Shiunbird wrote:josehill wrote:I seriously will never forget the moment almost 30 years ago when I was wrestling with equations for my Physical Chemistry course, and I finally understood entropy at the mathematical level. Entropy has no mercy...probably the most sobering thing I learned in college.

Could you share something on the matter?

A short-ish read?

That sounds fascinating!

I'll look around to see if I can find something. The challenge is to bridge the gap between simple (but reasonably accurate) analogies about disorder (like throwing a deck of playing cards in the air and expecting them to land in numeric order, i.e. the chances of things becoming more disordered or "breaking" vastly outnumber the chances of maintaining the status quo or improving, or "errors accrue, and they kill us") and the collection of math skills and related knowledge needed to make you say, "Yeah, it really is true." I understood all the analogies when I was a teenager, but it took a lot of math and physics courses before I had enough working knowledge to have a breakthrough in understanding. I also have little doubt that a professional physicist in the field would consider the level of hard-won understanding I had in college to be woefully naive.

I had a similar experience "doing the math" for relativity. It's one thing to be told that the apparent mass of an object increases as it approaches the speed of light, in a way that ensures it never can reach the speed of light, but it's quite another to build up the math skills and physics knowledge that let you evaluate the equations and see it for yourself. It's when you go from "surely there must be a loophole that will give us warp drive, because I want to be Captain Kirk," to "Wow, we'd need an entirely new understanding of how the universe works to think about going faster than the speed of light in any useful way. It ain't happening soon."