Abstract
The notion of a coming technological singularity is a key concept in contemporary science fiction, futurism and popular science. It is the central theme in block-buster movies such as The Matrix (1999) and The Terminator (1984) and a number of science fiction novels, such as William Gibson’s Neuromancer (1984) and William Thomas Quick’s trilogy Dreams of Flesh and Sand (1988), Dreams of Gods and Men (1989), and Singularities (1990) (see Esterbrook 2012, for further references and analysis of the science fiction literature). Furthermore, there are dozens of popular science books, hundreds of academic papers and even a congressional report on the singularity. There is a Singularity University and an annual singularity conference, where top academics and intellectuals including Douglas Hofstadter, Rodney Brooks, David Chalmers and Stephen Wolfram have given talks. So, yes, the singularity is a concept to be taken seriously.
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Notes
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Full list of speakers and mp3-recordings of the talks are available at http://intelligence.org/singularitysummit/.
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The mathematical content of the proposition is not consequential for us here. For those interested, Robbins’ problem in brief consists in showing a particular set of equations, including the so-called Robbins equation (¬(¬(x + y) + ¬ (x + ¬ y)) = x), form the basis of a Boolean algebra.
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As an example a toy problem could be: Show that the expression: “(R⊃~P)⋅(~R⊃Q)” can be transformed into the expression: “~(~Q⋅P)” given a twelve formal rules determining how to manipulate expressions containing the four logical operators “⊃”, “⋅”, “~” and “∨”. This was the main example considered in (Newell and Simon 1963).
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For those interested in the mathematical content a group (G,*) consists of a non-empty set of elements G and a binary composition * on the elements such that (G,*) satisfies the following four axioms:
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There is neutral element in G, i.e. an element e such that e*a = a for any element a in G.
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G is closed under the composition *, i.e. if a, b is in G, then a*b is also in G.
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The composition is associative, i.e. for all a, b, c in G, (a*b)*c=a*(b*c).
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All the elements of G have inverses, i.e. for any element a in G there exists an element a −1 in G such that a*a −1 = e.
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Johansen, M.W. (2017). Science Fiction at the Far Side of Technology: Vernor Vinge’s Singularity Thesis Versus the Limits of AI-Research. In: Baron, C., Halvorsen, P., Cornea, C. (eds) Science Fiction, Ethics and the Human Condition. Springer, Cham. https://doi.org/10.1007/978-3-319-56577-4_3
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