When the signal dies out of the last human being, that narrow band of focus which is conscious attention, what will become of that consciousness? Which thoughts will leave an impact? Which beliefs will transcend annihilation?
For millennia we have followed a certain chain of thoughts, the origination of which is unknown. Certain innovators have some staying power, like Greek philosophers some religions, but when all is said and done will it matter one wit?
Thousands of cultures have been completely erased, each having their own chains of thought. But now we live a sophisticated life, above the ethnosphere of origination. But I think they had something we do not, or we are attempting things that may have already (or nearly) destroyed us more than once.
I wonder if primates would again evolve into humans, or something more? I wonder what we would call ourselves.
“If life on Earth offers any measure of life elsewhere in the universe, then intelligence must be rare. By some estimates, there have been more than ten billion species in the history of life on Earth. It follows that among all extraterrestrial life forms we might expect no better than about one in ten billion to be as intelligent as we are, not to mention the odds against the intelligent life having an advanced technology and a desire to communicate through the vast distances of interstellar space”—Niel DeGrasse Tyson
“The universe appears to be 13.8 billion years old. The earth about 4.5 billion years old. In another half billion years the sun will expand and make life impossible on earth, which means that if had taken consciousness 10% longer to evolve it would have never evolved at all”—Elon Musk

Then there is the timing thing. Our ability to send messages is about a hundred years now—an infinitesimal window of time compared to the age of anything out there.