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The Knave's Cosmological Theorem

The Knave's Cosmological Theorem

Tuesday, October 17, 2023 10:00 am
Tamsyn Morrill
Trine University

Abstract: The Look-Say sequence is a classic example of recursion. Its terms are verbalized descriptions of their predecessors --- initialized at 1 --- 11, 21, 1211, and so on. Conway demonstrated that the asymptotic growth rate of this sequence is the unique real root of a degree 71 monic polynomial. The general idea is to recast the problem in linear algebra through use of his Cosmological Theorem.

Today I present a variation of this problem. A knave (of Smullyan's famed door-keeper puzzle) now controls the recursion. After working through some small examples, we will remake the Cosmological Theorem in the knave's image.

Holly Swisher