Small Talk

Have you ever been out for a walk at night and mistaken the constellation Orion for a human being? Certainly not: Orion’s just a random scattering of stars that from our vantage point here on Earth resembles, at best, a child’s stick-figure drawing of a person. We all know Orion’s a defined entity, virtually 100% empty space, with a few particles of matter tossed in.

How profoundly different Orion is from a real human being: humans are solid creatures with the ability to sense the outside world, form concepts, write essays. Orion, not so much.

But let’s check the math concerning one of the differences between the constellation Orion and a human being. Orion’s already figured out: virtually 100% empty space with a few particles of matter tossed in. Much more mass of course, but practically zero density. And a human being? Well, we know we’re composed of cells which are composed of molecules which are composed of atoms which are composed of subatomic particles. And we all get that there’s quite a bit of empty space between and within the atoms in our bodies. But we don’t usually think about exactly how much empty space.

How much physical space would you occupy if all of the empty space between and within the atoms of your body were subtracted out, so that all that was left of you were protons and neutrons, all jammed together? (We’ll ignore the pesky electrons which constitute something like 1/2000th the mass of protons or neutrons.) A good approximation of this compact state exists within neutron stars, which leads to a surprisingly easy math problem to solve since neutrons and protons are almost identical in size and mass. So to figure out how much space you'd occupy we need only calculate how many protons and neutrons there are in 70 kilograms, which is the average mass of a person, and then multiply that number by the amount of space each one of those little guys takes up.

Using a bit of scientific notation you’d occupy about 1.8 x

10^-16 cubic meters if all the empty space between and within your atoms were subtracted out. That number's pretty incomprehensible, so let's describe it making use of an everyday item, a sewing needle.

How much of you would fit inside the eye of a needle if all the empty space in you were subtracted out? A finger? Your entire hand?

All of you actually, with room to spare. A typical city bus might carry 40 passengers: if you were on that bus, how many of your fellow travelers would fit into the eye of that needle with you? Everyone. Again, with room to spare.

Ever attended an outdoor professional sporting event? A reasonable 'ballpark' for stadium capacity is 70,000 people; how many of the attendees would fit inside the eye of the needle with you if all their empty space were removed? All of them.

A fair-sized city like Philadelphia, or Vienna, has a population of about 1.5 million people—but you know where this is going: all of them, with room to spare.

In fact, a total of 1.7 million people like you and me would fit inside the eye of one sewing needle.

So, just how solid are we? If we weren’t being puffed up like balloons by electromagnetic and other forces within and between the atoms of our bodies, each one of us would be invisible except under an electron microscope. We are, for all practical purposes, 100% empty space with a few particles of matter tossed in, just like the constellation Orion.

One more number: the entire population of planet Earth, 7.9 billion people, would occupy about 1.7 cubic centimeters of space if all the empty space in them were removed.

Put a nickel in the palm of your hand; imagine it now as sphere of the same diameter. That’s humanity, in a nutshell. As human beings, when we experience the outside world it leads to forming concepts, making choices; we want to possess or experience some things, to push away or destroy others. We’re taught, or form our own ideas about what’s right and wrong; good and bad; deserving of love, or fear, or hatred.

Think of the untold suffering and sorrow that chip of humanity in the palm of your hand causes itself every day. And the love and compassion it surely is capable of as well.

In addition to our physical existence, do we possess a spirit? It’s a question each of us asks and perhaps answers on our own. But it turns out our physical bodies are as ephemeral as a dawn mist—we are in fact walking ghosts.

Literally spirits, in the flesh.

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Small Talk is from a short speech I gave in 2010; although I’d done the math several times back then I wasn’t positive my result was that close to the actual value because of the possible inaccuracy of my measurement of the volume of the eye of my needle, but mostly because I wasn’t positive my application of the density of a neutron star was a valid approach. A year or two later I stumbled upon a University of Maryland physics professor’s website (https://www.astro.umd.edu/~miller/nstar.html), in which he presented a detailed but non-technical discussion of the interiors of neutron stars and commented that the human population of the Earth, if compressed to the density of a neutron star, would be about the size of a sugar cube. I had to laugh when I saw this, because for my speech I’d actually cut a small cube out of a Pink Pearl eraser and painted it white to use in the presentation, but never thought of referring to it as a sugar cube even though that was exactly what it looked like. Since that talk, the population of the Earth has increased from 6.9 to 7.9 billion people.