Briefly — very briefly, unless you want me to copy some insights into Riemannian manifolds and Laplace-Betrami, whatever they are — Brownian Motion is an eminently intuitive notion: that particles suspended in a fluid collide in such a way as to create totally random motion. It's a "stochastic process," a series of sequential movements in which the direction and size of each move is randomly determined.
If you are, or have meaningful experience with, an ADHDan, a light bulb should be going off about now. You know why. Because this is the way your mind tends to work, at least in its worst-case scenario. Your focus, which you'd like to stay in one place so you can get some work done, gets bumped by some random thought. Then another one, totally unrelated. And it just keeps going, until, if you were able to draw a picture of your mind's peregrinations, it would look something like this...
On a really bad day, you can start out saying to yourself, "I'd better get started on that project now or I'll have to work on it all weekend." So you fire up your computer and open the spreadsheet you need to complete; as you're typing you notice that you have a hangnail; looking for the nail file, you find the spare set of car keys you misplaced last week, the ones you can't get duplicated because there's a computer chip in them and so it's gonna run you about $200 to copy them; you're happy about that, until you remember that you haven't paid a parking ticket and it's about to go into collection; then you remember that you didn't move the car last night, and you're probably going to get another one. You run downstairs, just in time to see a smirking meter maid putting a parking ticket under your wiper blade. Cursing, you stomp over to the car and see that you didn't get a ticket.
You got two tickets. Why? Because you forgot to get your car inspected.
Now you're furious. So you decide to . . . no, you don't want to start drinking at 10 am. Or even if you do, you recognize that you shouldn't. So you head for Dunkin' Donuts, and get a large coffee and a dozen doughnut holes. You get back home and set down your coffee and sugar bombs, only to notice that the sticky you'd put on your monitor to remind you to call your mom and wish her a happy birthday, it already being too late to send a card. Now it's too late to call. You slam your fist on the desk, causing your nice, sweet coffee to fall over. The top pops off and your keyboard gets a caffeine bath. As do all the notes for your project.
What project? The one you set out to finish, five miserable hours ago.
Random, and in this case, disastrous, movements, leading nowhere. Or, as they said in that physics class...
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