The nano scale, fingernails, and using yourself as a research subject

A nanometer is one billionth of a meter. It’s hard to visualize something that small. To try to put it in understandable terms, Robyn Williams said this on The Science Show (I think).

By the time you finish this sentence, your fingernails will have grown one nanometer.

And for some reason, that little claim stuck with me. I kept wondering, “Is that accurate?”

Last fall, I asked students in my Biological Writing class to estimate how much time it would take for fingernails to grow one nanometer. We had talked about Fermi problems in class, using some examples in the book Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin (Amazon). Out of 13 estimates, eleven ranged from 0.09 to 1.6 seconds, and I had two outliers of 60 and 600 seconds.

But estimates just weren’t good enough. I wanted real data. When the new year came, the next time I trimmed my fingernails, I opened up a spreadsheet and wrote down the date. When I needed to cut them again a few weeks later, I got out calipers that could measure to 0.01 mm. I measured each fingernail at three points to get an average rate of growth and to even out irregularities from my cutting the nails.

I was going to measure the rate of growth (nanometers per second) five times. I managed to fracture a couple of my nails at one point, making correct measures of length tricky for them, so I went another time. I ended up with five or six measures of growth rate for ten fingers.

The results of my somewhat obsessive self-study:

An average fingernail growth rate of 0.92 nM / sec. My Biological Writing students had come up with quite decent estimates – certainly better than you’d get by just guessing! The mode estimate from the class was that it would take about one second for a fingernail to grow one nanometer.

I was a bit surprised to see that growth isn’t as even as I might have expected. It fit my subjective impressions that the ring fingernails looked like they needed trimming first, though I wouldn't have expected the middle fingernail was growing just as fast.

Getting back to the original claim, we need not only the rate of growth, but the time of the sentence. It took me about 3.77 second to say, “By the time you finish this sentence, your fingernails will have grown one nanometer” (n = 10, timed with stopwatch).

This means that the original claim is quite conservative! By the time you finish saying that sentence out loud, your fingernails will probably have grown something like three and a half nanometers (3.47 nM, if you wanted to be precise), not just one.