I Don't Understand Ergodicity

I don’t understand Ergodicity

Ergodicity? Ergonomic city? What?

As the title says, I don’t understand ergodicity. I have come across it many times before, primarily in the college thermodynamics class that I learned nothing from and the physical chem class that I learned a lot from. To be honest, I have always been overwhelmed by statistical physics. I like the inherent beauty in determinstic continuous systems (big Diff eq fan here). But I am masochist and I am curious about the things I am bad at or don’t understand so I did quantum optics in college and then decided that was not enough so decided to study the brain instead. However, in the process of searching for potential theoro-neuro and comp neuro advisors, I recently read Cosma Shalizi’s blog/blog-like post on it. If you don’t know who Cosma Shalizi is, check out his horrifyingly 90s website [https//bactra.org], you can thank me later. Ok, what did I understand (and not understand) from reading Cosma’s write-up, some of the references and the Wikipedia page (obv I’d read the wikipedia page)? In the simplest of terms it is a property of a dynamical or stochastic system/process. A property that expresses the idea that given the appropriate amount of time, a point will explore almost the entirety of the space that the system circumscribes. Hence, given a long period of time, a snapshot of the microstates of the system will be identical to the macrostate of that same system. Ok, that’s cool, but why? What immediately comes to my mind are fractals. Given plenty of time, knowing the geometry of a small space of the fractal tells us about the geometric properties of the fractal as a whole, as they are repeating. Think of zooming in on the radial center of a spiral sea conch if you will. In the context of statistical mech, we learned about ergodicity or rather when it breaks in a system. The classic example being of a ferromagnetic object. to be continued, I gotta go fidget of some shit

But why Ergodicity?

I had a dream As above as below And I knew everything Except when the dream ended