TLDR: The "technological singularity" was an important and useful term with a clear meaning. Then it became the "Rapture of the Nerds". We need a new term.
I first heard the word "singularity" in the context of black hole physics; it dates back at least to the early 20th century:
ChatGPT 4 2023: "At the singularity, the laws of physics as we know them, including space and time, break down, and our current understanding of the universe is insufficient to predict what happens within it."
Not much later, in the 1950s, the term was applied by von Neumann in a technological context (from a 1993 Vernor Vinge essay):
Stan Ulam paraphrased John von Neumann as saying: "One conversation centered on the ever-accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue."
Brad Delong used to write about this kind of non-AI historical singularity. My favorite description of what it would be like to a approach at technological singularity was Vinge's short story "Fast Times at Fairmount High". (This prescient story appears to be lost to time; he wrote a similar full length novel but I think the short story was better).
The core idea is there's a (virtuous?) recursive loop where technology improves technology with shorter and shorter cycle times. Many processes go exponential and even near term developments become unpredictable. One may assume social end economic structures train to keep pace. The historical singularity exponential curve was part of The Economist's y2K Millennium issue GDP per person historical graph:
We will soon create intelligences greater than our own ... When this happens there will be a technological and social transition similar in some sense to "the knotted space-time at the center of a black hole"
A decade later, in his 1993 essay later published in Whole Earth Review (non-Olds cannot imagine what Whole Earth Review was like), Vinge revised what he meant by "soon":
... Based on this trend, I believe that the creation of greater-than-human intelligence will occur during the next thirty years. (Charles Platt has pointed out that AI enthusiasts have been making claims like this for thirty years. Just so I'm not guilty of a relative-time ambiguity, let me be more specific: I'll be surprised if this event occurs before 2005 or after 2030.) ...
So by the year 2000 we had the concept of a historical technological singularity (eminently sensible) that had become focused on a specific kind of self-improving technology - the superhuman intelligence with an upper-case S Singularity (presumably AI). Those were useful concepts - "technological singularity" and "superintelligence" Singularity.
In 1993 Vinge predicted the Singularity would happen before 2030, later experts like Scott Aaronson predicted after 2080. (Aaronson has since revised that prediction and works for OpenAI; Vinge's 2030 dates looks pretty good.)
After 2000 though the word Singularity went off the semantic rails. It came to be used for for a peculiar future state in which human minds were uploaded into simulation environments that were usually described as pleasant rather than hellish. This is, of course, antithetical to the original idea of unpredictability! This peculiar meaning of "The Singularity" came to be known as "The Rapture of the Nerds" based on the title of a book by Charles Stross and Cory Doctorow. More recently that vision underlies a weird cult called longtermism that seems to have infected some vulnerable minds.