Models of a Singularity (extended abstract)

Models of different categories of technological singularity

Anders Sandberg, Future of Humanity Institute

The set of concepts today commonly referred to as “technological singularity” has a long history in the computer science community. Concerns about automated reasoning outpacing human reasoning can be found in Samuel Butler’s Erewhon (1872), John von Neumann and Stanislaw Ulam conversed in the 1950’s on how ever accelerating progress would lead to “some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue”, and I.J. Good in 1965 delineated the possibility of an “intelligence explosion” where sufficiently advanced artificial intelligence would rapidly self-improve.

Mathematical singularity and technological singularity (Yoram Hirshfeld)

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In the discussion of civilization and technology and their development in time, some terms with mathematical origin are used, specifically "singularity" and "exponential growth". There is some relation by association between objects with the same name in two different disciplines, but they usually do not mean the same. It would be very strange, if a philosopher of human behavior would try to apply Euclid's theory to love triangles, or if a geometer would launch into a long explanation why Euclid's mathematics is not relevant to this kind of triangles. Ironically, I find myself doing it; writing a note insisting that mathematical singularity has no bearing on the research of technological singularity. I will explain what is a mathematical singularity, and what exponential growth is, and is not. I can guarantee that the mathematics in the note is correct, but the philosophical claims are intuitive, based on common sense and on merely mild mathematical expertise. (Read more)