I started out wondering about the etymology of the word, “sublime.” (it’s one of those words I look up every few years, then forget again.) So I looked it up on dictionary.com.
Once there, I wondered how it could be from a root meaning “to raise” if the word “sublimate” means kind of the opposite. So I had to look it up too.
On that page, I noticed that there was a lesser definition denoting a process in chemistry. Off the top of my head, I couldn’t think of what substance or element could go from solid to vapor and back to solid without passing through a liquid state; so I went to wikipedia and looked up the process.
At the bottom of the page was “phase diagram” listed under, “See Also.” I wasn’t clear what the connection was, so I clicked the hyperlink.
From there I went to “phase space,” “chaos theory,” “Lorentz Attractor,” (God, they’re beautiful!) and I wound up on the page for, “Takens’ Theorem.”
This is where I gave up:
“Assume that the dynamics f has a strange attractor A with box counting dimension dA. Using ideas from Whitney’s embedding theorem, A can be embedded in k-dimensional Euclidean space with
k > 2 d_A.
That is, there is a diffeomorphism φ that maps A into Rk such that the derivative of φ has full rank.”
Uh, okay. I’m glad you guys are on top of this stuff.
I think I’ll have some soup and go to bed.