I know Nick likes to claim mathematical ignorance. But I doubt his claim. So this paper seems interesting:
The mathematics of the ensemble theory https://www.sciencedirect.com/science/article/pii/S2211379722000390 The 1st 2 assumptions make you read some math. But it's not that hard. Symbols are symbols, no matter which way you cut it. The 3rd is stated in English. I don't know how trustable this article is. Hell, since y'all trust ChatGPT so much, ask it to translate the math to English for you. Maybe use o3 if you have access to it [⛧]. But the idea of cutting down on the assumptions required for reifying some arbitrary math pleases me. I have a lingering desire to reject Marcus' conception of nihilism as a blank slate into which one pops and pushes arbitrary axioms. But I want to get through Nihilistic Times first. [⛧] https://lifehacker.com/tech/openai-promises-chatgpt-o3-model-better-at-reasoning Once you get its answers, you might go over to Claude and, using that English, ask it for some proof-assistant code to re-formalize it. Only when the two match could you call it trustable in any sense. On 12/29/24 15:30, Jochen Fromm wrote:
Quanta Magazine recently had a nice illustration of entropy https://www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/ I would say addition of heat increases disorder/entropy in general because in a typical thermodynamic system which is isolated from the environment * Heat increases the kinetic energy of particles which start to move faster * Faster movement leads to more collisions and diverging paths. In effect this means small changes in one state of the system can result in large differences in later states, i.e. to random motion * More random motion increases the disorder/entropy of the system -J. -------- Original message -------- From: Nicholas Thompson <thompnicks...@gmail.com> Date: 12/29/24 12:15 AM (GMT+01:00) To: The Friday Morning Applied Complexity Coffee Group <friam@redfish.com> Subject: [FRIAM] Boltzmann Distribution FWIW, I have been struggling with the concept of entropy for the last month. One of the puzzles was why entropy increased with addition of heat. I bullied George for a few hours and he finally admitted not only that the mean and variance of the B-distribution are correlated, but that its variance is the square of its mean. Why that is the case is beyond both of us. He also coughed up eventually the reason that adiabatic compression and decompression don't alter entropy: there is a trade off between spatial constraint and kinetic energy such that as the gas is confined its kinetic energy goes up and with that a compensating increase in the variance of the KE. Yeah. I know. Fools rush in where wise men fear to tread.
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