I like Ivan's large numbers; when you do even small calculations (on the backs of very small envelopes), you can see why Mr Clarke says 'staggering'.
A million years is <1% of the time it takes the Sun (plus us, of course) to go once round the Milky Way, yet it's at least 10 times as long as homo sapiens has (apparently) possessed the ability to reason abstractly, and approx 100 times as long as there's been 'permanent' human settlements. In this context, 'cultural' considerations (thanks Tony) start to make your brain hurt.
Another of Arthur's sayings seems apposite, something about advanced technology seeming like magic; what would the people who made those wonderful cave paintings (in France, for example) thought of the PC? or a Bose-Einstein Condensate? And that's 'only' ~1,000 generations (the Sun takes well over 5 million generations to make just one journey round the Milky Way).
So, where is ET?