[loup-vaillant]

There are now 3 core concepts that we may call "Singularity".

1) Event horizon: past the point where there are entities smarter than us, we virtually can't predict anything.

2) Accelerating change: things will get bigger/better/smarter at an exponential rate. The "Singularity" is a point somewhere on that exponential curve. (Or something)

3) Intelligence explosion: if it's smarter than us, it will be made by us (whether it is an AI, or brain computer interface, or whatever). Therefore it can recursively improve itsef to super-intelligence very quickly.

Taken loosely, those 3 visions are mostly compatible. But taken to their extremes, they are contradictory. It is important to distinguish the 3 to avoid confusion.