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Alien Encounters - Introduction

Gavin Hitchcock
- A dramatization, in two Acts, of the struggles of European mathematicians of the seventeenth and eighteenth centuries to come to terms with the newly admitted negative numbers.


My objectives in this dramatization are mixed: the imperatives of the dramatist's art, of authentic historical reconstruction, of effective pedagogy, and of pure entertainment, exert a combined pull - often in conflicting directions. My solution is a personal one, but is guided by one over-riding aim: to combat the false and repellent stereotype of cut-and-dried mathematics, appearing suddenly out of nowhere, ready-made, to be force-fed to its victims. I want to expose the deceit of conceiving the mathematical art as a solitary, joyless, unexciting grinding of intellectual mills to pre-determined ends, by offering a glimpse of the mathematical community in colourful, fully human, engagement. By watching mathematics-in-the-making, and sharing something of the motivations and struggles of the trail-blazers, the student may come to appreciate more of the spirit of communal excitement, fellowship and adventure that is so much a feature of living, growing mathematics.

The underlying philosophy can be encapsulated as: ESSE is OPERARE, and OPERARE is COGNOSCERE. To be is to act, and to act is to know. Ideas (whether literary, mathematical, or anything else) once enacted become part of the actor-learner. Theatre is, then, a medium of communication that can reach the deepest levels of perception. By involving the whole person - engaging reason and imagination and the bodily senses together, a completely new quality of attention is commanded. In taking part in such a piece of theatre, or in being drawn into identifying with a gifted reader/actor, the learner shares something of the adventure of creation. Dialogue incorporates a reciprocity ("mutual contagion", give-and-take). This question-and-answer form is true to the universal human experience of learning and knowing as a process, a developing relationship beween a community of knowers and an evolving body of knowledge. Answers can only be appreciated when questions have previously been asked. Concepts and theories are born and shaped in response to challenge and crisis. For understanding ideas, as for understanding people, their stories and their ancestries are indispensable.

In theatre, bare, abstract mathematical ideas may be clothed with human emotions, activated by human desires, and set in their cultural and historical context, and so come to life that their story is seen to be part of the human story. In this way, mathophobic anxieties are lulled; brittle, reflex defences are softened; and learning is carried forward on waves of enjoyment, with humour playing its indispensable role as an entrée to the mind via the heart.

I have not done any systematic research on the specific cognitive effects of this particular play for classes of different ages and ability levels, but my experience of staging this and other mathematical plays, in whole or in part, indicates that the following at least can be expected of a High School group:

  • initial puzzlement at the unusual packaging of mathematics in a "fun" play context, and at basic mathematical ideas being contested at all;
  • astonishment (even disbelief) that great mathematicians should have struggled with these ideas;
  • much amusement if the dialogue is read/acted with appropriate spirit and passion;
  • a lightening of atmosphere and subsequent increased receptivity to mathematics in general;
  • a potentially liberating realization that mathematics is not divorced from the rest of human life, and that mathematical ideas too have passed through a period of growth and formation and are never grasped instantly, so that the learner is in good company in finding them difficult at first.

To hint at a fuller picture of mathematics-in-context, I have included in the play allusions to the theological and political storms of 17th and 18th century Europe, to nationalist factions, and to the explosive rise of science taking place on a wider stage, as well as to differing, deeply personal motives for doing mathematics. Learners with insufficient background may not appreciate the full import of these allusions, but I think that there is no harm, and much gain, in these gentle reminders of the continuity of mathematics with the wider contours of human life. A comment is in order on the inclusion of the (perhaps less engaging) classroom monologues in Act 2. It is naturally of interest that so much effort was invested in explanations and proofs concerning the negative numbers. But beyond this, I think that introducing these characters - the blind but famously good lecturer Saunderson, the aging Euler (also blind and naturally a little irascible at this time), the quintessentially French and politically adroit Laplace - helps to make the point that great teachers may have quite different styles and approaches, and that pedagogical fashions and standards do change. There is also the point that the gallery of mathematicians through history is peopled with wonderfully colourful and culturally diverse personalities.

Gavin Hitchcock , "Alien Encounters - Introduction," Convergence (May 2011)