The Friday Fillip: Mirror rorriM

I remember when I was a kid there were a couple of things (at least) that could take me to the dizzying edge of imagination, where I’d stall in frustration and wonder.

One was lying in bed at night doing the expanding address thing: Simon Fodden, Walton Drive, Halifax, Nova Scotia, Canada, the world, the universe… and? What was on the other side of the universe, beyond it? Try as I might, I couldn’t imagine.

The other was found in the barbershop — you remember those, don’t you? the smell of bay rum, the combs in the jar of blue juice, the badger bristle shaving soap brush, the leather strop, the all-important striped (and, if you were lucky, rotating) pole. And there were mirrors on the walls in front of you and behind you, at least in the ones I remember. From the height of the throne you could glimpse yourself getting smaller and smaller as you veered off to the side, finally to disappear in miniature. The puzzle for me was how to, and what if you could, get the receding images to stay within the mirror. I never managed to solve the puzzle.

At least now I know why, in a manner of speaking, I failed in the second puzzle. It’s (simply!) a matter of physics: two mirrors set up exactly parallel and facing each other set up a recursive reflection (a “Fabry-Perot optical resonator,” I’m told). All well and good, though apparently fiendishly difficult to get the things exactly parallel. Now introduce a seeing eye into this “optical cavity” and you either block the significant portion of the event, seeing only the eye looking back, or, if you view from an angle, the light beams striking the eye walk step by step to the side and eventually slip off the field.

Thanks, however, to art and now technology prayed in aid to art, we can produce the effect I wanted to have as a kid in the barber’s chair. And charmingly, it’s known as the Droste effect, in honour of the ad for a Dutch brand of cocoa powder that used the recurring image theme. Technology lets us do something similar and even more intense, as you’ll see in this brief (Dutch — what is it with the Dutch and recursion? double Dutch…?) video in which a camera films a monitor which shows the filmed monitor. Et cetera.

And now Wolfram-Alpha ramps it up, as you might expect. Mathematica enables the numerate to do the barbershop mirror thing with photographs right to the point of invisibility. The explanation is all here, but thank heaven there’s also a lot of illustration because the math takes me not just to the dizzying edge of my imagination but over that edge into confusion.