so that's where this craziness began...

As I'm approaching my sixth late night of writing up stats reports in LaTex for this take home exam that's due tomorrow afternoon I ask myself "why am I doing this, again? A stats degree doesn't make me a scientist anyhow, and those kids in Comparative Social Policy have way more free time than I do..."

So it occurred to me tonight, as I was biking home from watching a panel of a Muslim, a Jew, and a Christian talk about religion in the public square, that my dad would frequently share a bit of thinly-veiled statistical wisdom with me as a boy. "Aaron, what's the probability that if you flip a coin 10 times and it comes up heads every time, that the next flip will be tails?" "Mmmmmmm, I don't know," I would say, as kids who aren't quite sure where their parents are "going with this" do. "Exactly the same!" my dad would say with a gleam in his eye and that little boy's grin that he still has today when he gets excited about something (probability theory?!). How incredible that, in spite of all that past baggage, all those failed attempts to be tails, an evenly-weighted coin had a clean slate, a 50% CHANCE, to be tails at each new trial.

"Wait a minute," I thought, "something about this seems fishy..." But of course I was still learning to do things that I still struggle with today, like basic arithmetic, multiplication by 11, and spelling, so I just let that sense of unease percolate in the back of my brain. Day, after day, after day. And only now, after stomping off on this wild goose chase of a degree, am I able to frame the issue more clearly. You see, it's a very simple question of joint versus individual trials involving an outcome that can only take one of two values. As it turns out, the probability of flipping a coin 11 times and only observing tails on the 11th flip is (almost) exactly 1/2048, even if the probability of each individual flip attaining that outcome is constant at 1/2. Remember that, guys: joint trials of independent events tend to be less probable than the aggregated individual outcomes of which they are composed. There's some real life-directing wisdom in this, so use your imagination and reach for it.

But where I was going with all this is to say that it's your fault, dad, that the muddled fascination (or perhaps confusion) with mathematical quantification of uncertainty that you planted in my brain 17-odd years ago drove me into this masochistic choice of degree here at Oxford. Which is, of course, my back-handed way of saying that I am in awe of your fascination with the world and deeply grateful for all that your sense of wonderment, especially in things as simple as a coin flip, has contributed to the odd character I am today.

Thinking of coins and campfires as I write time series models and wrestle with spatial statistics tonight,
Aaron