3 ms·

Half a year after that talk Wolfram appeared on a popular podcast [1] to discuss his book on the Second Law of Thermodynamics [2]. That discussion contained the

Half a year after that talk Wolfram appeared on a popular podcast [1] to discuss his book on the Second Law of Thermodynamics [2]. That discussion contained the best one-sentence description of entropy I've ever heard: > Entropy is the logarithm of the number of states that are consistent with what you know about a system. [1]: Mystery of Entropy FINALLY Solved After 50 Years? (Stephen Wolfram) - Machine Learning Street Talk Podcast - https://www.youtube.com/watch?v=dkpDjd2nHgo https://www.youtube.com/watch?v=dkpDjd2nHgo [2]: The Second Law: Resolving the Mystery of the Second Law of Thermodynamics - https://www.amazon.com/Second-Law-Resolving-Mystery-Thermodynamics/dp/1579550835 https://www.amazon.com/Second-Law-Resolving-Mystery-Thermody...

frank20022 2y ago
By that definition, the entropy of a game of chess decreases with time because as the game moves on there are less possible legal states. Did I get that right?
- dist-epoch 2y ago
  Is about subjective knowledge, not objective. So entropy is not related to the number of remaining legal states. If I know the seed of a PRNG, the entropy of the numbers it generates is zero for me. If I don't know the seed, it has very high entropy. https://www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/ https://www.quantamagazine.org/what-is-entropy-a-measure-of-...
  - HelloNurse 2y ago
    Low entropy in chess means effective prediction of future moves, which is far less useful than dedicating equivalent effort to choosing a good next move for ourselves.
- infogulch 2y ago
  Sure. Lots of games result in a reduction in game state entropy as the game progresses. Many card games could be described as unnecessarily complicated ways to sort a deck, as an example. When analyzing games wrt the Second Law, consider that "the system" is not simply the current game state, but should at least include captured pieces and human choices.

frank20022 2y ago

By that definition, the entropy of a game of chess decreases with time because as the game moves on there are less possible legal states. Did I get that right?

dist-epoch 2y ago
Is about subjective knowledge, not objective. So entropy is not related to the number of remaining legal states. If I know the seed of a PRNG, the entropy of the numbers it generates is zero for me. If I don't know the seed, it has very high entropy. https://www.quantamagazine.org/what-is-entropy-a-measure-of-just-how-little-we-really-know-20241213/ https://www.quantamagazine.org/what-is-entropy-a-measure-of-...
- HelloNurse 2y ago
  Low entropy in chess means effective prediction of future moves, which is far less useful than dedicating equivalent effort to choosing a good next move for ourselves.
infogulch 2y ago
Sure. Lots of games result in a reduction in game state entropy as the game progresses. Many card games could be described as unnecessarily complicated ways to sort a deck, as an example. When analyzing games wrt the Second Law, consider that "the system" is not simply the current game state, but should at least include captured pieces and human choices.