This article seeks to show that the role of experience in Descartes’ philosophy cannot be considered independently of his claims on pure intellectual knowledge. First, as a brief introduction, some passages of Descartes’ works, which highlight the importance of experimentation, will be reviewed. Then, the role of ‘common experience’ and sensation in Cartesian scientific explanation is shown. Fi...

A Descartes configuration is a set of four mutually tangent circles in the Riemann sphere, having disjoint interiors. Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. Part I shoewed there is a natural group action on Desc...

We give a new, elementary, purely analytical development of Descartes’ theorem that a smooth connected surface is a perfect focusing lens if and only if it is a connected subset of the ovoid obtained by revolving a cartesian oval around its axis of symmetry.

n t odern healthcare operates under the banner of “evidencebased” medicine. The pursuit of such evidence, however, is ot exclusively driven by need, but by the vailability of funds, which in turn deends partly on the likelihood of profit. ore portentously, the pursuit of data is ounded by the prevailing conceptions of iological plausibility. This essay makes he case that such borders are not re...

The first half of the 20th Century was filled with a stunning group of scientists, Einstein, Bohr, von Neumann and others. Alan Turing ranks near the top of this group. I am honored to write in this Centennial Volume commemorating his work. How much do we owe one mind? His was a pivotal role in cracking the Nazi war code that profoundly aided the defeat of Nazism. His invention of the Turing ma...

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Collins und Akritas (1976) have described the Descartes method for isolating the real roots of an integer polynomial in one variable. This method recursively subdivides an initial interval until Descartes’ Rule of Signs indicates that all roots have been isolated. The partial converse of Descartes’ Rule by Obreshkoff (1952) in conjunction with the bound of Mahler (1964) and Davenport (1985) lea...

Descartes's distinction between material and thinking substance gives rise to a question both about our knowledge of the external world and about our knowledge of another mind. Descartes says surprinsingly little about this second question. In the Second Meditation he writes of our (single) judgement that the figures outside his window are men and not automatic machines. It is argued in this pa...

Let L be any number field or p-adic field and consider F := (f1, . . . , fk) where fi∈L[x 1 , . . . , x±1 n ]\{0} for all i and there are exactly μ distinct exponent vectors appearing in f1, . . . , fk. We prove that F has no more than 1+ ( ln(μ− n+ 1)min{1,n−1}(μ− n)2 log μ )n geometrically isolated roots in Ln, where l is an explicit and effectively computable constant depending only on L. Th...

Sue Savage-Rumbaugh and her co-authors have written a densely argued book about one of the most fascinating topics in semiotics “How do we recognize the presence of language?”. This encompasses ‘What is Language? What is its function? and where does it come from in terms of mentation?’. The major study subject of this book, Apes Language and the Human Mind, is a Bonobo named Kanzi who is widely...