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<body><><><><><><><><><><><><>--This is the Language List--<><><><><><><><><><><><><><BR>
<BR>
<br>
<br>
Hubey wrote:<br>
<blockquote type="cite"
cite="mid20021021015017.27417.qmail@linguistlist.org">
<pre wrap="">Actually this is simply a matter of definition. It goes like this:
random + deterministic = random
random*deterministic = random
The former is "additive noise" and the latter "multiplicative noise",
and both are random. "Random" is not equal to "uniforrmly random",
thus one can find broadbrush patterns in random phenomena.
</pre>
</blockquote>
<br>
Looking at the Eonix page where I read:<br>
<br>
<font size="2">At a time when theories of evolution are undergoing
renewed controversy, discussion is hampered by the remoteness
of the phenomenon of evolution, and the use of indirect inference
to speculate about natural selection in processes that have
never been observed. Adherents of Darwinism often defend textbook
versions of the theory that have, in any case, often been held
in question. The assumption that evolution occurs, and must
occur, by random mutation and (non-random) natural selection
is the crux of the dispute, and one unreasonably confused with
issues of religion and secularization. The demonstration of
non-random evolution in the eonic effect must severely caution
Darwin's incomplete theory. </font><br>
<br>
<br>
I realize I have to expand what I wrote.<br>
<br>
It is best explained via equations. Let f(t) be some function of time, and
r(t) be a random function of time.<br>
Then if y(t)= r(t)*f(t) and x(t)=r(t)+f(t), both x(t), and y(t) are random
processes. This is due simply to<br>
definition of randomness. To apply directly to evolution, let the "evolution"
of something very simple<br>
be given by the equation <br>
<br>
dz(t)/dt + a(t)*z(t) = f(t)<br>
<br>
This is the simplest, first-order, linear, ordinary differential equation
and has a solution in the most<br>
general case i.e. a(t) is a function of time (not constant). Here, a(t)
is a coefficient of the DE, and<br>
f(t) is known as the "forcing function" or "source term". The reason for
it is physical. The DE can be<br>
solved without f(t) and that is known as the homogeneous solution. It is
an exponentially decaying<br>
solution, that is, it goes to zero as time goes to infinity. However, if
f(t), say, is sin(t), then this sinusoidal<br>
function "drives" the system (e.g. the value of z(t)) in the sense that it
does not go to zero. That is<br>
why f(t) is also known as "forcing". It forces the system to behave in a
way that it would not behave<br>
if left alone. In other words, without f(t) the equation describes the behavior
of the system itself, and<br>
f(t) is then considered external to the system but which obviously affects
the behavior of the system.<br>
<br>
Rewrite it as L(t)z(t)=f(t) where L(t) is a (linear) operator. Obviously,
L(t) is nothing more that<br>
d/dt + a(t). This "operates" on the system (i.e. z(t)). To generalize, suppose
z(t) is now a vector.<br>
It is a set of variables. This particular way of looking at a system is that
z(t) is a set of variables that<br>
describes the system, and at any time the specific values of these variables
is the "state" of the system.<br>
So, we can think of evolutionary states in similar ways. For example, it
could be 30,000 dimensions<br>
for humans. That is the state of each gene. Or better yet, let the state
of the system be 30,000*N where<br>
N is the number of humans in the world. Then the "state" is the set of all
genes of all humans. <br>
<br>
So then if a(t) (which is also a vector) is random, then the operator L(t)
now generates random <br>
mutations in the gene pool of humanity. And here is the crux of the matter:
the f(t) now<br>
determines which direction evolution moves by forcing the system state to
some direction. <br>
So mathematically we now have a description. Caveats:<br>
<br>
1. It is linear and simple. Real evolution is likely not. But the mathematical
description can be<br>
extended to nonlinearity easily.<br>
<br>
2. Both mutation (a(t)) and environment (f(t)) are now part of the description.<br>
<br>
3. Because the solution is a function of both f(t), and a(t) it is still
random.<br>
<br>
4. We see that f(t) models environment, however, nobody can predict the environment.
As<br>
Bohr quipped "prediction is difficult, especially the future". So unfortunately,
f(t) must also<br>
be thought of as a random variable. The effects of f(t) at any time is direct,
but knowing what<br>
it is or will be, mathematically it must be modeled as a random variable.
The difference is this:<br>
a(t) acts on a fast scale, but f(t) acts on a slower scale. <br>
<br>
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