How Small Is Small?

The book’s ladders of scale, rung by rung: how wide a molecule is, how faint one part per trillion is, how quiet a whisper is, with the math.

This book asks you to picture several kinds of small, and they are easy to mix up. Take them one at a time, each on a ladder you can climb. This first one measures how wide a thing is, edge to edge.

Begin at a single atom and walk up, step by step, to something you could hold in your hand.

One entry sits off the ladder. A neuron has an ordinary cell body, ten to twenty-five micrometers wide, but a single axon can run the length of a meter, spine to toe, one cell up to a hundred thousand times longer than it is wide. Human sperm cells have ~20 micrometers long tails (~50 nm total length) that degenerate after fertilization.

Set the rungs side by side and the trap shows itself. A molecule like BPA is about five atoms across. A nanoplastic particle is the size of a virus, small enough to slip through the critical barriers. A speck of microplastic is the size of one of your own cells, which is why it can lodge in among them. And the molecule that does the hormonal damage is a thousand times smaller again. It falls below the wavelength of visible light, so no light microscope brings it into focus and no lens films it. It falls below the mesh of any household filter by orders of magnitude, so nothing strains it out of the water; a filter that catches it does so by chemistry, not by mesh. The thing that turns the lock rides in on particles that are themselves too small to see.

The count of how few of these molecules it takes, the concentration in parts per trillion, is a different scale again.

A trace is the word for an amount too small to matter, everywhere but here.

Take a pinch of sugar, about sixty-five milligrams, what clings to a wet fingertip. Drop it into a fish tank, some seventeen gallons, and stir. The water now holds one part sugar in a million. A laboratory instrument can find it. No sense you own can.

Drop a second identical pinch into a backyard swimming pool, seventeen thousand gallons, and you have one part in a billion. One second out of thirty-two years.

Now divide a third identical pinch into a thousand parts, and drop one part into each of a thousand pools set end to end, a line of pools five miles long. That is one part in a trillion. One second tick in thirty-two thousand years.

Thirty-two thousand years ago, mammoths walked the plains with dire wolves at their heels; ice was still building toward the sheet that would grind over the Great Lakes; and, by torchlight on a cave wall, humans painted the earliest images of animals we can still find. Agriculture had not been thought of. The chemical industry lay thirty-one thousand eight hundred years away in the future.

Your own hormones give their orders at parts per trillion. The system that reads them was built to answer a signal that faint. These chemicals arrive at the same pitch.

That is the volume they come in at. Not a shout the body can flinch from. A whisper it was built to obey.