## Small scales, huge numbers

I’ve recently been reading a bit about nanotechnology, and I realized the contradiction that thinking of such insanely small scales brings. You’ll always end up dealing with huge numbers.

In order to try to grasp something as tiny as a nanometer, we try to convert it to the next best thing – the smallest tangible, imaginable distance, the smallest scale on your average rule: a millimeter. This conversion forces us to use hard to imagine scales: a billion nanometers are supposed to fit in between one of the ten tiny lines on your ruler which divide a centimeter. One billion, in such a tiny space? To me, it’s impossible to even imagine such a number. Let alone to mentally chop up this centimeter-space on a ruler in a billion bits. How do I know – other than ‘very tiny’ – how big a nanometer is?

One example I recently came across stuck with me. Supposedly, during the time it takes us to pronounce the word ‘nanometer’, our hair grows ten! This fact impressed me. But, this hair example is not a stranger when it comes to imagining small scales. There are a few often-used examples of making nanometers or other small scales imaginable, one of them being to use the width of a human hair to illustrate the nano-scale.

But how helpful is that? According to one source, the average width of a human hair can vary from around 17 to 181 µm (that’s micrometer: a millionth of a meter. Huge compared to a nanometer). That means a human hair can vary from 17.000 to 181.000 nanometers. Let’s take a look back at our hair growth example. While your hair grows ten nanometers in one direction (in the time it takes you to pronounce the word ‘nanometer’), the other direction can be up to 181.000 nanometers long. That puts this impressive fact into perspective.

In the end, a nanometer is an abstract unit of measure we cannot use it in everyday life. And why would we? We can’t use it for ‘real-life’ measurement. We either use it when downscaling from bigger scales, and consequently end up with huge numbers. Or we use it when we deal with the totally abstract world of molecules and atoms, and then we end up in the even harder to imagine abstract world. Any attempt to make the scale tangible deals with intangible smallness. We’re always stuck with the contradiction of using huge numbers to imagine tiny scales.