Everything is a number, but what is a number? Philolaus and Pythagoreans

When
Start: 09/22/2010 - 4:15pm
End  : 09/22/2010 - 5:15pm

Category
Colloquium

Speaker
Richard McKirahan Pomona College

Abstract

In this talk we discuss the successes, failures and limitations of early Pythagorean (6th and 5th centuries BCE) mathematics and the little known contributions of Philolaus (4th century BCE). The early Pythgoreans made important contributions in geometry, number theory and the concept of mathematical proofs, but like other Greek thinkers of their time they carried their ideas to excess. For example, their discovery of the numerical basis of the basic musical intervals prompted the generalization that all things are (positive whole) numbers, which led to a wild goose chase of an attempt to identify particular numbers with particular things. Nevertheless the interest in numbers and their relation to the world and particularly to harmonics persisted and not only in Pythagorean circles. In the fourth century, Philolaus revived and updated the old Pythagorean idea that numbers are basic to things, expanding the notion of number to include ratios of numbers (which are di fferent from fractions) and using the old example of the basic musical intervals in new ways to justify his broadened conception of number.

Where
Millikan 134, Pomona College

Misc. Information

Refreshments served at 3:45 p.m.
Harry Mullikin Room, Millikan 209
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The dinner will be hosted by Prof. Judith Grabiner
If interested in attending, call ext. 73160