Natural Selection, Levelling, and Eternal Recurrence

Time and Personal Identity in Nietzsche’s Theory of Eternal Recurrence

Friedrich Nietzsche’s theory of eternal recurrence is an essential part of his mature philosophy, but the theory’s metaphysical commitments and practical implications are both obscure. In this essay I consider only the metaphysical elements of the theory, with the aim of determining whether it is possible that we live our lives infinitely many times, as the theory maintains. I argue that the po...

Natural Language and Natural Selection

Many people have argued that the evolution of the human language faculty cannot be explained by Darwinian natural selection. Chomsky and Gould have suggested that language may have evolved as the by-product of selection for other abilities or as a consequence of as-yet unknown laws of growth and form. Others have argued that a biological specialization for grammar is incompatible with every ten...

Pipe Dreams: Eternal Recurrence and Simulacrum and Foucault's Ekphrasis of Magritte

Levelling an unknotting tunnel

It is a consequence of theorems of Gordon–Reid [4] and Thompson [8] that a tunnel number one knot, if put in thin position, will also be in bridge position. We show that in such a thin presentation, the tunnel can be made level so that it lies in a level sphere. This settles a question raised by Morimoto [6], who showed that the (now known) classification of unknotting tunnels for 2–bridge knot...

A Natural Prime-generating Recurrence

For the sequence defined by a(n) = a(n−1)+gcd(n, a(n−1)) with a(1) = 7 we prove that a(n) − a(n − 1) takes on only 1s and primes, making this recurrence a rare “naturally occurring” generator of primes. Toward a generalization of this result to an arbitrary initial condition, we also study the limiting behavior of a(n)/n and a transience property of the evolution.