"[PB]What in your view would be the advantage to an advanced alien race of directly contacting a far less advanced one? What in your view would compel them? The desire to help us? Their need for material or energy resources? Simply because they're following some rule of exponential expansion?"
Deliberately contact us? Probably none. Hypothetical-- we've hurled several remote sensing platforms at Mars. Had there been a Martian village at our landing point, would our technology have politely avoided it and landed harmlessly nearby? No, we'd have landed right on top of a martian hut, and beamed back amazing pictures of a crushed martian hut. And, if we had landed in a pool of bacterial goo that had formed itself into crude beehive approximations of hexagons, we'd have scooped it up and gleefully thrown it into an oven, to detect signs of carbon based life, and beamed that all back to the giddy folks at JPL, who would have all been smoking cigars.
Never mind the Incas, if we are talking millions of years, I hope we aren't the 'goo.'
Why did we do it? Because we were curious, and that doesn't even depend on my theory of expansion pressure based on 'geometric pi'[*] What we have done, at our scale of technology, I'd imagine some fraction of other possible civilizations may or may not do. That says nothing at all about the frequency of such occurrences, I tend to agree with you that the probabilities are exceedingly small. But when near infinitely small probabilities battle near infinitely large possibilities and a near infinitely long amount of time, well, crap happens. Kinda like the same deal that lets us sleep at night without excessively worrying about the next species ending event/asteroid.
"[PB]Do you believe that the nearest alien race would be much closer to us in time, far less ahead of us in other words, and if so, why?"
My guess would be, because of the rapid nonlinear rate at which 'technological time' advances, an even slight random offset would create a near infinite impedence mismatch between us and any other technologically advanced civilization within our neighborhood. If we're not first in the local race, we're the goo.
"[PB]Although they are quite different, my analysis and the Drake equation are in fundamental alignment as to the conclusion that advanced alien races are probably quite rare. If you feel differently, what is your case for this? And if they are exponentially, aggressively expansive, why aren't they here?"
Some have pondered this and concluded, because the real 'filter' is the ability to self-destroy, to move faster than evolutionary time, and to succumb to hubristic, constructivist beliefs.
But as well... somebody's got to be 'first' in any local neighborhood. It seems we were 'first' on this planet, anyway. Well, bees build hives, and ants build nests, and so on, but can you imagine a matched species technological competitor? The slightest advantage in time would maginify to an immense actual advantage.
Maybe we are likely first in our Solar System. Maybe in our near Galaxy neighborhood. How much farther? The entire Galaxy? Unlikely. But, in a sufficiently large neighborhood to buy us a few winks of cosmic time to believe 'we are all alone? I don't buy that EMR is the universal medium of interstellar communication. It might only be a brief interim sign of an emerging technological civilization that has not discovered the really good stuff yet. I don't know, its rare, but people do win the lottery. It is just equally extremely unlikely that we were first everywhere, as an explanation.
A more likely explanation is, it is indeed rare, but the selfish unanswered question is, is it indeed rare because it seldom happens at all, or is it indeed rare because it happens often and always snuffs itself out after a brief, rapid flare? Or, something in between? If the latter, and due to the rapid nonlinear advance of technological time, there is an exceedingly low probablility of co-existence in any local neighborhood, I'd think.
But when and if it flares up, I'd assume it does so under myriad paradigms, incentives, and motivations-- sustainability being one, stealth based growth being another, and loud, obnoxious growth being yet a third.
Tonite is probably not the night to ask, "which would we be?"
Happy New Year!
[*] In a geometric growth paradigm, domain grows faster than border, where border is a kind of predatory/conflictive 'cost.' (You run the risk of having to defend border. You run the risk of conflict at the border. You run the risk of exposing yourself to a more advanced foe at the border.) In a 2D growth paradigm, border grows as technological range, while domain grows as range squared; domain grows faster than border. In 3D volume, border grows as technological range squared, and domain as range-cubed, even if sparsely, in fits and starts(just like it did in a 2D surface paradigm.)
THis geometric 'pi', in our 2D growth paradigm, largely explains why, with the exception of a few geographically impressed exceptions, geopolitical entities are roundish 'blobs' and not randlomly skinny thin 'streaks.' Technological range determines the ability to exert C^4, and goepolitical entities and/or economies exert influence via their technological range. There is not only geopolitical pressure to expand (because domain grows faster than border/cost), but geopolitical pressure to expand as a roundish 'blob', because that has the highest ratio of domain to border.
Plus...it's what bubbles do in response to expansive pressure.