6. Mathematics Overview

The video lecture is incomplete this week due to exceeded space on my iPad (Sorry!).  Refer to the overview below:

This week we began an introduction into Mathematics as an Area of Knowing.

5 simple objectives:

1. Math as "future knowing"?
2. Math as History of Thought.
3. Math as a challenge of certainty.
4. Math as a Process
5. Math as Cultural Purpose


Summary of Lecture.  Students completed the following:

1. A magic trick connected to the perceived certainty of mathematical theorems.  All our numbers, no matter the choice, converged into a single result.  We compared this type of "future knowing" with the study of probability, using Nate Silver as a contemporary example.

2. We compared the philosophy of mathematics from Newton, Leibnitz, and Kant, asking the question "how might math give us knowledge of the "thing in itself" beyond normal empirical observation?" Kant believed that Math was, in fact, a logical and synthetic (both rational, and really in the world) type of knowledge.

3. We challenged the assertions with a brief discussion of special relativity.  Einstein change the "certainty" of mathematics by proving the existence of time and space as contingent on perspective, gravity and relative space between objects.

4. We looked at how various theorems (a set of axioms creating a formula about the world) can be proven by coherence, exhaustion (computer programs, probability, etc.). While no theorem can be philosophically certain, we described how Math attains a higher level of consistency than other areas of knowing.

5.  Lastly, we very briefly talked about the purpose of math.  We looked at mathematical proofs, learning, and utility across three cultures.  How might this be related to the objectivity of math considering the different needs of society?

Next week, we will discuss your readings and argue it out topic (climate change), as well as have a little fun and competition using mathematical probability and the Monty Hall problem.  We will also continue our question of math's discovery vs. creation by contemplating its use as a principle of Art and Music.

I found this excellent 1 minute recap of special relativity for those who need clarification: