Today's common conception that the worlds of art and science exist in two non-intersecting realms with wildly different expertise and orientation is fairly recent and rather puzzling to anyone with experience with either field.

Perhaps this notion is merely a reflection of our highly specialized age which tends to preclude the appearance of people with wide-ranging abilities. Or perhaps we have been unduly influenced by Nobel Laureate Roger Sperry's research in the 1960s which demonstrated a profound distinction between the left and right sides of the brain.

Most neuroscientists now believe the stereotype of the coldly logical mathematical and analytic left brain versus the imaginative, emotional and "synthetic" right brain is naïve and inappropriate.

The prevailing view of modern scholarship is that the distinction between the two hemispheres is more justly attributed to processing style, with all mental faculties shared across the brain.

Yet popular conceptions of science die hard, particularly when they are buttressed by an enormous number of self-help books placating math-phobes by explaining that their difficulties with times tables are linked to their inherent right brain dominance, while urging logic puzzle aficionados to "get in touch with their creative side."

The strangest thing about this view is not its simplicity or occasional self-servingness, but that it flies in the face of recorded experience. From Aristotle to Einstein, from Leibnitz to Pascal, history is littered with examples of outstanding intellects with wide-ranging interests who made fundamental contributions across the spectrum of the sciences and humanities.

Among the greatest examples of this conflation of interests is the history of equal temperament in music, popularized in a recent bestselling book by pianist and composer Stuart Isacoff.

Isacoff traces the story back to Pythagoras in the sixth century BC, who was the first to develop a mathematical understanding of musical harmonies. He recognized that the sounds most pleasing to our ear (octaves, fifths, fourths) could be expressed by mathematical relationships between the lengths of the vibrating strings.

This link between the previously disparate worlds of mathematics and music became the bedrock of Pythagoras' world view and, through its effect on Plato, laid the foundation for an approach to science and mathematics that was to profoundly influence the development of the entire Western rationalist tradition.

But that's another story. The temperament story is based on a more concrete question: how can you keep an instrument -- particularly a fixed string instrument like a keyboard -- in perfect tune based on these golden ratios? For although starting from one note and going up by consecutive perfect fifths (12 times) should result, at the end of the day, in the same note that is obtained by raising the same note by seven series of octave, it doesn't. It's close, but not precisely the same -- and this notion of different scales caused by two different choices of a fundamental interval only gets considerably more complicated when one introduces other harmonious intervals (such as major thirds, minor thirds, sixths).

The beauty of this perplexing discovery is that the issue has a clear mathematical underpinning: since octaves are based on multiples of two (2:1 string length ratio) and fifths are based on multiples of three (3:2 string length ratio), there is naturally no way for powers of two to give precisely the same answer as powers of three, since they are both prime numbers.

The only way to ensure that the notes will be coherent throughout a fixed structure is to make tiny adjustments to all the ratios other than one fundamental scale (typically the octave) by establishing 12 perfectly equal tones -- hence "equal temperament." This keeps the tuning coherent throughout the instrument, but a significant price is paid: intervals such as previously "perfect" fifths no longer remain in 3:2 ratios and hence, to the well-trained ear, lose much of their lustre.

The great struggle to create appropriate temperament (Isacoff emphasizes that although equal temperament has mostly won the day, some prefer other systems) involved a litany of intellectual luminaries of the arts and sciences throughout the ages: Da Vinci, Descartes, Kepler, Voltaire, Newton, Rousseau, Diderot.

The list reads like a who's who of human intellectual accomplishment unconstrained by any arbitrary categorization of disciplines.

And that is really the point: interesting questions attract intelligent and dynamic people to solve them. Period.