[language] Re: 13.2704, Disc: Darwinism & Evolution of Lang

[H.M. Hubey]

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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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