Dear Edwin,
The analogy you draw is interesting. There are some illuminating similarities between various statistical distributions in nature and the distribution of money in a developed human society. I agree with you that an equal distribution of money, or of material goods in general, is not possible and would be undesirable. This is so, whether the units to be equalized are taken to be individual persons, adult persons, households, or whatever.
One thing that I do not understand clearly about your picture is the relationship between stability and freedom. On page 2 at the bottom where you set forth the two possible goals you appear to suggest that the appropriate goal is stability (that is, the continued existence of human society). Stability would seem to be the appropriate goal, because the other suggested goal, namely, equality, is neither possible nor desirable. One interpretation is that maximization of freedom is the way to achieve stability. But another interpretation would suggest that freedom for individuals and social stability are two different things. On that view, the goal is to achieve social stability while doing the best we can to also achieve as much freedom for individuals as possible. This interpretation is suggested earlier on page 2 with the statement, "Our 'cost function' will be individual freedom - we wish to maximize individual freedom while reaching our goal."
Another important question is whether freedom is defined largely, or even solely, in economic terms. We can ask, "Who should be free?" We can also ask, "Free for what or free in what ways?" On your view, the first question has a clear answer: the appropriate bearers of freedom are adult human individuals who have not been legally determined to be mentally incompetent or guilty of certain crimes. But I am not so sure that the second question has so clear an answer. What I have in mind is that economic freedom might sometimes be at odds with other kinds of freedom. If people are generally free to buy, sell, trade, participate in markets, accumulate wealth, and so on, then those people who are most proficient at these activities will gain greater capacity to promote their ideas. But if those ideas are considered solely as ideas, they may not be as valuable in a "marketplace of ideas" as some other ideas presented by people who are less economically astute.
At any rate, these are a few comments. I appreciate the opportunity to read your essay, and I appreciate the comments you made about my essay a few weeks ago.
Laurence Hitterdale