A very rough guess is better than nothing, especially when the stakes are high.
No, a rough guess that's wrong can give people unwarrented confidence that they think they know something when they know nothing.
At the very least you should at confidence intervals. That way you discover that you know nothing.
Correct. That is why all serious treatments of the Drake Equation give low and high estimates for every factor, and low and high results from those estimates. The same could be done with the equation I'm proposing.
I expect everyone here has an opinion on the Drake Equation. (Comment if I'm wrong.) And that's because it is an easy story to remember and spread. Never mind its glaring inadequacy or the symbols it uses: it gives you a number of alien civilizations and somehow that sticks. I'd like to see if a science meme with similar properties could be created to carry a transhumanist payload. So. Could you convince a random person of the following three points if you wanted to?
I think you could. And if you do, and if you can give a number of light-years, regardless of how much you emphasize the low confidence, aliens will suddenly seem more real to that random person. And so will, if not full transhumanism, at least some vague notion that intelligence must grow much like life does. I think that could reach a lot of people.
(If anybody complains that the expectation of some Singularity-like development is ideological: no, it is a reasonable guess based on the current evidence, much like Drake's expectation of every technological civilization's eventual self-destruction was reasonable in his Cold War era.)
The brain I'm typing this from knows too little math or astronomy to do this locally, so I'm throwing out the idea. Anyone care to play with this?