The equal dignity of all human beings?

January 25, 2008

Would it be possible to make a scientific approach to the question of equal dignity of all human beings? If all religions and -isms are products of evolution, it should perhaps be possible. According to the theory of Gaussian adaptation, evolution strives to solve a collective survival problem by increasing mean fitness and diversity in parallel. A reasonable assumption is that survival has a high priority. Then, suppose that the following question may be answered: To what extent may every individual contribute to the solution of the collective survival problem? Would it be possible to make a scientific approach to the question of equal dignity of all human beings? If all religions and -isms are products of evolution, it should perhaps be possible. According to the theory of Gaussian adaptation, evolution strives to solve a collective survival problem by increasing mean fitness and diversity in parallel. A reasonable assumption is that survival has a high priority. Then, suppose that the following question may be answered: To what extent may every individual contribute to the solution of the collective survival problem?

Suppose also that the answer is that all humans contribute equal. This is what the blog is about.

The idea that all humans have equal dignity is merely an agreement based on emotions and a religious or human view among a sufficiently large number of individuals. There are also many other values. For instance, if we ask an employee, the answer will probably be that we have different market values, and a biologist may say that we have different survival values etcetera. I prefer the latter, which has a higher priority, because if we do not survive, we may forget about all values.

The first survival value that comes to our mind is perhaps the fitness of the individual, which can hardly be equal for all. But there are other possible definitions. Considering that evolution strives to solve a very complex collective survival problem by increasing the mean fitness and diversity in parallel, where the degree of difficulty is far beyond the mental ability of man, we may ask the following question: To what extent may every individual contribute to the solution of the collective survival problem? Suppose the answer to be that all contribute equally. In such a case, all humans should have equal dignity.

How do we arrive at such a conclusion? Let us see a 2-dimensional experiment of thought shown in the figure below. Suppose that the two quantitative characters are uniformly distributed (represented by the even blue color) over the rectangle, which may be moved around over the white region of acceptability (limited by the red curve), in accordance with the rules of genetic variation, which is of course an utopian situation, but allowed in an experiment of thought.

In this case, the mean fitness is the hitting probability of the blue distribution on the region of acceptability. That the rectangle is optimally placed follows from the fact that the green edges to the left and right have equal length, and likewise to the top and bottom. Because if the rectangle is slightly moved in some arbitrary direction, the surface attained on one side is lost on the other side. Thus, the hitting probability (mean fitness) of the uniform distribution on the region of acceptability is maximal.

http://picasaweb.google.com/gregor744/GA_figures02?authkey=Gv1sRgCNLYgpO...

Suppose that the small red circle inside the square does not belong to the region of acceptability. Then, because the distribution is uniform, it follows that this circle may be moved around inside the rectangle without violating the optimal position. This means that all individuals having parameter values falling inside the rectangle have no effect whatsoever on the solution of the problem. In other words, the only individuals having any survival value in this sense are those whose parameter values fall exactly on the edges of the rectangle; all other individuals are useless.
This means that in order to maximize the mean fitness of the uniform distribution, using the condition of optimality according to the Hardy-Weinberg law with coinciding centers of gravity between parents and offspring, then the distribution has to be changed to a distribution along the edges, which contradicts the original task. Then, if all blue individuals are giving weight to the centre of gravity and the red circle is not placed at the centre of the rectangle, it can no longer be optimally placed.

But, because of the entropy law and that a Gaussian is most disordered as compared to all other distributions having the same moment matrix, we may expect the Gaussian to be a more commonly apparent distribution of characters in a large population. And according to the theorem of Gaussian adaptation, all distributions that deviate from Gaussian have to be changed. To my knowledge, the Gaussian is the only distribution by which the problem may be exactly solved without any changes, at least from a theoretical point of view. And in this case all individuals have equal survival value.

In practice, however, the problem can never be exactly solved, because the number of individuals is always limited giving rise to a statistical uncertainty. And because of the tremendous complexity of the process in many dimensions, when the real distribution of parameters is not known, it will be extremely difficult to evaluate different individuals with respect to their survival value. Thus, we may as well presume that all individuals have equal dignity.

Gkm

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