# Steve Cotler

## Smallness

When Richard Feynman came back to Ojai’s Summer Science Program in 1960 for a second, unscheduled visit, his topic was what he called “smallness.” Today that field, in which he was a visionary, is called nanotechnology.

Having been mesmerized by Feynman’s brilliance and wit during his talk on Relativity a couple of weeks earlier, we 26 science/math nerds were energized when he began by asking us to…

“Imagine that you have a machine into which you can insert your hands, and everything you do is replicated at the other end of this machine by another pair of mechanical hands, but at one-tenth scale. Forget about friction, mechanical slop, and so forth.”

Eyes wide, we all did that.

“Then, use that machine to build an identical machine, so that your mechanical hands build another that is one-tenth the size. Hook them together in series, and repeat this four more times, so that you have a chain of six. At the far end, your actions will be reduced to by a factor of one million. Now build a replica of a Black & Decker power drill with a quarter-inch drill bit. Insert the bit and then drill a hole in a piece of plastic. At the far end, your one-millionth-scale power drill will drill a one-millionth-scale hole in its tiny piece of plastic. Right?”

He looked out at us for a response. Was this a trick question? Was it even an interesting question? We knew he was he driving at something, but not one of us knew what that was.

Before you read further, ask yourself the same question: what happens at the small end of your machine?

[Quiz show thinking music goes here.]

[…continues…]

[Time’s up.]

Some actions do not scale down.

Feynman explained: “Let’s say that your full-scale power drill operates at 3,000 rpm. That means that a quarter-inch bit, which has a circumference of pi times a quarter-inch–just over 2.3 inches–lays about 7,000 inches of cutting edge against the plastic per minute. That’s more than enough to cut through plastic. But the circumference of the tiny drill bit is 2.3 times ten to the minus six, and since it’s still operating at 3,000 rpm, you have only 7 times ten to the minus three cutting inches hitting the plastic per minute, one-millionth as much. Clearly not enough to cut through plastic.”

We sat silently digesting this.

“Size scales, angular velocity does not. To get equal cutting edge against the plastic, your tiny drill would have to rotate one million times faster than the big drill.”

He then described several other oddities about “smallness,” but I was still thinking about that little drill.

Feynman was a fountain of unusual insights. I wish I could remember what else he said.