Many futurists and not a few science fiction writers hold the idea that computer technology is developing toward a point where artificial intelligence will begin to develop new technology instead of people. At that near-future time, they argue, the progress of technology will no longer be predictable. It is a “singularity”, beyond which no laws of technological progress can apply.
This idea has been around for many years and has its merits. I just wanted to point to a comment by the physicist Sabine Hossenfelder, who suggests that word doesn’t mean what they think it means: “What is a singularity?”.
What one typically means with a singularity is a point where a function behaves badly, so that one or several of its derivatives diverge, that is they go to infinity. The ubiquitous example in school math is the poles of inverse powers of x, which diverge with x to zero.
However, such poles are not malign, you can remove them easily enough by multiplying the function with the respective positive power. Of course this gives you a different function, but this function still carries much of the information of the original function, notably all the coefficients in a series expansion. This procedure of removing poles (or creating poles) is very important in complex analysis where it is necessary to obtain the “residuals” of a function.
Hossenfelder points out that von Neumann first introduced the analogy in reference to technology.