We walk, bicycle, drive, and fly by orders of magnitude

One of the things that happened when I gave up car ownership was that I began to see my surroundings in a different way. I walked more, and on the street you see faces and encounter other human beings at close range in real time. You can even stop and have a conversation. You can certainly stop and smell the roses, or look in a store window, or anything else.

Walking is slower than bicycling, which is slower than a bus, which is slower than a car, and so on. But each successive system of propulsion gives up in intimacy what it gains in speed.

On foot, you are one with the land. You can see and hear and touch it. On a bicycle, you’re faster but a little less connected. In a car, you’re in your own private room that you can direct, and on a train, you’re in a public room you can’t. In an airplane, of course, you’re not on the land at all.

You’ve probably seen a variation of the video that zooms out from a woman’s hand into the Universe and then zooms back in, all the way to sub-atomic particles in the cells of her skin. The size of the picture increases or decreases by a factor of ten, an order of magnitude.

This is a phrase often misused by math-indifferent writers, and a concept often misunderstood. An order of magnitude is a step in an exponential series: 10, 100, 1,000. Exponential growth starts slowly but gets huge in a hurry. When you read that traffic has “increased exponentially,” smile and be thankful that it hasn’t. No one would be able to move.

I first learned of magnitude from the stars. The system is an overlay of modern astronomy on a framework devised by the ancient Greeks, who classified stars by brightness. Stellar magnitudes run in reverse: the lower the number, the brighter the star. Prominent stars are first-magnitude stars. A few very bright stars have negative magnitudes. The faintest stars on the edge of visibility are magnitude 6. Anything fainter requires a telescope. Each magnitude is approximately 2.512 times brighter than the one below it.*

Have I lost you yet? What do orders of magnitude have to do with cars and transportation?

Well, I was just thinking…

The base doesn’t have to be ten. Average human walking speed is about four miles per hour. Some people walk faster or slower, of course. But that’s what we’re built with: four miles an hour.

Multiply that by four, and you get the approximate speed of a bicycle: 16 mph. It’s possible to go much faster, but hills and age and obstacles will take a big bite out of your average speed.

At 16 mph you’ll miss things you would have noticed on foot. You’ll wave at the friend on the sidewalk instead of stopping for a word or two. Traffic demands more of your attention because you are on the road instead of alongside it. You can still stop and revert to walking any time you want. But it’s an order-of-magnitude distance – small, because the numbers are still low.

But multiply by four again, and you get the speed of a car on an unencumbered roadway: 64 mph, or nine miles an hour over the speed limit, a typical operating speed for a car.

It’s another order-of-magnitude step, but a much steeper one. You’re fortified in your own private bubble, and you consider it your private space even as you move it about in public. You’re restricted to the roads and parking lots, subject to many more rules. Your interaction with the land and the people on it is limited to the places you choose to stop. You communicate with your fellow drivers through gestures, some of them friendly.

Four times 64 equals 256, or 44. Both China and Japan have developed high-speed trains capable of speeds higher than 256 mph. In service, they operate at speeds of around 200-220 mph. I’ve never traveled on a train that fast, but the experience on a train is that of an observer, as the world scrolls by.

Multiply by four again and you’ve got the Concorde: 1,024 mph. Passenger planes fall somewhere between it and the bullet train. But any kind of flying strikes me as an order of magnitude above any kind of land transportation.

Next: How orders of magnitude (should) shape traffic laws.


* – A star of magnitude 1 is 100 times brighter than a star of magnitude 6. The number 2.512 is an approximation of the 5th root of 100, so that (2.512)5 ≅ 100. Every five magnitudes means a 100-fold difference in brightness. In this way the old Greek system is preserved, and can be extended to extremely bright or faint celestial objects.