"How Much More Time?"

Kids in a car will drive you up a wall by asking the question, “Are we there yet?”. Every 2 minutes. And that’s if you are lucky; more often, they’ll ask the same question again within a minute. Is that because they’re so damned impatient and so easily bored?

Or is it just not possible for kids to visualize distances or the passage of time? The point hit me when my daughter was watching this cartoon about 2 naughty school kids, Badrinath aur Buddhadev. The class was told that there’d be a 5 km marathon, upon which one kid promptly responded:

“Just 5 km? What’s there in that? I can run that much in just 5 minutes.”

Most adults immediately know that’s impossible. But if you step back to see how adults know that, it’s not because we can visualize the distance of 5 km or the amount of time 5 minutes implies. Rather, our brain uses the proxy called “speed” to assess the claim: 5 km in 5 min means a km per minute, which is 60 kmph. Cars go at that speed, not humans, therefore there’s no way anyone could run at that speed.

Notice how many adult concepts it took to figure that? Division. Conversion to a unit of speed that we are familiar with (kmph). Knowing an entity that travels at around that speed. Is it at all surprising that kids can’t evaluate such things at all?

But wait, it gets even worse. The difficulty to visualize distances is compounded by the choice of units we use: meters, kilometers, miles, whatever. None of them map to anything that we can visualize naturally. The non-metric 12-inch “foot” was at least more intuitive. But all units break down with the second problem: we can’t visualize large numbers. To see what I mean, try visualizing how tall a 2,000 foot hill is. I bet you can’t, unless you apply a proxy technique, like assuming each floor of a building is 12-15 feet (or whatever), then calculating how many floors 2,000 feet translates into, then thinking of a building you know with that many floors…

The “problem” of time is even worse. I don’t know of any unit of time that is intuitive to comprehend. Try telling when 5 minutes have passed without a watch or any other reference hardware (that rules out Galileo’s pendulum and atomic clocks). Richard Feynman tried to track time in college, and his attempts were a total failure. If Feynman couldn’t do it, is it at all fair to expect kids to be able to do estimate the time elapsed?

And so I end up with the gloomy conclusion: “Abandon hope all ye who enter here”.