The Nuances of Time Quantification

We were expecting company today, and Ian asked me when they would arrive. I told him, "Probably in the next half hour or so." He was horrified that it would take them such a long time, but he set to work grappling with the implications of this time-unit.

The time on the stove's digital clock in the kitchen was 3:12. Ian explained: "Hey! How can I tell when that's gonna be, if it's not on 3-0-0 [three-o-o] or 3-3-0 [three-three-o]?"

This statement points out two aspects of Ian's relationship with the measure of time. One is his integer-based reading of the time shown on a digital clock; he reads "digital" time as true digits: what we call "thirty" he calls "three-o". One of my younger sisters did the same thing at his age. This is probably more appropriate in our post-analog age, and very much in keeping with the metric approach to measurements overall. What we naively call a "digital" clock is really just a "wrapper" to boring old Base-60, but the kids will surely come up with something purer and internally consistent.

The other issue introduced by this statement is the age-old enigma of "How do you know a half hour has gone by, if you didn't start timing on the hour, or the half-hour?" If we started counting at 3:30, everyone knows a half-hour would have past as of 4:00, but if you start running the meter at 3:12, it's anyone's guess what the clock would look like a half-hour later. I tried to introduce a more additive approach to the problem, where a half-hour is reduced to the lowest common denominator of "30 minutes," but he wasn't very interested in all the mundane arithmetic involved in that approach.

(February 27, 2011)