Jack Salem

The Salem Witch Project

The received view is that the grammar of meaning claims is descriptive. It is our purpose in what follows to deny this consensus.. . . We offer, instead, a radically normative position on meaning claims. That is, we do not content ourselves with the relatively common view that part of the pattern characterized in ascribing meanings is the structure of socially accepted norms of a society. Rathe...

Small Salem Numbers

Galois theory of Salem polynomials

Let f(x) 2 Z[x] be a monic irreducible reciprocal polynomial of degree 2d with roots r1, 1=r1, r2, 1=r2, . . . , rd, 1=rd. The corresponding trace polynomial g(x) of degree d is the polynomial whose roots are r1 +1=r1, . . . , rd +1=rd. If the Galois groups of f and g are Gf and Gg respectively, then Gg = Gf=N , where N is isomorphic to a subgroup of Cd 2 . In a naive sense, the generic case is...

Salem numbers of negative trace

We prove that, for all d ≥ 4, there are Salem numbers of degree 2d and trace −1, and that the number of such Salem numbers is d/ (log log d). As a consequence, it follows that the number of totally positive algebraic integers of degree d and trace 2d − 1 is also d/ (log log d).

Witchcraft or mycotoxin? The Salem witch trials.

BACKGROUND The Salem witchcraft trials of 1692 have been studied by many historians looking for the complex social, political, and psychological determinants behind the community-wide hysteria that led to a travesty of justice and the deaths of 20 innocent Puritans. Recently, ergot poisoning has been put forth by some as a previously unsuspected cause of the bizarre behaviors of the young adole...