N = R* × fp × ne × fl × fi × fc × L

where:

N = the number of civilizations in our galaxy with which communication might be possible;

and

R* = the average rate of star formation per year in our galaxy
fp = the fraction of those stars that have planets
ne = the average number of planets that can potentially support life per star that has planets
fl = the fraction of the above that actually go on to develop life at some point
fi = the fraction of the above that actually go on to develop intelligent life
fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space
L = the length of time such civilizations release detectable signals into space

One easy way to deal with the Fermi Paradox is to plug in low numbers for fl, fi, fc and L. It’s pretty easy for me to see how it could be rare for life to arise, but I find it quite implausible that there are very many living planets out there that won’t at some point create intelligences capable of making radios. Most of this is moot, however, because the Drake equation deals only with present civilizations, not past ones. It’s my understanding that any civilization with a level of technological power greater than or equal to where we’ll be in a century or so would be able to easily make Von Neumann probes.

A Von Neumann probe is essentially a self-replicating spaceship capable of autonomously exploring the galaxy. On each probe is a beacon that broadcasts its findings as it explores and when it finds a new system it establishes a factory that makes more probes. Each factory also has a beacon, so the probes know to avoid previously-explored systems. Because of the self-replication factor a single Von Neumann probe would likely be able to blanket the entire galaxy with beacons in less than ten million years. Initially this seems like a long time, but considering the galaxy has been around for over 12 billion years it’s a curiosity to me that SETI has been operating for so long without any trace.

So how do I resolve the Fermi Paradox, especially considering self-replicating artifacts? Just recently I found a hypothesis which seems reasonable, and I’ll lay it out in the form of axioms and conclusions. When I talk about “power” below I mean ability to reach assorted goals. Intelligence, resources, and knowledge are all forms of power. When I talk about “the singularity” I mean an intelligence explosion that leads to a civilization being controlled by artificial intelligence (which may or may not be acting in accordance with the desires of its makers.)

Axiom: Contact with a less intelligent alien has no significant power benifit post-singularity.

Axiom: Contact with a more intelligent alien has a mild power benefit if they are benevolent.

Axiom: Contact with a more intelligent alien is incredibly dangerous if they are hostile.

Axiom: A society capable of inter-stellar spaceflight is almost certainly going to be post-singularity.

Axiom: A constructed intelligence will always destroy an alien that might possibly interfere with its goals if said alien is not an asset and protection or existence of said agent is not explicitly a goal.

Axiom: Evolved intelligences will typically not state explicit preservation goals for aliens when building their superintelligence. (Many will likely not even code in preservation goals for their own species.)

Therefore: Alien civilizations will either be major existential threats or of no real value.

Therefore: A rational intelligence will avoid attracting attention from aliens if not actively hiding from them.

Therefore: A civilization will have only a tiny window between when they develop radios and when they are either wiped out or hidden away by advanced AI.

Therefore: There may be plenty of intelligent life out there, but it’s likely hanging around star systems hidden by Dyson spheres.

Okay, so it’s not quite predicate calculus but it was the easiest way for me to organize my thoughts. If you find errors with my logic or disagree with an axiom please leave a comment. ^_^