13.2721, Disc: Darwinism & Evolution of Lang

[LINGUIST List]

LINGUIST List:  Vol-13-2721. Mon Oct 21 2002. ISSN: 1068-4875.

Subject: 13.2721, Disc: Darwinism & Evolution of Lang

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1)
Date:  Mon, 21 Oct 2002 10:06:05 -0400
From:  "H.M. Hubey" <hubeyh at mail.montclair.edu>
Subject:  Re: 13.2704, Disc: Darwinism & Evolution of Lang

-------------------------------- Message 1 -------------------------------

Date:  Mon, 21 Oct 2002 10:06:05 -0400
From:  "H.M. Hubey" <hubeyh at mail.montclair.edu>
Subject:  Re: 13.2704, Disc: Darwinism & Evolution of Lang


Hubey  wrote:

>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.
>
>

Looking at the Eonix page where I read:

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.


I realize I have to expand what I wrote.

It is best explained via equations. Let f(t) be some function of time,
and r(t) be a random function of time.  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 definition of randomness.  To apply directly to evolution,
let the "evolution" of something very simple be given by the equation

                   dz(t)/dt + a(t)*z(t) = f(t)

This is the simplest, first-order, linear, ordinary differential
equation and has a solution in the most general case i.e. a(t) is a
function of time (not constant).  Here, a(t) is a coefficient of the
DE, and f(t) is known as the "forcing function" or "source term". The
reason for it is physical. The DE can be solved without f(t) and that
is known as the homogeneous solution. It is an exponentially decaying
solution, that is, it goes to zero as time goes to infinity. However,
if f(t), say, is sin(t), then this sinusoidal function "drives" the
system (e.g. the value of z(t)) in the sense that it does not go to
zero. That is why f(t) is also known as "forcing". It forces the
system to behave in a way that it would not behave if left alone. In
other words, without f(t) the equation describes the behavior of the
system itself, and f(t) is then considered external to the system but
which obviously affects the behavior of the system.

Rewrite it as L(t)z(t)=f(t) where L(t) is a (linear) operator.

Obviously, L(t) is nothing more that d/dt + a(t).  This "operates" on
the system (i.e. z(t)). To generalize, suppose z(t) is now a vector.
It is a set of variables. This particular way of looking at a system
is that z(t) is a set of variables that describes the system, and at
any time the specific values of these variables is the "state" of the
system.  So, we can think of evolutionary states in similar ways. For
example, it could be 30,000 dimensions for humans. That is the state
of each gene. Or better yet, let the state of the system be 30,000*N
where N is the number of humans in the world. Then the "state" is the
set of all genes of all humans.

So then if a(t) (which is also a vector) is random, then the operator
L(t) now generates random mutations in the gene pool of humanity.  And
here is the crux of the matter: the f(t) now determines which
direction evolution moves by forcing the system state to some
direction.  So mathematically we now have a description. Caveats:

1. It is linear and simple. Real evolution is likely not. But the
mathematical description can be extended to nonlinearity easily.

2. Both mutation (a(t)) and environment (f(t)) are now part of the
description.

3. Because the solution is a function of both f(t), and a(t) it is
still random.

4. We see that f(t) models environment, however, nobody can predict
the environment. As Bohr quipped "prediction is difficult, especially
the future". So unfortunately, f(t) must also be thought of as a
random variable.  The effects of f(t) at any time is direct, but
knowing what it is or will be, mathematically it must be modeled as a
random variable. The difference is this: a(t) acts on a fast scale,
but f(t) acts on a slower scale.

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