Nature is lazy and will seek out the most efficient way to do something. It is the job of mathematics (or “maths” as the British say) to search for and recognize nature’s patterns and put them to use.
The Story of Math Collection consists of 5 DVDs containing 10 episodes produced as a documentary by the BBC. The episodes are narrated by British mathematician Marcus du Sautoy. Total run time is about 8 hours.
The first part of the collection, “The Story of Math” takes us (in four episodes) on a journey to examine how the ancient Egyptians, Babylonians, and Greeks developed mathematical concepts, both as a philosophic exercise and for some practical reasons. After all, bureaucrats had to figure out the area of odd pieces of land in order to tax them. And, in order to easily count things and do calculations, one had to have an efficient system of numbers. The journey continues through China, India (where the very important concept of zero was developed), Arabia, and back to Europe. We see the development of algebra, geometry, trigonometry and calculus. The last episode explores celestial mechanics and the concept of infinity.
“The Story of Math” contains a bonus disc, “The Music of the Primes” (two episodes) which examines prime numbers (numbers divisible by only themselves and 1). Prime numbers seem to be related to many natural phenomena. Bernhard Riemann proposed a hypothesis that seems to explain the distribution of prime numbers but he could never prove it. The Clay Mathematics Institute still offers a $1 million prize to someone who can prove the Riemann hypothesis.
Most interesting to me was “The Code” (in four episodes) which explores patterns in nature and why certain numbers keep cropping up. These episodes deal with a variety of subjects such as Pi, the ratio of a circle’s diameter to it’s circumference, fractals in nature and in Jackson Pollack’s art, laws of motion, and some strange relationships.
For example, we find some musical chords pleasing because of the ratio of frequencies between notes. These same ratios are used in architectural design to make structures with proportions pleasing to the eye.
Cicadas are insects that hibernate for very long times. One species comes out every 13 years while another species comes out every 17 years (both prime numbers). Why? Possibly to avoid predators; the great swarm makes it impossible for predators to eat them all and most predators can’t wait around that long. Another reason is to avoid interbreeding. The 13-year cycle and 17- year cycle would coincide once every 221 years.
Why do the wax honeycombs of bees have hexagonal chambers? The hexagon is the most efficient shape and uses the least amount of wax. Economy of material is also why a basalt flow in Ireland, the Giant’s Causeway, cooled and contracted into hexagonal columns.
The collection takes you on a journey of the mind and on a travelogue around the world. It is entertaining and thought provoking.