04e MATHEMATICS

Mathematics probably had multiple origins. The money math in early economics may have been independently created from the mathematics of early geometry and the recording of movements in the sky. I have not researched this in any detail.

The “full nature” of “mathematics” remains emergent, in spite of the extensive commentary over the ages. The precision-of-fit in material reality, e.g., fixed ratios (before numerical quantification), were used (if not consciously discoursed about) in everyday life. Mathematics emerged as a means to represent, and thus communicate, this precision (also useful for technological development – tool making).

For math phobic students in a Community College I created a course, LEARNING TO LEARN AND LOVE MATH. It worked!  I presented math as a family of concrete languages. There is NO ABSTRACTION in math. Math has a concrete visual foundation – symbols (with well defined shapes) in very specific arrangement on a two dimensional surface.  Or lines and curves in a space.  Everything is concrete, visible, explicit, and manipulable. Mathematicians can often imagine these patterns in their visual imagery, and don’t have to write them all down. Some can use their subconscious minds to infer the result of transFORMation sequences between concrete math forms. ALL mathematics reduces to (potentially) concrete, perceivable, and manipulable FORMS.

The utility of these concrete math languages is to describe abstractions, to bring abstract concepts into perceptual reality. Unfortunately, math departments – who gain their prestige from their claimed elevated abstraction – eventually blocked my teaching this successful course.

Representing observed natural phenomena (and later artificially constructed laboratory phenomena) in concrete, visible, manipulable math languages gave rise to PRECISION thinking – an essential tool for the future survival of humankind and Gaia.