor and all other previously-occurring organisms
could be effectively impossible.
Yet, this is what ID theory depends on. It must show
that some organisms exist that could not have evolved
naturalistically from any prior organisms, or from
replicating autocatalytic sets of molecules, etc. It must
do this by showing that the gaps involved have always
been too large to bridge naturalistically. I'd like to be
able to offer some help, but I'm afraid the ID folks are
on their own on this one, because I doubt that there
ever *have* been gaps too large for existing
organisms to evolve across naturalistically, gaps that
have been present over a sufficiently long and
appropriate period of time, etc. To show that early
hominids did *not* evolve into modern man, for
example, they'd have to show that the spatio-temporal-
genetic gap was too large in one dimension or another
(or that modern man appeared on the scene *before*
any other suitable hominid ancestor-prospects, etc.).
It's interesting that, although ID claims to be a
positive theory, it can only be meaningfully validated
by showing that naturalistic evolution theories are
false.
This is because of one simple mathematical fact:
Random variation on a replicating genetic population
can eventually reach *any* possible genome and thus
any physically possible biologically viable organism.
It's conceivable, of course, that some such organism
could be too far, in all possible "directions" from all
earlier-appearing organisms to come into existence
naturalistically if there is a "zone of non-viability"
around it. But, this seems unlikely in the case of real-
world species. We can *imagine* such creatures, of
course (such as a pig-fish-tree-like animal with
feathered wings and a tendency to write books on
mathematics; such a creature might be to far from any
other creature we know of to be considered a likely
*natural* descendant of any *other* creature in
Earth's history).
Hmmm. This started out as merely an exposition of
the interesting features of one-dimensional evolution.
Sorry.
--Chris
This archive was generated by hypermail 2b29 : Sun Sep 24 2000 - 18:27:30 EDT