Hmm. It had been a long time since I read that. I forgot that EY specifically compares the Vinge singularity to an event horizon. It's an apt comparison, although the event horizon is not a singularity (well, it's a co-ordinate singularity in some co-ordinate systems, but that doesn't count*). I took a quick look on the internet to see if I could find Vinge actually making that connection, but I didn't see it. The 1993 document, for example, doesn't refer to space-time or black holes at all (but it did remind me that, contra Wikipedia [and me above (ETA: actually I didn't make the erroneous claim, but I think I believed it)], Von Neumann deserves at least part of the credit for being first to say 'singularity', since Ulam was paraphrasing him).
There is possibly a tension here between those who instinctively perceive the word 'singularity' as a mathematical term and those who perceive it as a (speculative) historical one. Many of us, presumably, can go either way depending on the context, treating the two things basically as [the referents of] homonyms. But with my bromide immortalized in that image, I was attempting to point out what they all have in common: they are by their very nature holes in a structure, not elements of a structure. When the structure in question is a map, they are points where the map fails. When the structure in question is the object of investigation, as it is in mathematics, they are merely discontinuities; but they are not things, they do not exist. For me, the very word 'singularity' connotes the tenuousness of our maps.
Of course, it is also important to make a literal/figurative distinction here. Singularities in math and physical theories are literal singularities; historical ones are figurative. And some are more figurative than others; as I'm sure has been pointed out, Kurzweil's singularity is pretty hard to see in any kind of superexponential growth curve, but perhaps running into a vertical asymptote can be charitably interpreted as hyperbolic.
* That's actually a good example of what I mean, though. Co-ordinate singularities are in some maps but not others (that we know how to make); 'real' singularities (the word is here quoted for bogosity) are in every map we know how to make.
Yes, I was actually thinking of the intelligent explosion type singularity as being the one that resided the most in the map. And the point about the difference between a mathematical singularity and a non-mathematical singularity is a very good one (and the analogy about an event horizon is also interesting. Although even then, there's a strong territory aspect there because once one is inside the event horizon one cannot send a signal out by any means.)
...And some are more figurative than others; as I'm sure has been pointed out, Kurzweil's singularity is
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