Tilting Drake's Equation

I was having a conversation with a friend about the likelihood of the existence of other forms of intelligent life out there. He was arguing that if life was out there, we'd have seen better evidence of it by now. I'd been thinking about related issues, but was more interested in the question of what conditions are really needed for the evolution of intelligent life on another planet. My proposal was then that we should all have our own competing versions of the Drake equation over which to argue. Here's my version.

First, I haven't been able to find any stories that describe a satisfactory form of life that doesn't originate as water+carbon based, so let's assume that's the kind life we're talking about.

We have good data now that planets are common -- as common as stars. 10's of billions ($10^{10}$).

$10^{-2}$ of those planets are in the habitable zone (rough guess)

There should be a factor for the planet being just the right size -- large enough to hold water down, but small enough that it's gravity well is easy to escape, but let's skip it and let the astronomers help out there.

All of these develop life (I think life is common on these planets with liquid water, though this is clearly a personal bias.)

Now, what's the chance life evolves to our level of complexity?

$10^{-3}$ because you need a crooked planet! Only on a planet with strong seasonality with fore-sight be evolutionarily beneficial. But too large a tilt could make the place un-inhabitable.

$10^{-3}$ because you need enough fossil fuel to provide a long window of opportunity during which interplanetary life is established, AND nuclear war is avoided.

That puts us at around $100$ space-faring civilizations in the galaxy (at a given time).

A tilt-term isn't in the original drake equation. One of the tasks implicit in the use of the Drake equation is to determine what conditions are necessary for the emergence of ``intelligent life'' from the primordial ooze. Defining ``intelligence'' or sapiency is perhaps a fool's errand -- Roadside Picnic and Solaris give good metaphors for the inherent challenges, and the Turing test we do have is so very disappointing. But even assuming we know ``intelligence'' when we see it, when can intelligence evolve? To me, intelligence is an ability to learn and plan ahead to deal with predictable changes in the world successfully. If your world never changes, there's no reason for intelligence. So,... intelligence will only appear on worlds that (1) possess stable tropical regions where life can get a foothold, and (2) other regions where large regular variations in which survival requires anticipation and preparation.

On our own planet, this has happened in three ways. First, earth rotates daily and always has (unlike mercury, for example). That's got to be pretty common, but we shouldn't forget it. Second, our moon drives mild ocean tides on a daily basis. This may have created the most important opportunities for the evolution of terrestrial vertabrate lifeforms. Third, earth is tilted relative to it's orbital plane around the sun. This probably happened during the earths creation billions of years ago. This creates seasons and the opportunity for complex terrestrial life-cycles that exploit annual variation in environment. So, at two important transitions complexity, earth has been special.

Once that leap to intelligent life happens, it seems trivial for some form of life to disperse through the galaxy, and we should be able to find evidence. This makes me think that rapid sublight traversal of the interstellar voids may be a much more hazardous undertaking than one might estimated at first pass.