If the ant lived in a forest somewhere in South America, for many generations it would see nothing in the skys above it.
Then, in 1920, it might see a biplane or two, once a year. By 1960, it might see a regular stream of airliners, and in 1980 a Concorde passing by. Then the Concorde would stop, and gradually the stream of planes would get less as an economic slump occured. By 2020 it might see no planes at all, as people started to use virtual reality communications more and more.
So, over the millions of years that ants have been in existence, for a short 100 years the ant might have an opportunity to discover our civilisation with a telescope. If antkind had developed a telescope in the 1650s it would not see an aircraft even if it waited for 100 years - similarly if it developed a telescope in 2050 when we had stopped using aircraft.
Now, each ant lives for about 2 years. So very many ants will live their lives and die without being able to detect our technology. I think we would have to be incredibly lucky for an alien civilisation to be operating a technology that we could have a hope of detecting at the same time as we were actually looking, and I can't see why this vanishingly small opportunity should occur in our lifetimes....
Oh, and, Colin, who's your favourite SF author? I have a great respect for James Blish, but you don't see much of his work around anymore....
Nope not quite right for a couple of reasons unless you're agreeing with my very first post.
First is you are thinking all lifeform will ultimately go down the line of a virtual reality existence. Some may but, again, if the galaxy is teeming with life as it is supposed to have, just as many would not pursue this avenue.
Second, you bring economics into the equation. However, one thing which for any lifeform will trump any economic angle is the need for energy as a world's energy consumption increases. Eventually, intelligent lifeforms will harness the output of their stars. This is a dyson sphere. It has nothing to do with economics, power or wealth. It is a need to provide limitless energy for a civilisation to sustain itself. These dyson spheres are far bigger than stars. They should be far easier to spot than stars due to their immense size which in turn would warps space so much, they'd stick out bigger than an ocean liner in your local pond.
Thirdly, you're comparing timespan in the singular ie ant and airliner on earth, and not from the perspective of the age of the galaxy. Your example uses time pertinent to all life here on earth but you need to look at it from the timespan of the galaxy when earth did not even exist.
Being some 10+ billion years old, intelligent lifeforms could have arisen and become extremely advanced
before the earth was even created. Any number of intelligent lifeforms should have evolved, many to the extent of harnsessing their star's out put via dyson spheres. Some should have migrated to the stars. It would only take then about 5 million years to colonise the entire galaxy not just travel from one end to the other.
All this could and should have been achievable within the first 5 billion years of the galaxy existing. Then, lets suppose they all died out. After 4.5 billion years intelligent life of sorts evolved here. Whether the intelligent life exists in the galaxy now is not relevant.
We should easily detect such artefacts of previous lifeforms such as dyson spheres which are far bigger than stars, extending out as far as the planet of the intelligence that built it.
The only way your hypothesis works is if ants are the first lifeform on the planet (because they dont see any airliners with their telescope in 1650) which, goes back to my very first post ie we are the first or only intelligent lifeform in the galaxy in this epoch.