**Editor for this issue:** Renee Galvis <reneelinguistlist.org>

- H.M. Hubey, 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.Mail to author|Respond to list|Read more issues|LINGUIST home page|Top of issue