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 MacLane 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 SpringerVerlag, (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.