1. Domains of Knowledge:
The nature of Science, Art and MathematicsUntil the past few decades, knowledge was formally divided into two domains: the arts and the sciences. University degrees came for the most part in only two flavours. The proliferation of "boutique degrees" is a relatively recent phenomenon, linked to an increasingly utilitarian view of education: undergraduate degrees now have become far more specialised, increasingly vocational: Bachelors of Education, Design, Economics, even Bachelors of Multimedia.
But let us, for a moment, ponder the traditional division of human knowledge into the arts and the sciences. What defines each, and where to place mathematics?
I propose that the sciences may essentially be viewed as starting in the real world and ending in the mind. What we do in science is to observe aspects of reality and theorise about these: formulate ideas, ponder commonalities and hypothesise. We then test these hypotheses and formulate theories.
Sciences Reality => Mind Art, on the other hand, may be viewed as beginning in the mind and ending in reality. The artist – sculptor, musician, painter – begins with an idea, an inspiration and then in some tangible way makes it real. Art that does not take some physical form is not art.
Art Mind => Reality Mathematics occupies an unique central position, sharing elements of each but occupying the same ground as neither. Mathematics begins and ends in the mind, but frequently digresses through the real world. Mathematics has no need of the real world (unlike science, which depends on reality to justify its existence). And yet mathematics describes the real world surprisingly well. To mathematicians, however, it matters not whether we work within three dimensions or seventeen. Mathematics does not just describe and explain the real world: it describes and explains all possible worlds.
Mathematics Mind => Mind
Mind => Reality => Mind At its core, science exists to explain and understand the world around us. Mathematics, on the other hand, provides a means and a language which supports and enhances these observations; at its heart, however, mathematics is best thought of as a search for patterns and relationships. To DO science is to observe, describe and seek to explain reality and, in so doing, to be able to predict and act with intention; to DO mathematics is to look for regularities, to observe and understand patterns and so support such prediction.
In this sense, then, science, art and mathematics complement each other well with mathematics, if anything, providing a bridge between these two domains of knowledge. Although fundamentally different, science and mathematics are far from incompatible and so the prospect of integration remains possible. Which is the more creative pursuit? I leave that to others to argue!
For comments & suggestions, please e-mail Steve Arnold.