I’m finding that I’m becoming increasingly fascinated by shape. It seems such a simple thing yet scratch the surface only a little and the complexity comes pouring out. Take simple tiling problems; I can tile my floor with squares or regular hexagons, but not regular octagons - they’ll always leave annoying gaps. From a statistical mechanics point of view those gaps are very important, little sources of entropy that you can’t get rid of....
Probability can do strange things to your mind. This week I had a probability problem where every time I tried to use intuition to solve it I ended up going completely wrong. I thought I’d share it as I think it’s interesting. Consider a one dimensional random walk. At each time step my walker will go left with probability \(p_l\), and right with probability \(p_r\). It stays where it is with probability \(1 - p_l - p_r\)....
It’s been ages since my last post. This is because I’ve been busy doing lots of interesting physics, met a bunch of interesting physicists, maybe I’ll write something about it. For now, something I’ve been meaning to write about for a while, and for once it’s something that’s timely. The journal Soft Matter has an issue out with a membrane biophysics theme. You can read the editorial for yourself if you have access, otherwise make do with my ropey understanding of it....
I’m finally getting around to sharing what, for me, is the most beautiful piece of physics we have yet stumbled upon. This is the physics of the critical point. It doesn’t involve enormous particle accelerators and it’s introduction can border on the mundane. Once the consequences of critical behaviour are understood it becomes truly awe inspiring. First, to get everyone on the same page, I must start with the mundane - please stick with it, there’s a really cool movie at the bottom…...
I’ve been meaning to post something interesting about stat-mech about once a fortnight and so far I’m not doing so well. For today I thought I’d share my perspective on entropy. If you ask the (educated) person in the street what entropy is they might say something like “it’s a measure of disorder”. This is not a bad description, although it’s not exactly how I think about it. As a statistical mechanition I tend to think of entropy in a slightly different way to say, my Dad....