Thursday, February 13, 2014

Mathematical beauty

A recent paper in the Frontiers in Human Neuroscience journal shows that the region of the brain – medial orbito-frontal cortex – is uniformly involved in the assessment of beauty, whether it is in art, music or mathematics. In a study where mathematicians rated formulae on a beauty scale, their brain activity seem to correlate with such assessments in other pursuits, including art and music. This fundamental and universal neuro-biological basis to beauty, possibly points to humans seeking elegance in abstract constructs and equating such a notion to beauty. Humans appear to generally crave for mathematical elegance, perhaps because elegance takes the least amount of energy to understand, imagine and internalize. Elegance, thus, is the most energy efficient sensation – something that is intuitively pleasing and inherently memory-forming – characteristics that are wrapped into a more complex construct of beauty. In this context, perhaps beauty can be measured by the overall entropy of sensation – lower entropy indicating higher beauty.

In a world, mired in complexity, nearly every field is rushing to higher order solutions to marginal problems. In the process, they create truly ugly solutions, creating chaos but not much else. In business, collecting big noise and crunching them with big computers in anticipation of insights is ugly. In Physics, nurturing the particle zoo and constructing heavy steel to smash particles in anticipation of the validation of the stated hypothesis is ugly. In medicine, mass manufacturing of the same dose pills and shoving them down the throats of willing patients is ugly. In economics, the complex dance between monetary and fiscal policies, fine tuning in anticipation of growth and inflation is ugly. In politics, the bureaucratic friction among the institutions of yesteryear that would not allow effective modern policies is ugly.

Elegance is beauty. Complexity is ugly.