3 ms·

For once, a good article. Short, clear, to the point. Thank you, author.

by junon 5y ago

nextaccountic 5y ago
I love John Baez's blog too! But actually I think his long winded, mathematically challenging posts are more interesting. Like this series https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/ https://johncarlosbaez.wordpress.com/2012/01/19/classical-me... https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ https://johncarlosbaez.wordpress.com/2012/01/23/classical-me... https://johncarlosbaez.wordpress.com/2021/09/23/classical-mechanics-versus-thermodynamics-part-3/ https://johncarlosbaez.wordpress.com/2021/09/23/classical-me... https://johncarlosbaez.wordpress.com/2021/09/26/classical-mechanics-versus-thermodynamics-part-4/ https://johncarlosbaez.wordpress.com/2021/09/26/classical-me... An excerpt from the first article: > The big picture > Now let’s step back and think about what’s going on. > Lately I’ve been trying to unify a bunch of ‘extremal principles’, including: > 1) the principle of least action > 2) the principle of least energy > 3) the principle of maximum entropy > 4) the principle of maximum simplicity, or Occam’s razor > In my post on quantropy I explained how the first three principles fit into a single framework if we treat Planck’s constant as an imaginary temperature. The guiding principle of this framework is > maximize entropy > subject to the constraints imposed by what you believe > And that’s nice, because E. T. Jaynes has made a powerful case for this principle. > However, when the temperature is imaginary, entropy is so different that it may deserves a new name: say, ‘quantropy’. In particular, it’s complex-valued, so instead of maximizing it we have to look for stationary points: places where its first derivative is zero. But this isn’t so bad. Indeed, a lot of minimum and maximum principles are really ‘stationary principles’ if you examine them carefully. > What about the fourth principle: Occam’s razor? We can formalize this using algorithmic probability theory. Occam’s razor then becomes yet another special case of > maximize entropy > subject the constraints imposed by what you believe > once we realize that algorithmic entropy is a special case of ordinary entropy.

For once, a good article. Short, clear, to the point. Thank you, author.

by junon 5y ago

For once, a good article. Short, clear, to the point. Thank you, author.

I love John Baez's blog too! But actually I think his long winded, mathematically challenging posts are more interesting. Like this series https://johncarlosbaez.wordpress.com/2012/01/19/classical-mechanics-versus-thermodynamics-part-1/ https://johncarlosbaez.wordpress.com/2012/01/19/classical-me... https://johncarlosbaez.wordpress.com/2012/01/23/classical-mechanics-versus-thermodynamics-part-2/ https://johncarlosbaez.wordpress.com/2012/01/23/classical-me... https://johncarlosbaez.wordpress.com/2021/09/23/classical-mechanics-versus-thermodynamics-part-3/ https://johncarlosbaez.wordpress.com/2021/09/23/classical-me... https://johncarlosbaez.wordpress.com/2021/09/26/classical-mechanics-versus-thermodynamics-part-4/ https://johncarlosbaez.wordpress.com/2021/09/26/classical-me... An excerpt from the first article: > The big picture > Now let’s step back and think about what’s going on. > Lately I’ve been trying to unify a bunch of ‘extremal principles’, including: > 1) the principle of least action > 2) the principle of least energy > 3) the principle of maximum entropy > 4) the principle of maximum simplicity, or Occam’s razor > In my post on quantropy I explained how the first three principles fit into a single framework if we treat Planck’s constant as an imaginary temperature. The guiding principle of this framework is > maximize entropy > subject to the constraints imposed by what you believe > And that’s nice, because E. T. Jaynes has made a powerful case for this principle. > However, when the temperature is imaginary, entropy is so different that it may deserves a new name: say, ‘quantropy’. In particular, it’s complex-valued, so instead of maximizing it we have to look for stationary points: places where its first derivative is zero. But this isn’t so bad. Indeed, a lot of minimum and maximum principles are really ‘stationary principles’ if you examine them carefully. > What about the fourth principle: Occam’s razor? We can formalize this using algorithmic probability theory. Occam’s razor then becomes yet another special case of > maximize entropy > subject the constraints imposed by what you believe > once we realize that algorithmic entropy is a special case of ordinary entropy.