Mathematics 5
Winter Term 2000
The World According to Mathematics

Dwight Lahr and Josh Laison

Weekly Schedule: Week #1

Readings:

Lahr's manuscript—From the beginning through 1.2

Exercises:

Due Friday 1/7

•Exercises 1.1: 1-4 and 1.2: 1-7

Friday discussion:

The discussion will center around the following quote, as well as the homework
from Lahr's manuscript. In particular:

•In the Measure of Realityby Alfred W. Crosby (Cambridge, 1997), the
author discusses the shift from qualitative to quantitative descriptions of
reality in the late Middle Ages and Renaissance. He says (p. 228):

In practical terms, the new approach was simply this: reduce what you are trying
to think about to the minimum required by its definition; visualize it on paper, or at
least in your mind, be it the fluctuation of wool prices ... or the course of Mars
through the heavens, and divide it, either in fact or in imagination, into equal quanta.
Then you can measure it, that is, count the quanta.
Then you possess a quantitative representation of your subject that is, however
simplified, even in its errors and omissions, precise. You can think about it
rigorously. You can manipulate it and experiment with it....
Visualization and quantification: together they snap the padlock—reality is
fettered (at least tightly enough and for long enough to get some work out of it...).

Think about the above description and critique it in light of how well it
applies to today's world. Do you think that all of reality can be fettered
according to the above approach? From your own experience, can you
identify a field that takes a very different approach to gaining understanding
through knowledge? Are you clear in your own mind about what constitutes
reality? [Crosby says on p. 23: Reality[is] a word I will use to mean
everything material within time and space, plus these two dimensions per se.]