Professor of Computer Science and Law, Emeritus, Rutgers University.
I have been working on AI and Law for a long time. I am particularly interested in bridging the gap between machine learning and logical rules, which is an important issue today for legal technology. You can find most of my papers on ResearchGate: https://www.researchgate.net/profile/L-Thorne-Mccarty
Before I kick the bucket, I want to figure out how these frameworks fit together:
classical mechanics
classical statistical mechanics
classical field theory
quantum mechanics
quantum statistical mechanics
quantum field theory
thermodynamics
and probably some more. For example, one famous weird thing is that if you take classical statistical mechanics and replace
1/(Boltzmann's constant × temperature)
with
i × Planck's constant × time
in all your equations, you get quantum mechanics - more or less. So if you ignore the constants, this is saying that "imaginary time" - whatever the hell that is! - acts like "inverse temperature".
Physicists use this fact a lot, but remain divided on whether it's "just a trick". I don't think something this big can be just a trick!
But there are other ways to set up this analogy. I wrote a paper with Blake Pollard where instead we said inverse temperature is analogous to i × Planck's constant. We pushed this other analogy to the point of figuring out what in quantum mechanics corresponds to 𝑒𝑛𝑡𝑟𝑜𝑝𝑦 in classical statistical mechanics. We called it "quantropy", and worked out this nice chart.
But now I'm wishing we hadn't set Boltzmann's constant equal to 1. And I want to compare our analogy to the usual one, and figure out what the hell is going on. When there are multiple mathematically rigorous analogies between frameworks you should get serious and study them all, not just pick one and ignore the rest.
I'm also annoyed that we didn't notice that the thing analogous to free energy, which I called "free action" or Φ, is what physicists call the "effective action".
Here's our paper:
There is a well-known analogy between statistical and quantum mechanics. In statistical mechanics, Boltzmann realized that the probability for a system in thermal equilibrium to occupy a given state is proportional to exp(-E/kT) where E is the energy of that state. In quantum mechanics, Feynman realized that the amplitude for a system to undergo a given history is proportional to exp(-S/i hbar) where S is the action of that history. In statistical mechanics we can recover Boltzmann's formula by maximizing entropy subject to a constraint on the expected energy. This raises the question: what is the quantum mechanical analogue of entropy? We give a formula for this quantity, which we call "quantropy". We recover Feynman's formula from assuming that histories have complex amplitudes, that these amplitudes sum to one, and that the amplitudes give a stationary point of quantropy subject to a constraint on the expected action. Alternatively, we can assume the amplitudes sum to one and that they give a stationary point of a quantity we call "free action", which is analogous to free energy in statistical mechanics. We compute the quantropy, expected action and free action for a free particle, and draw some conclusions from the results.
I wrote a thread last week on LinkedIn in which I discussed these three articles and explained how they fit together in a broader context. Rather than repeating the thread here, I will just link to it:
https://www.linkedin.com/posts/lthornemccarty_machinelearning-deeplearning-generativeai-activity-7197269535287058434-4d6l?utm_source=share&utm_medium=member_desktop
Comments and questions are welcome!
#MachineLearning #DeepLearning #GenerativeAI #DiffusionModels #NeuroSymbolicAI
Cool and normal
@mainec - Thanks. English translation:
"The events from 1933 to 1945 should have been combated by 1928 at the latest. Later it was too late. One must not wait until the struggle for freedom is called treason. One must not wait until the snowball has become an avalanche. One must stop the rolling snowball, since no one can stop the avalanche. It only rests when it has buried everything beneath it. That is the lesson, that is the conclusion of what happened to us in 1933. That is the conclusion we must draw from our experiences, and it is the conclusion of my speech. Threatening dictatorships can only be fought before they have taken power."
Erich Kästner, Über das Verbrennen von Büchern
This is on my mind all the time now. I don't think it's inevitable, but our weak response to this growing possibility makes it more likely. Please, everyone, fight back now when it's easier.
You can read the article here:
Here are some things you can do:
1) Vote for the Democratic presidential nominee.
2) Talk to people: inform the uninformed.
3) Contribute money or time to the Democratic presidential campaign.
4) Help get out the vote, for example:
https://traindemocrats.org/blog/ultimate-guide-gotv/
5) Contribute money or time to organizations who are fighting voter suppression, like the ACLU:
MikeDunnAuthor
Jesse Skinner
John Carlos Baez
Dan Goodman
jonathankoren™
Mark A Lemley