Scientific Studies of Magic Squares

While magic squares are recreational in grade school, they may be treated somewhat more seriously in linear algebra courses. The smallest and earliest is the ancient Chinese 3×3 Lo-shu magic square of the num-bers 1..9, which has a magic line constant of 15 for rows, column, and diagonals. This square motif appears in the same time frame as yin-yang schema (I Ching, Feng Shui) in early Chinese cosmology and philosophy. Over the past few years I have made several novel contributions, often through work with undergraduate summer students, finding pandiagonal non-magic squares, turning the compounding method into a computer code to produce the world’s largest magic square, obtaining theorems for the moment of inertia and electric quadrupole tensors, and Monte Carlo estimates of populations of these squares. I will show very fruitful interdis-ciplinary interactions between mathematics, computing (digital design), physics (mechanics and electricity) and philosophy (Carl Jung’s depth psychology).