On essential singularities
Jul. 30th, 2026 08:01 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
lloydwoodIn complex-analysis mathematics since the nineteenth century, an essential singularity is a point beyond which nothing can be predicted; the function that leads to it becomes unmanageable.
But is the coming AI singularity and end of the world as we know it an essential singularity? I got into a discussion on LinkedIn about it.
Vernor Vinge, The Singularity, 1993:
Vinge says essential a couple of more times in that piece, in normal use. Let's go and read his citation in more detail:
[28] Stanisław Ulam, John Von Neumann, 1903-1957, Bulletin of the American Mathematical Society, vol. 64, no. 3, part 2, May 1958:
"some essential singularity"? Is that a complex-analysis essential singularity?
Ulam uses some variation of essential five more times in that tribute, all in normal English usage. It's really hard to tell if that one mention next to 'singularity' is special. But that memoriam was written by a mathematician and published for an audience of mathematicians.
Von Neumann was born Hungarian, but Ulam was born Polish. Did niezbędny [essential, indispensable, necessary, required (that which one cannot do without)] have any special significance in Polish as Ulan's favourite word? I'm told that in Polish the mathematical concept of an essential singularity translates as the different istotna osobliwość.
My thanks to Cheryl Anne F. for an interesting discussion.
But is the coming AI singularity and end of the world as we know it an essential singularity? I got into a discussion on LinkedIn about it.
Vernor Vinge, The Singularity, 1993:
I think it's fair to call this event a singularity ("the Singularity" for the purposes of this paper). It is a point where our old models must be discarded and a new reality rules. As we move closer to this point, it will loom vaster and vaster over human affairs till the notion becomes a commonplace. Yet when it finally happens it may still be a great surprise and a greater unknown. In the 1950s there were very few who saw it: Stan Ulam [28] 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.
Vinge says essential a couple of more times in that piece, in normal use. Let's go and read his citation in more detail:
[28] Stanisław Ulam, John Von Neumann, 1903-1957, Bulletin of the American Mathematical Society, vol. 64, no. 3, part 2, May 1958:
"some essential singularity"? Is that a complex-analysis essential singularity?
Ulam uses some variation of essential five more times in that tribute, all in normal English usage. It's really hard to tell if that one mention next to 'singularity' is special. But that memoriam was written by a mathematician and published for an audience of mathematicians.
Von Neumann was born Hungarian, but Ulam was born Polish. Did niezbędny [essential, indispensable, necessary, required (that which one cannot do without)] have any special significance in Polish as Ulan's favourite word? I'm told that in Polish the mathematical concept of an essential singularity translates as the different istotna osobliwość.
My thanks to Cheryl Anne F. for an interesting discussion.
