Beauty, the Human, and Mathematics: Elements of a Case for Homo Maestheticus William Higginson Faculty of Education Queen's University at Kingston higginsw@educ. queensu. ca
Being - I: Outline Notes, and II: References and Related Reading, for a presentation at the Third International Conference on Ethnomathematics Cultural Connections and Mathematical Manipulations University of Auckland 2006 02 16 1030 - 1115 This file is a Powerpoint version of a handout given to session attendees. A ‘paper’ version will, deo volente, appear on the conference website.
I: Outline Notes Preliminary comments: phatic and emphatic Assumptions (ANW) Professorial purpose Caveats Analogies with Music and Medicine Summary
Differences and Similarities A Plea for Balance and Plurality The Homo 'X' Game The 'monocularity' of contemporary mathematics - 3 images Nelson, Cyclops, and the Kingdom of the Blind Mathematicians as the ultimate ethnomathematical research challenge
'TIRED' mathematics education Nardi, East Anglia - "Tedium, Isolation, Rote learning, Elitism and Depersonalisation" Jules Henry The ebb and flow of Nature/Nurture. The promise and perils of ethnomathematics.
Ellen Dissanayake on Homo Aestheticus and making special. Saunders Mac. Lane on the roots of mathematics. Evolutionary aesthetics, human predispositions and the roots of mathematics. Folding, Fitting and Balancing [Weaving, Knitting, Braiding …. ]
Examples - Manipulations (Cultural and Mathematical) on Squares & Rectangles Questions and Discussion.
II: References and Related Reading For reasons of space and time minimal detail is given in the following list. Almost all names/titles can be explored using the multifold tools available on the World Wide Web. General recommendations include Google, Google Scholar, Amazon. com, and abe (the Advanced Book Exchange).
Maesthetics: The literature on maesthetics, per se, is tiny. In Creative Mathematics: Exploring Children's Understanding (Routledge, 1997) I (with my coauthors Rena Upitis and Eileen Phillips) explored a number of closely related ideas, in particular, the idea of constructive aesthetics [the making of personally meaningful artifacts] as a pedagogic methodology in a primary mathematics class. An edited collection (with Nathalie Sinclair and David Pimm) Mathematics and the Aesthetic is scheduled to appear June of 2006 from Springer. Verlag, (see http: //www. springer. com/sgw/cda/frontpage/0, 11855, 4 -10042 -72 -105287180 -0, 00. html ). A revised version of Sinclair's (Mathematics, Michigan State) doctoral dissertation Mindful of Beauty (Queen's, Education, 2002) will be published by Teachers College Press in 2006. Dr. Sinclair has pointers to a number of significant papers at her MSU web site.
The Ethnomathematical Canon: The list of books and papers published over the past three decades on ethnomathematical themes is impressive. Primus inter pares are two scholars whose work is of particular importance to this meeting, Claudia Zaslavsky and Ubiratan D'Ambrosio. Other contributors to any comprehensive collection of texts in this field would need to include: Martha Ascher, Alan Bishop, Ron Eglash, George Joseph and Paulus Gerdus. From a more general perspective I find the work of Jared Diamond (Guns, Germs and Steel, and Collapse) to be of particular significance.
The Nature-Nurture pendulum has swung hard toward Nature in recent decades. Philosophers and scientists contributing to this shifted perception include E. O. Wilson, Stephen Pinker, Daniel Dennett and Richard Dawkins. Modest claims for embodied mathematical abilities have been advanced by Brian Butterworth, Stanislas Daehane and Keith Devlin with varying degrees of rigour. George Lakoff and Rafael Nunez's more ambitious Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being has rattled a number of mathematical cages. Ellen Dissanayake's three books fall into the general (recently rejuvenated) field of evolutionary aesthetics. Another stimulating thinker in this field is Christchurch University's Dennis Dutton.
Mathematicians have not often been known for their social and introspective skills (note the very popular Hollywood productions of Proof and A Beautiful Mind and their concomitant stereotypes) and these inabilities carry over in almost all cases to rather naïve views on the social impact of their discipline. Outstanding exceptions to this general rule are Philip Davis and Reuben Hersh (most recently with his Unconventional Essays collection) and the activities of the Bridges and Friends of Thales groups. The recent work of David Corfield (Philosophy of Real Mathematics) is a refreshing break from the aridity of classical philosophy of mathematics texts. Many outstanding mathematicians have, however, acknowledged the centrality of aesthetic principles to their scholarly functioning. Penrose, Coxeter and Conway are examples of this phenomenon.
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