The only way of discovering the limits of the possible is to venture a little way past them into the impossible (Arthur C. Clarke's 2nd law)

Saturday, 5 February 2011

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)

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