Posted by Mark Liberman
https://languagelog.ldc.upenn.edu/nll/?p=74439&utm_source=rss&utm_medium=rss&utm_campaign=singularities-von-neumann-good-vinge
https://languagelog.ldc.upenn.edu/nll/?p=74439
The OED gives citations for singularity going back to the 14th century, e.g. this example from 1398 in the sense "The fact or condition of being alone or apart from others; solitariness":
Men vsyd to ete togyders in open place, leest syngularite schuld brede lechery.
A mathematical singularity, as Wikipedia tells us,"is a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as by lacking differentiability or analyticity", with an obvious example being what happens to the reciprocal function 1/x at the point x=0. I'm not sure when that usage began, but it's easy to find references back to the 19th century, e.g. Charlotte Angas Scott, "On the higher singularities of plane curves", American Journal of Mathematics 1892.
Most uses of the term these days involve a metaphorical extension of the mathematical concept to the idea of a technological singularity, which Wikipedia describes as "a hypothetical event in which technological growth accelerates beyond human control, producing unpredictable changes in human civilization."
The first documented use of this metaphor is attributed to John von Neumann in a 1958 posthumous tribute by Stanislaw Ulam:
Quite aware that the criteria of value in mathematical work are, to some extent, purely aesthetic, he once expressed an apprehension that the values put on abstract scientific achievement in our present civilization might diminish: "The interests of humanity may change, the present curiosities in science may cease, and entirely different things may occupy the human mind in the future." 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.
Then in the early 1960s, I.J. Good presented "Speculations Concerning the First Ultraintelligent Machine". Good doesn't use the term singularity, but he clearly expresses (a version of) the idea. From his Introduction:
Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an 'intelligence explosion', and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make, provided that the machine is docile enough to tell us how to keep it under control.
And from his Conclusion:
It is more probable than not that, within the twentieth century, an ultraintelligent machine will be built and that it will be the last invention that man need make, since it will lead to an "intelligence explosion." This will transform society in an unimaginable way. The first ultraintelligent machine will need to be ultraparallel, and is likely to be achieved with the help of a very large artificial neural net. […] The machine will have a multimillion dollar computer and information-retrieval system under its direct control. The design of the machine will be partly suggested by analogy with several aspects of the human brain and intellect. In particular, the machine will have high linguistic ability and will be able to operate with the meanings of propositions, because to do so will lead to a necessary economy, just as it does in man.
The whole article is well worth reading carefully, and it's a scandal that the only available (and somewhat corrupted) version is on the Wayback Machine. For more on I.J. Good, see my 2009 post "Good is dead", which sketches his contributions (with Alan Turing) to the world's first Language Model, as part of the Enigma decryption effort more than 80 years ago.
The next step (that I know of) was taken by Vernor Vinge, in a 1983 op-ed in Omni Magazine (I've typed out the contents because the original, black type on a dark grey background, is hard to read):
A favorite game of futurists is to plot technological performance – computer speed, say – against time. Such trend curves climb ever more steeply. Extrapolated 30 or 40 years, they are so high and steep that even the most naive futurist discounts their accuracy. Some who talk about that era predict a leveling off of progress. After all, saturation effects are observed in other growth processes.
There is an important reason why this process won’t level off. We are at the point of accelerating the evolution of intelligence itself. The exact means of accomplishing this phenomenon cannot yet be predicted – and is not important. Whether our work is case in silicon or DNA will have little effect on the ultimate results. The evolution of human intelligence took millions of years. We will devise an equivalent advance in a fraction of that time. We will soon create intelligences greater than our own.
When this happens, human history will have reached a kind of singularity, an intellectual transition as impenetrable as the knotted space-time at the center of a black hole, and the world will pass far beyond our understanding. This singularity, I believe, already haunts a number of science-fiction writers. It makes realistic extrapolations to an interstellar future impossible. To write a story set more than a century hence, one needs a nuclear war in between – to retard progress enough so that the world remains intelligible.
In a 1993 article "Technological Singularity", still (for now) available on the web, Vinge elevates singularity into the title. He quotes Ulam/von Neumann and Good, and concludes by speculating about "the Best We Can Ask For". The whole thing is worth reading.
It's striking how accurately some recent developments were foreseen by von Neumann and Good and Vinge 30-70 years ago — but what strikes me most about the current situation is how much of it was not predicted. None of those seers told us about Data Center politics; AI hallucinations; the socio-political and cybersecurity effects of AI bots and agentic AI; the economics of a possible AI bubble; and so on.
Maybe this is just temporary turbulence as a smoothly-flowing post-singularity future is forming, whether utopian or dystopian or both. But from where I sit, the foreseeable future of (things called) "AI" looks even more chaotic, which is one more reason to doubt that the concept of a singularity is really helpful.
A different metaphor is implied by Richard Dooling's 2009 book Rapture for the Geeks , as well as a 2012 work the rapture of the nerds by Cory Doctorow and Charles Stross. Both allude to the (religious) Rapture, which is conceived in many different ways by different individuals and groups, but is generally seen as an abrupt event that's positioned in the middle of other variously defined and described times, and affects different groups of people in very different ways.
See also "Another meme collision", 7/8/2024.
https://languagelog.ldc.upenn.edu/nll/?p=74439&utm_source=rss&utm_medium=rss&utm_campaign=singularities-von-neumann-good-vinge
https://languagelog.ldc.upenn.edu/nll/?p=74439
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