Motus Mentis

On an end-table next to where I do most of my reading there is a lamp with a ‘three-way’ bulb. Last night one of its filaments burned out, and I found that I had no more of these bulbs in the house.

I’ll go looking for another tomorrow. I know that these ‘three-way’ bulbs were once on a short list of incandescent lamps that our Federal overlords had graciously allowed us still to purchase, but I haven’t bought any in at least a year or two, and things may have changed — as these things relentlessly seem to do, generally without my ever having been consulted.

It will be a pity if these bulbs are now forbidden to us. I’ve always liked ‘three-way’ lamps, even though I suppose they offer no rational advantage over a dimmer; generally, the range of luminance options they offer has always seem to me more than adequate for a table lamp.

The name ‘three-way’, however, is obviously wrong, because these lamps offer not three, but four possible states: off, low, medium, high. And that’s another reason why I’m fond of them: I realized long ago that they offer a splendid tool for explaining the binary number system to children:

The bulb I have to replace has two filaments: one that uses fifty watts and one that uses a hundred. Each has two possible states: off, which we can represent with a 0, and on, which we can represent with a 1. If we put the fifty-watt filament in the ‘ones’ place, and the hundred-watt filament in the ‘twos’ column, then we can represent the four states of the bulb as:

      0 0 – Off.
      0 1 – Fifty watts.
      1 0 – One hundred watts.
      1 1 – One hundred fifty watts.

In binary terms, we’d say that the fifty-watt filament is the ‘lower-order’ bit, and the hundred-watt filament is the ‘higher-order’ bit. The bulb, then, is a four-state binary display.

This also means that it’s easy to tell which filament is burned out (if you should happen to care). If the fifty-watt, low-order filament is the one that still works, then as you turn the switch the bulb will cycle through the pattern off-on-off-on (which, of course, is the sequence of ones and zeroes in the right-hand column of our little table above). If it’s the hundred-watt filament, then the pattern will be off-off-on-on.

I’m sure these lamps are not long for this world — no doubt the environmental clerisy has already determined, in its ‘settled’ way, that there’s a fjord missing its glacier somewhere solely on account of my lingering attachment to this primitive technology — but if they still have these bulbs at the hardware store tomorrow, I’m going to buy as many as I can carry home.