Descartes' Contributions to Optics

Baroque Optics and the Disappearance of the Observer: From Kepler’s Optics to Descartes’ Doubt

Dualism: from Descartes and Bacon to AJNR.

T he Oxford English Dictionary defines duality as " an opposition or contrast between two concepts or aspects. " 1 In the American Journal of Neuroradiology (AJNR), I see these aspects reflected in the nature of our articles, which are either basic research or clinically oriented. Basic research articles tend to be multiauthored, hypothesis-driven, and thus prospective, blinded, and controlled,...

The Descartes Rule of Sweeps and the Descartes Signature

The Descartes Rule of Signs, which establishes a bound on the number of positive roots of a polynomial with real coefficients, is extended to polynomials with complex coefficients. The extension is modified to bound the number of complex roots in a given direction on the complex plane, giving rise to the Descartes Signature of a polynomial. The search for the roots of a polynomial is sometimes ...

Arithmetic Multivariate Descartes' Rule Arithmetic Multivariate Descartes' Rule

Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x ±1 1 , . . . , x ±1 n ]\{0} for all i and there are exactlym distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( σm(m− 1)2n2 logm )n geometrically isolated roots in Ln, where σ is an explicit and effectively computable constant depending only on L. This gives a sign...

Philosophy and memory traces: Descartes to connectionism

his limitations. Yet, the malaria problem would prove to be a task worthy of Ross's relentless search for approval. Quite apart from being a stubborn obstacle to British colonialism in India and elsewhere, the plasmodia had become an international phenomenon. It offered Ross a stage for recognition. It also brought Ross and Manson together. While on furlough in the spring of 1894, Ross solicite...