That's pretty good as far as I'm concerned. Took me a couple years to really grasp electrical impedance. Breakthrough for me was a concise book written in 1976 by Rufus P. Turner.
Subtle things take a while to get.
It took me 10 years to understand entropy
41–50 of 295 posts
Re: It took me 10 years to understand entropy
#42I had an art teacher who was very philosophical. One day he described to the class what entropy was. I took a lot of physics and even astrophysics. Little did i know he had a better conceptual understanding and explanation than i've ever heard before. Too bad i don't remember exactly what he said.
Re: It took me 10 years to understand entropy
#43Of all of physics, entropy is the most depressing part.
Re: It took me 10 years to understand entropy
#44The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
Re: It took me 10 years to understand entropy
#45One aspect of entropy that I always find counterintuitive is that unlike mass, charge, etc. it is not a physical quantity. In fact, from the point of view of an experimenter with perfect information about a physical system, the entropy of the system is exactly conserved over time (as made precise by Liouville's Theorem). The Second Law survives in this setting only in the most trivial sense that a constant function d…
Not really. Even from a point of view of an experimenter with perfect information, the entropy of the system declines over time as fewer and fewer bits are needed to describe the system. For example, start with a Glas of warm water and an ice cube in it. Over time, the ice will melt and the range of different temperatures of the molecules decline. Consequently, you need fewer and fewer bits to describe the complete s…
What is perfect information?
I understood perfect information to include infinite precision knowledge of non-quantized values like position and momentum. To store that information we'd almost always need infinite bits to express the state of even one particle.
(...and cough ignoring uncertainty...)
Using a finite number of bits was described in the comment above as "lumping positions into pixels".
Re: It took me 10 years to understand entropy
#46The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
> that a human body could theoretically spontaneously form out of particles given a long enough time span.
To be fair, isn't this precisely what happened?
Re: It took me 10 years to understand entropy
#47Here's another head-spinning application of the concept of entropy, in quantum information theory:
https://www.cambridge.org/core/books/abs/quantum-information...
> "The first fundamental measure that we introduce is the von Neumman entropy. It is the quantum analog of the Shannon entropy, but it captures both classical and quantum uncertainty in a quantum state. The von Neumann entropy gives meaning to a notion of the information qubit. This notion is different from that of the physical qubit, which is the description of a quantum state in an electron or a photon. The information qubit is the fundamental quantum informational unit of measure, determining how much quantum information is in a quantum system."
Incidentally chem.libretexts.org, a collection of open-source chemistry textbooks, has a good overview of the physical-chemical applications. The site is kind of a mess but you'd want chapter 18.3:
https://chem.libretexts.org/Bookshelves/General_Chemistry/Ma...
Re: It took me 10 years to understand entropy
#48I had an art teacher who was very philosophical. One day he described to the class what entropy was. I took a lot of physics and even astrophysics. Little did i know he had a better conceptual understanding and explanation than i've ever heard before. Too bad i don't remember exactly what he said.
Not to poke holes in your nostalgia, but how do you know he had a great explanation if you don’t remember it after further study?
Re: It took me 10 years to understand entropy
#49The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
> that a human body could theoretically spontaneously form out of particles given a long enough time span. To be fair, isn't this precisely what happened?
If you leave out "spontaneously"!
Re: It took me 10 years to understand entropy
#50The author mentions Boltzman brains and that a human body could theoretically spontaneously form out of particles given a long enough time span. Of course, nothing like this can ever happen. It’s the fallacy of thinking infinite time means infinite possibilities.
I think this more about the arrow than the entropy.
Considering the ‘arrow of time’ a function on each microstate lends itself better to ”can” questions.
I think both the author and you are assuming your definition for the arrow is correct.
It is still unknown if the arrow allows any arbitrary state to become another, or if there is a strict genealogy for the change of the state that can be seeded from an existing state that ensures it will evolve into a specific other under some time scale, or whether either of those permit Boltzmann brains, or even if there is some control the state has over itself (free will?).