We are already on the catastrophe curve to the Singularity, the point where the curve of technological advance goes vertical and we become gods capable of defining what “humanity” means. The countdown began the instant HUGO was completed.
Julian Jaynes believed that consciousness is only about 4000 years old, and that it arose as a direct result of the agrarian revolution. Suddenly you had large, permanent settlements which required specialization by occupation, which meant you could no longer rely on the communal generalization of the hunter/gatherers. We had a revolution of the mind, and invented the “I.”
Today, our cities are virulently dysfunctional. We have rapidly rising levels of depression, bipolar disorder, autism, and sociopathy. Consciousness is no longer sufficient for dealing with the level of complexity our society has reached. The individualist story-cycle of the Hero is ending, and when we hit the Singularity, we will invent an entirely new series of narratives on which to base all understanding. At this point, humanity as we understand it is over forever.
More than half of all the animal biomass on Earth is in the form of ants. Clearly, this planet could support orders of magnitude more humans. A population of 70 billion or 700 billion is easily attainable — provided we were willing to live sensibly and logically in arcologies. Unfortunately, human consciousness is clearly not yet ready for this. We need a revolution of the mind to clear away what we recognize as humanity and replace it with something better suited for a technological culture (rather than a bronze age tribe of violent primates, as we are evolved to be now).
Whatever emerges from the other end of the Singularity, it will not be anything we would currently recognize as human. That means within our lifetimes, humanity will perish.