380 Solar Systems (Another Reason Why Humans Will Never Find Intelligent Alien Life)

There’s a back-and-forth in The Genesis Project, Chapter 7, that goes like this …

“What, you find aliens or something?”
“There are no aliens.”
“You sure about that?”
“Think about it,” I said. “there’re a billion species of bacteria on Earth but only one species of intelligent life — if that’s what you’d call us. And the odds get worse from there. Shrink the Earth’s diameter down to a human hair’s diameter and the universe’s still 380 solar systems across. So even if aliens exist, the odds of us finding them are zero.”

So, how did I arrive at 380 solar systems? Let’s do the math.

Human Hair, Cross Section

Technically, the Earth is an “Oblate Spheroid,” but, for our purposes, we’ll assume it’s a perfect sphere with a radius of 6.371 million meters. Its diameter is twice as much — 12.742 million meters.

Our hair, for this exercise, is 50 micrometers in diameter. As such, the Earth to Human Hair “Shrink Factor” is 3.924e-12. In other words, a human hair’s diameter is about four trillionths the Earth’s diameter.

The radius of the observable universe is 4.4x10²⁶ meters, which is 46.507 billion light years. The diameter of the observable universe is twice that, or 93.013 billion light years. (Our Solar System, for comparison, is a little less than one thousandth of a light year across.)

Shrinking the observable universe by four trillionths means multiplying its diameter by a “shrink factor” of 3.924e-12. When reduced to four trillionths its current size, the observable universe is 3.453x10¹⁵ meters in diameter — a little more than 1/3 of a light year. Which is still pretty big.

How big?

If we use Neptune’s aphelion (Neptune’s farthest point from the Sun) as the Solar System’s radius, the Solar System is 9.09x10¹² meters in diameter. To calculate the ratio of the Solar System’s diameter to the “shrunken” universe, we divide the diameter of the shrunken universe by the diameter of the Solar System. And, voila! With the Earth inside a human hair, the universe is still about 380 Solar Systems in diameter.

Far too large to find, much less encounter, intelligent extra-terrestrial life.