I had a random idea a while back and decided to chase it down. I saw that Gibbs method of statistical mechanics relies on operations of certain distribution functions, like the Gamma distribution or the Normal distribution. In my work I kept on coming across the Log-Normal distribution. It is everywhere. So I decided to have a look and see what I could derive. While I did this for the Log-Normal and Gibbs did it for the Gamma and Normal distributions, this approach is applicable to any other distribution.

Theory is no good unless you can test it and see it in our data. So I tested it on income distributions, reported in the the attached paper, bitcoin transactions (work in progress), and radiation exposure to cells (unreported work).

In my work, I derived the Cobb-Douglas function as a property of the Log-Normal distribution. Yesterday a friend tweeted a link to a blog The entropy of nations. If you have not read it I suggest you do. The author identifies maximum entropy as Adam Smith’s “invisible hand”. I emphatically agree with his analogy. The tendency towards maximum entropy is seen in the process of price discovery it is the invidible hand that drives arbitrage.

His work motivated me to finish mine and with a boring and non descriptive title to boot! Various Properties of the LogNormal Distribution. Can you say math fun? The policy stuff is in the last section if you are so inclined and the mathy stuff is in the front two sections. I found income distributions obey the second law of thermodynamics. This is great news! The bad news and what inspired my evocative title is that while we can propose policy and develop theories that say it will work, that no quantity of ink or PhD’s is going to change the second law. If you are not aware that it applies, so well. There is a chance you got the theory right, but its just not very likely. I had a Commanding Officer tell me, “Cal, Hope is not a plan. A plan is a plan.” Wise words. He left out that my plan actually better be possible. Hope as a policy is wishing for unicorns. That is my best description of any progressive policy, wishing for unicorns. It explains why what we get isn’t what we were sold. Somewhere along the line reality hit.

Here to any progressives that follow me or stumble across this blog, there is my gauntlet laid at your feet. I invite your responses.