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Originally Posted by roachboy
i thought the question posed in the op was in itself religious.
from any other viewpoint, the makes no sense.
gregor: your posts are interesting. i confess, though, that i can't quite figure out how the demonstrations you provide either do or do not speak to anything to do with evolution in a darwinian sense.
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Well, at a first glance, the only connection to Darwinian evolution is that Gaussian adaptation (GA) uses random variation and selection. It is an example of “simulated evolution” using a computer with a Gaussian random number generator. Assuming that the rules of genetic variation – such as crossover, inversion etcetera - may serve as a random number generator for phenotypic parameters (morphological polygenic characters or even mental parameters as IQ, for example), GA would serve as a fairly good second order statistical approximation of the natural evolution.
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Originally Posted by roachboy
they seem to speak more to questions of modalities of change. which isn't the same thing, simply as a function of the time-frame involved and the imputing of a directedness to very long-term biological processes (an imputing that may or may not be a massive example of a teleological fallacy, there is no way to know).
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According to the fundamental theorem of biology (due to Fisher, 1930) evolution, like the GA-model, strives to a maximum in mean fitness. Briefly, the theorem states that: the rate of increase of mean fitness of any organism at any time is equal to its variance at that time. And a process that maximises something is goal seeking and may therefore be directed towards a maximum or a goal.
There is a difference, however, between the fundamental theorem and GA. In Fisher’s case the mean is determined over the set of genes in a large population assuming that a gene may have a fitness of its own and be a unit of selection. References may be found in
http://www.evolution-in-a-nutshell.se/references.htm
In the GA-case the mean is determined over the set of individuals leading to a different result. I think that GA is better off, because it is the selection of individuals that rules the selection of genes.
According to the fundamental theorem of biology (due to Fisher, 1930) evolution, like the GA-model, strives to a maximum in mean fitness. Briefly, the theorem states that: the rate of increase of mean fitness of any organism at any time is equal to its variance at that time. And a process that maximises something is goal seeking and may therefore be directed towards a maximum or a goal.
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Originally Posted by roachboy
but it seems that you have a set of assumptions about the formal language of mathematics and the kind of information about the world that it can generate that i find curious--the sort of thing that make some physicists imagine that there is are theological dimensions to string theory. this is itself a religious question because it only functions when you cross frames of reference. but it's a bit hard to tell: can you explain how you understand the relation between mathematics, its formal expressions, and theology or theological questions?
the obvious response would probably be that you see mathematics are a device that lets you describe the underlying rationality of physical phenomena even as it is itself a type of metaphysics (the language and its procedures). but it'd be better if you could explain it a little.
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I can only explain the mathematics used in the GA-model. If s(x) is the probability that an individual having the phenotypes x (an n-dimensional vector) and N(m – x) - where m is the mean of N - is the distribution of phenotypes in a large population, then
P(m) = integral s(x) N(m – x) dx is the mean fitness.
If x is only one parameter it is easily verified (high school level) that m = m* is a necessary condition for a maximal P. In a high-dimensional case matrices must be used for the proof and university level is recommended.
But it is also possible to maximise the disorder/mean information/diversity (all the same) keeping P at a suitable level. m = m* is the same condition of optimality as before. A new condition of optimality is M proportional to M* for the moment matrix of the Gaussian. These conditions are necessary to maximise disorder, keeping P constant.
This shows the difference between Fisher’s theorem and GA. Our interpretation is that GA maximises both mean fitness and phenotypic disorder simultaneously. The maximisation of disorder seems to have been missed in Fisher’s theorem. For more details see:
http://www.evolution-in-a-nutshell.s...adaptation.htm
My interpretation is that the GA-model explains both good things (maximum mean fitness) and evil things caused by the disorder, which stands for imagination and creativity, but which also is a reverse of the medal.