Please tell me, just how would we become extinct in 500 years? — ssu
"The world" will not literally come to an end, unless a black hole stops by and vacuums it up before moving on to more pressing business. Homo sapiens will (probably) not literally vanish in 500 years, unless aliens stop by to rid the universe of whatever threat we pose to their own schemes. Eliot was writing poetry not prognostication, and I am not an extinction enthusiast.
However, we can speculate on how our species might meet its demise. It's a worthwhile exercise because we want to avoid coming close to extinction, let alone finding out what extinction feels like.
My guess is that we could at least come close to extinction through a combination of disasters, which are from "fairly" to "remotely" possible. All of them happening at once or in a maximally destructive sequence is not likely.
Disaster #1: A 'limited nuclear exchange' and the resultant firestorms cause a dramatic increase in CO2 and other greenhouse gases in the atmosphere.
Disaster #2: Global warming becomes quite severe over the next several centuries, and a very large percentage of humans die, owing to starvation and familiar diseases.
Disaster #3: Novel viruses and/or bacteria arise and kill off a significant portion of the humans who managed to survive severe global warming.
Disaster #4: A meteorite large enough to cause large-scale damage further depletes the remaining (small number of) humans. Or, the volcanic eruption of the Yellowstone Caldera would cause the same kind of damage as a meteorite impact.
The least imaginative apocalyptic fiction call for annihilation by means of multiple, well-timed disasters. We escape to the vicinity of Alpha Centauri and continue along our merry way.
What is quite possible are disasters # 2 and # 3, and we don't escape at all. In the worst-possible global warming scenarios, feedback loops accelerate the rate of warming. Some predictions say that by the end of this century, day-time temperatures may be too high for people to work outside for extended periods (like they do in agriculture, for instance) in areas of the world that are normally hot. In subsequent centuries, the zones of 'too damn hot' will cover presently temperate areas.
Even a moderately slow rate of global warming will be too fast for environments to adapt, and many species of plants and animals will fail.
Humans probably won't die of heat exhaustion; we are more likely to die from starvation, because food production will become difficult long before 500 years is up. A starving population will fall prey to ordinary illnesses. (One can safely assume that scientific capabilities will be diminished as people die off.)
What might bring us to our needs during a period of exhaustion and starvation is a novel disease. I have no idea what that disease might be, but in the last half century several new diseases have appeared (AIDS and Ebola) or appeared in new areas (West Nile Virus and the Zeka virus). Some bacteria have become, or are rapidly becoming, immune to antibiotics.
A limited nuclear war is a real possibility. "Limited" meaning... don't know. 100 to 500 nuclear explosions in a desert would probably not result in a rapid increase in death rates over the long run. Nuclear war, however, will not result in many desert test site explosions. Most of them will occur where there are large numbers of people and structures. Those explosions would be 'dirtier' both in terms of radiation and CO2 production.