imaginary family values presents

yesh omrim

a blog that reclines to the left



24 January 2007

There are many Deep and Meaningful and Significant things I would like to ramble about at great length, which of course is one reason why I haven’t posted anything here for six weeks. So here’s a shallow and insignificant thought for the day.

Our microwave oven has a button touch-sensitive blob labelled “ADD MINUTE”. If you push it, it doesn’t actually add a minute to the cooking time; it adds thirty seconds. But if the timer is already above a certain threshold, or maybe when you push the button enough times in rapid succession, each press does add one minute to the cooking time.

But now I have a vision of the world’s most concise microwave-oven interface (imagine putting this on one of those itty bitty cubes): two buttons touch-sensitive blobs, “+” and “✕”. If you press “+” the time on the clock goes up by ten seconds, and if you press “✕” the time on the clock triples. So thirty seconds is “+✕”. One minute is “++✕”. Five minutes would be “+✕✕+✕”. (From what I’ve read about ternary arithmetic, I suspect that making “✕” use any factor other than three would make the average button-pushing sequence longer, but I’m too lazy to work out a proof.)

I release this innovative user interface into the public domain for the benefit of microwave-oven users everywhere. Please, don’t be too effusive in your thanks.

P.S.: As long as I’m on the topic of weird number systems, I direct your attention to golden-ratio base, a system for representing numbers in base φ (or, if you’re a Da Vinci Code fan, base PHI). Since φ+1 = φ2, any integer can be represented by a finite sequence of base-φ digits, even though φ is irrational. There must be some practical use for this, but I haven’t thought of one yet.