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This is essentially a mathematics problem, with a lot of estimated values. However, even if you use very low probabilities for the various factors (probability of a planet in the liquid-water zone, etc.) you still get a very large number of should-be-inhabited planets when you multiply it by the total number of stars - very likely enough that we should see evidence of them. So another way to formulate the question is: What forces the various factors low enough that we don't see any evidence of extra-terrestrial life?

There was a science-fact article on that several years ago in Analog. They said the formulation is missing a key factor - what is the probability that a 'stubborn' species would develop?

The article examined the physical characteristics of man, and what that meant for an evolutionary niche. I won't go into all the evidence, but the result of being two-legged, with disproportionately large lungs, and better heat rejection (sweat) than other animals is that man is adapted to be a 'cursorial hunter.' That is a hunter who runs doggedly (a descriptor derived from the other known cursorial hunter) after a prey until the prey is worn down and can be killed.

To succees at that, the cursorial hunter has to be stubborn - unwilling to give up until the prey is worn out. The expression, "If at first you don't succeed, try, try again" is uniquely applicable to stubborn hunters. In contrast, Tony the Tiger's attitude is, "If at first you don't succeed, to hell with it."

Building a technical civilization takes heaps of stubborn. As Edison said, "Genius is 1% inspiration and 99% perspiration."

So, if you take the calculation of likely civilizations and add another factor that requires the sort of environment - wide, flat, reasonably dry plains with good lines of sight to keep an eye on the prey - you can drop the likelihood of another technological civilization down low enough that it's unlikely we'd see evidence of them, even if all the other factors are reasonable.

I'm not trying to 'prove' that analysis of Fermi's paradox, though the logic of man as a cursorial hunter was compelling.

The reason that I used the Smithsonian exhibit to do the calculation was (besides the fact I happenned to be there) that the exhibit provides all the numbers for you. (Such as, how many stars in a galaxy, how many galaxies in a universe, etc.) You get a very large number if you presume that life isn't so hard to come by.

General rule of thumb: Physicists tend to get enormous numbers. We biology types get much lower numbers. The amazing thing to me was that I could never have deliberately calculated how to get a number so close to 1. I mean think of all the numbers like 5x10^60 that go into such an equation!

" This is essentially a mathematics problem, with a lot of estimated values. However, even if you use very low probabilities for the various factors (probability of a planet in the liquid-water zone, etc.) you still get a very large number of should-be-inhabited planets when you multiply it by the total number of stars -.........

I think you're wrong. Are you sure you have all the variables accounted for? How about you list them, just to be sure?