The Long and Short of Dr. Manjul Bhargava
A while ago Princeton University Professor and Field Medal winner Dr. Manjul Bhargava gave an enthralling lecture at the Madras Music Academy on the relation between mathematics and music. This presentation revolved around the rhythms of ancient Indian poetry, music and the math behind them as expounded in various treatises such as the Nātyashāstra and the Sangeetha Ratnakara. He explained how even fundamental concepts in math could be understood in terms of poetry and rhythm thus demonstrating that the subtle yet vital connection between the poetry, the performing arts and mathematics.
At the start of the lecture, Dr. Bhargava posed the following question:
What are the possible ways you could fill up 8 beats with a combination of short (1 beat) and long syllables (2 beats)?
Here are some valid possibilities, n being the number of beats:
n= 1: 1
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