Question: Of the bound hydrogen atom eigenstates, which has the highest kinetic energy?
Answer: The lowest energy state.
Ain’t that curious? Kepler’s laws helped me understand this one. Oh, and this holds for all molecules - I leave the proof as an exercise.
Let’s say you have a box full of particles, and each of those particles is independently in one of N states. Each state has a probability of occuring. Let us further suppose that none of these probabilities are the same - if so, then there is one state with the highest probability. If there are then properties E and V which are diagonal and have a 1-1 correspondence to each other amongst all the states, then the most common E and most common V definitely are related to each other by E=MV^2/2.
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Examine the Speed and Energy distributions of the ideal gas. The modal values of these two distributions do not correspond to each other via the E = MV^2/2 relation. Paradox?
I’ve been reading What is Thought? by Eric Baum, a book on the mind by an AI researcher.
For part of the book, Baum describes solving Blocks World problems with a computational economics model. The problem is called Hayek, and it is described in this article. I will just describe the part that is most interesting to me.
Professor Chakraborty described some work identifying what is essentially an analog-to-digital circuit in the immune system. One thing he mentioned was the future use of renormalization group theory to study these systems.