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Around the World in 26 Steps

Josh McHugh headshot
Josh McHugh / Aug 12, 2019
Sports
Even after covering the technology industry for 20 years, I struggle with explaining the nature of exponential increase to people. That’s probably because I struggle to appreciate it myself.

Grain Elevator

The story most often used to illustrate exponential growth is the one about placing a single grain of rice (or wheat) on a chessboard square, two grains on the next square, four grains in the next square and so on until the chessboard squares have been accounted for. Spoiler alert: by the 64th square, the required number of grains would cover the globe in a layer of rice.

That is too much rice for me — a column of rice extending upward into space from a chessboard square is unwieldy to say the least (though it could make for an epic game of Jenga). But there’s a much simpler way to get it across:

Q: If the length of your stride doubled with every step, how many steps would it take to get all the way around the world?

A: 26.

Take a Walk

Here is the math. To keep it simple, estimate the first step at a yard. Using an equatorial circumference of 24,874 miles, converting to yards gives us 43,765,920.

Walking it backward from 43,765,920 yards by dividing the remaining distance in half each step… the 26th step takes us from 1.3 yards to .65 yards.

Going forward from one step, doubling 1 yard to 2 yards and so on, the 26th step takes us from 33.6 million yards to 67.1 million yards. You’d basically cross your starting point halfway through that 26th step.

There are some good takes on the 26 steps scenario in the last year or so — particularly from Peter Diamandis and from the folks at Singularity U.

Astride the World

Of course, when I ran this by my 10-year-old son while we were walking on the beach, he actually visualized it, and responded by asking me how tall you’d have to be to take that 26th stride that reached halfway around the globe. It took me much longer than I care to admit, but the answer to that one is pretty simple: assuming our stride is half our height (we’re walking fast, trying to keep up with the speed of exponential change, ok?), then on that final step, you’d be as tall as the Earth is round — 24,867 miles.

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