Note: originally, the blog was called Ergodicity in Thought.

Hey there, I hope you’re doing well :smile:.

I’m not entirely sure why you’re reading this (or why I’m writing this), but I’ll try and convince both of us that it’s worthwhile. If it’s not, I guess I could say you can find comfort in the idea it took me longer to write than you to read. Yet the whole point of these few lines will be to formalize the intuition that structuring one’s thoughts and taking time to express them has intrinsic value.

So why the blog and why that somewhat pompous title?

The reason for starting the blog is hidden in the title so let’s begin with that: Ergodicity in Thought. I first came across ergodic systems in a Statistical Physics class @ Mines ParisTech. For those who haven’t, this is (very roughly and with as little formalism as possible) what it means:

Say you have a system made up of N ‘things’ (probably particles, let’s be honest). Each of these N particles can take on a certain number of states, let’s call that number P. So if we can tell the N particles apart from each other, we have drumroll \(P^N\) number of, what we call, micro states. This is just the total number of configurations of our system, if we’re looking individually at what particle is in what state. Knowing the system’s micro state means knowing exactly what particles are doing what and odds are this doesn’t hold as soon as your system has a large number of them… Yet, we can still want to measure things about the system, it’s just we’re measuring macroscopic observables that are a sum of individual contributions of particles, each living its own life within the confines of our P possible states.

Ok, you might be wondering, but where on earth does ergodicity come in? Well, firstly it sounds fancy and like entropy I hope the mystery of it all will give me an advantage in any future debate. Second, let’s measure a macroscopic observable of our system, say it’s temperature. For ergodic systems this macroscopic observable can be calculated by taking an average over a certain amount of time or over the number of possible micro states. This means that the temperature we’re measuring over a period of time (short for us but very long in terms of micro state transitions for the system) is equal to the amount we could calculate at one fixed point in time by averaging over the possible micro states.

After this long detour you might understand what I’m getting at. Essentially, I’d like to think that my very own thought process, the ergodic system, can produce an observable, this blog, which will give over time an equivalent result to a blog produced by averaging over the space of ideas. Basically, I’d like these posts to explore many different ideas and hopefully let me enjoy myself along the way. There’s probably a few flaws in the analogy but I liked the sound of the title and it announces forthwith the color of this blog - a mix of random explorations containing book & paper reviews, discussions on daily habits such as meditation & intermittent fasting, brief overviews of topics such as the climate crisis with, of course, some technical mathy posts here and there to keep it spicy.