Two cups of water for Erwin

The topic has only burned in your mind in the last five years, and well-stoked fires in the engine room spread quickly when unleashed.

If data analysis is indeed the art of cohomology, I think you will have much to teach me. I am tempted to title my next paper as 'Cohomological Insulators', to challenge the Topological Insulator. However, I must retain a cool head and not let the excitement overrun my judgement. My knowledge of cohomology is too narrow, I have learned to navigate to one island in an ocean of unknowns. It is rich mathematics I am delving into, I understand so little of even the Wikipedia page on it. Somehow I am going to publish a paper on it? My goal is to learn this subject better, even abstractly. Some abstractions are just waiting to be actualized.

It is amusing how Erwin talks about entropy (or free energy, as he later qualifies) and the second law, and then flippantly applies these concepts to the human body. Yet his example of the second law is two cups of water, one sugar-saturated and the other clear. Entropy increases when water migrates from the clear cup to the one saturated, so that the sugar has more space to roam. Here, entropy is well-defined locally for each cup, which maintains local equilibration at each step of the migration; the sum of the two entropies will increase. Quite right, Erwin!