A Matter of Scale

If you look up into the night sky—at some remove from the city or other serious light polluter—you will see a universe that, for all practical purposes, is infinite: Trillions of stars in each galaxy, trillions of galaxies. I’m not even sure that we are equipped to grasp the magnitude of this.

Then, if you take a close look inside your own body you will discover that the number of cells and microbes and bacteria basketed by your skin also border the infinite: trillions and trillions of the little things.

Then, with an even better (yet-to-be-invented) microscope, take a look at the molecular: How small is a water molecule, really? Well, I read somewhere (I think it was Schrödinger) that you can fit so many water molecules in a glass of water that if you could (by some magical means) mark each one—say, paint them orange—and then pour this glass of orange water molecules into the ocean to then (by some other magical means) mix the oceans so well that your glass of water became equally dispersed throughout the seven seas, all the way down to the 10,000 meters depths; if you did this and now used your original (now empty) glass and filled it with ocean water anywhere in the world, at any depth, you would scoop up at least a few hundred of your original (orange) water molecules.

To me, this is beyond comprehension. We are talking so small as to be virtually immeasurable. Schrödinger goes on to discuss why they are so small—or why we are so large, rather—but that’s another story.

But here is the rub: Infinitely large and infinitely small is simply a matter of scale. The Universe is infinitely huge just because we only stand a fathom or so tall. Were we, say, the size of a solar system, perhaps the Universe would seem a little (though not much) less imposing. Were we, say, the size of the Milky Way, perhaps then we could get a handle on things size- and universe-wise. And if, well let’s just go all the way and assume the size of the Universe and behold: it’s not big at all, just our size, actuIally: nice fit.

The same, of course, applies in the other direction. Were we to assume the size of a bacterium, then all other bacteria and all those cells would seem very normal size-wise, and were we to assume the size of an electron, well, then the cell would be the size of the universe, just about—at least the size of a galaxy—and all these electrons just the right size to seem perfectly normal.

For some odd reason it appears to me that the here-and-now size we’ve adopted sits almost perfectly wedged in between the infinity of large and the infinity of small. To confound and intimidate? Who knows?

I think that we should adopt a more flexible attitude toward size and teach ourselves to assume whatever size would best suit the occasion: universe-sized to survey the outer (and still expanding, they say) rims (skin, now); electron-sized to take a closer look at the atoms and the small, small houses that they and their children live in.

I do not think—no, not really—that we are of permanently fixed size. I think we are the size we consider ourselves to be. We just have to gain some skill at changing our considerations.


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