The Drake equation is an example of thinking really big.
N = N* fp ne fl fi fc fL
N* = number of stars in the Milky way galaxy (100 Billion or so)
fp = fraction of stars that have planets
ne = number of planets capable of supporting life
fl = fraction of those planets where life evolves
fi = fraction of planets where intelligent life evolves
fc = fraction of planets where intelligent life evolves capable of communication
fL = fraction of planets life span during which intelligent civilizations live
Smack all your best guesses for each of the variable together, solve for 'N' and you have the number of likely intelligent alien species in the galaxy capable of communication with us.
Now, since you start off with such a HUGE number of stars (100 Billion give or take) the result of the equation is that the galaxy should be teeming with intelligent communicating alien species.
So where are they?
"So you send an ultra-powerful signal as a focused laser beam. How much energy would that take? How long could you afford to transmit? How many directions must you point the transmitter to cover the whole sky? (The answer to that one is 100,000 trillion). And what chance a citizen of an alien civilisation is tuned in when your one-second message whistles by at the speed of light? The arithmetic, says Trotman, predicts one-way communication with both antennae pointing at each other will happen for one second every 10 billion billion years. Assuming, that is, both civilisations are using the same wavelength.
Don't wait up for ET. Use your imagination instead."