Love, Impending Doom, and the Drake Equation

In 1950, physicist Enrico Fermi wondered, "where is everybody?", meaning that, given the billions of stars in our Galaxy, there should be plenty of evidence for extraterrestrial live. However, such evidence has never been produced by anyone. This seeming contradiction is now widely know as the Fermi Paradox. (Warning: massive time sink ahead!)

So what does this question tell us about our own future?

In the remainder of this essay, I'm making a few assumptions that may be debatable. It's just a thought experiment, feel free to disagree! :) Most importantly, I'm assuming that

When a civilization starts to use radio communication, a solid sphere of radio waves starts to emerge from their planet and extends in such a way that their planet is in the center of the sphere. Note that I'm using "radio" as a placeholder for any form of electromagnetic communication here.

When the civilization dies, the solid sphere becomes a hollow sphere. See figure 1 (click to enlarge).

The dot in the middle is the planet hosting the civilization. The arrows indicate the direction of radio emission, the ring around the arrows is a 2-dimensional projection of the hollow sphere. Inside of the inner surface and outside of the outer surface of the wall of the sphere, there are no signs of radio transmission from the civilization. The thickness of the wall (in light-time) equals the lifetime or longevity of the civilization (L)

When the longevity L is large, the walls of the spheres emitted by intelligent species will be thick (figure 2). In this figure, the dot in the middle represents our planet, Earth. If the civilizations out there in the the galaxy would last long, we should be in the intersection of lots of walls of radio transmission, so there should be plenty of evidence for intelligent life outside of Earth.

If, on the other hand, the average longevity L of an intelligent species was small, all of the radio transmissions sent by them may very well have passed by us in the past (figure 3; the dot in the center is Earth) or will only reach us in a distant future. In this case, although the galaxy was brimming with life, we would never know about it.

The idea of L is, of course, taken from the Drake Equation.

If the civilizations around us have a short lifespan, why should ours be an exception? What it might teach us (if it wasn't far too late to teach us anything at all ;)), is this:

If we take a look around, this is pretty obvious. Far more than 99% of outer space is boring: vast regions of nothing interesting, interspersed with a few star systems. Much more than 99% of a star system is boring, interspersed with a sun and a few planets. The vast majority of planets is probably uninhabitable, with very few exceptions. Most of the planets never develop intelligent life, with very few exceptions.

I like to call this the fractal principle (but I have no idea whether I picked it up somewhere or it just popped up in my head). You have to be the exception of the exception of the exception, etc to get here, like a fragile tiny structure in the borders of a Mandelbrot fractal.