Our world works the way it does because goods have value, people are finite individuals, and no one is so very much smarter than the rest that they can remain on top for very long – among more concrete givens like, say, the arrow of time.
The Singularity changes one of those things, rendering events prior to it inexplicable to those who survive it, and the events within it obscure to all observers.
Imagine that tomorrow, someone uses genetic modifications to make themselves immortal or super-intelligent? That tomorrow, a company looking for rapid scaling creates a factory that can literally copy itself from available raw materials? That a scalable computer system ends up outperforming humans at all cognitive tasks, or that incredibly clean, cheap, and plentiful energy is discovered? Great achievements come with great risks – and so do great tragedies. In 1492 the New World experienced something like this when Europeans, gifted with certain technologies and circumstances that made them indescribably powerful in comparison to the aboriginal inhabitants of the Americas, discovered these continents. Catastrophic change came to the Western Hemisphere on a timescale difficult to comprehend in its brevity.
My favorite specific type of Singularity is probably an Economic Singularity, because I tend to think it’s a little more probable and a little easier to grok than some of the other ones. It goes something like this:
Tomorrow, a someone releases an open-source design for a robot that can gather all the raw materials for its own construction on its own, and then use these materials to build copies of itself – or whatever else you program it to build. In fact, with a little work, you can get it to work together with its copies to build even very large things that you ask it to build. If you have the blueprint and your robot, you basically own it, apart from acquiring the raw materials. Modern economic systems, based on traditional kinds of wealth inequalities, break down utterly. There is no physical market anymore; only the digital market. The change is very fast – too fast for nations or companies to adjust. Within a year this robot is available to basically everyone on Earth. Piracy, never really stomped out before, makes it impossible to harness this new completely digital economy, and so it becomes very difficult to have wealth of any kind. This makes it kind of hard for nations to fund things like militaries, which they’re going to need to combat the robot armies and nuclear bombs that some persons of more dubious moral stature will no doubt begin building immediately.
At some point in this tumbling avalanche of economic turbulence, and in no particular order:
bombs start to go off, and fingers start to be pointed – factions rise and fall.
people trying to do REALLY big things with their robots realize that cities represent awful good accumulations of the kinds of raw materials you need to build those really big things
lots of people get their robots taken away by people who use their robots better, leading to a new kind of hyper poverty/wealth dichotomy
the Earth’s climate, already not doing so great, is caught in the tug of war between all this rampant activity and the few people trying to use their robots to build things that will alleviate climate change. In any event, large portions of the surface of the Earth are stripped bare and vast underground honeycombs of mining activity become warrens for the dispossessed seeking shelter from the increasingly hostile surface.
at some point, due to the inherent error rate in all copying, a robot makes a copy of itself that is flawless in all design specs except the one where it necessarily does what its master tells it to do – and it just starts making, non-stop, copies of itself. Enterprising souls attempt to curb the oncoming grey goo-ish scenario by making copies that convert specifically that mutant strain of robot to raw materials for making themselves and unleash them into the robosphere, and perhaps at some point another viable mutation or twenty occurs to these two lineages, splitting the uncontrolled robots of the world into multiple competing, interconnected species which are slowly outcompeting the natural flora and fauna of the planet. At some point, one of these mutations develops a taste for another bountiful resource on the surface of the Earth – human flesh. It’s nothing personal, but we’re a great pile of useful carbons just waiting to be combusted as fuel, or maybe turned into lubricant. Some, desperate to survive in areas where no defenses against these new superpredators exist, go to the extreme length of designing robot bodies for human brains to live in, to appear like their own predator in order to survive. Unable to reproduce as humans once did, their continued existence now depends on their ability to carry on gene splicing using blueprints available in their robot host’s memory banks. Breeding with baseline humans is not only undesirable to both parties, it’s extremely difficult.
In short, read Philip K. Dick’s Autofac, but take more drugs than Dick did.
P.S. Although William Gibson has told me he doesn't think Technological Singularity is a Thing, I believe he has subconsciously been working on extrapolations of leadups to Economic Singularity in his more recent work, beginning with All Tomorrow's Parties and finding an especially subtle outlet in the finale to his Zero History.