By Michael Kinyon, Glen van Brummelen

This e-book brings jointly for the 1st time the Kenneth may possibly Lectures that got on the annual conferences of the Canadian Society for historical past and Philosophy of arithmetic. All contributions are of excessive scholarly worth, but obtainable to an viewers with a variety of pursuits. they supply a historian’s standpoint on mathematical advancements and take care of quite a few themes overlaying Greek utilized arithmetic, the math and technology of Leonhard Euler, mathematical modeling and phenomena in historic astronomy, Turing and the origins of man-made intelligence to call just a couple of.

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Finally, the epicyclic sphere rotates, carrying embedded close to its surface the moon M itself, producing the primary anomaly. This physical model is wholly consistent with the Almagest model, except that Ptolemy abandons the special radius with respect to which the moon’s regular revolution on the epicycle is reckoned, instead stipulating that the moon’s revolution is uniform relative to the radius from the centre of the cosmos. At the beginning of the Planetary Hypotheses, Ptolemy writes that the models as set out in this work incorporate some revisions to the Almagest models based on newer analysis of observations, but also that he is making some minor simpliﬁcations purely for the sake of an easier construction of demonstration models; one is left uncertain which kind of change is being made here in the lunar model.

Et Corr. 336b16) Aristotle’s cosmology thus explains why we can have a mathematical astronomy. It does not, however, account for the possibility of mathematical sciences dealing with special aspects of the world of the four elements, although Aristotle recognized that possibility, since he classiﬁed optics and harmonics, along with astronomy, as sciences embedding mathematics, or indeed as branches of mathematics (Physics 194a6). Here and there in the Aristotelian corpus we encounter obiter dicta conﬁrming that Aristotle recognized that mundane phenomena could be subject to mathematical constraints, for example in the following passage where he speculates on a possible analogy between harmonic theory and colour theory: 2 Ptolemy’s Mathematical Models and their Meaning 25 We have to discuss the other colours [besides white and black], distinguishing the number of ways that they can arise.

But his works were well enough appreciated, in spite of their severe style and uncompromising technicality, so that the great part of them were preserved, almost the sole remnants of their kind of scientiﬁc writing from antiquity. Though ranging widely in subject matter, these books revolve around two great themes: mathematical modelling of phenomena, and methods of visual representation of physical reality. In the following, I wish to consider what Ptolemy thought the relationship was between his models and the physical nature that he was describing.