Ian Stewart’s books have really caught my attention nowadays. After reading his book, " Letters to a Young Mathematician", I gulped "Nature’s Numbers". The book is all about seeing nature from a mathematician’s POV.
The book starts off with an introduction of nature and patterns. Patterns of form and Patterns of movement are so widespread in the nature that it is difficult not to observe them. Ripples in the pond, Stripes on Zebra tiger, movement of horses, elephants, mammals all happen based on a pattern. Patterns posses beauty as well as utility. If one were to study the patterns, it would be the best thing to leverage those patterns in our daily life applications. When such a complicated creature like Nature can work with a pattern, it is certain that Pattern would work for a less complex purpose driven application.
Patterns are basically numerical patterns, geometric patterns, and movement (translation, rotation, reflection) patterns. A mathematician’s instinct is to structure the process of understanding by seeking generalities that cut across various sub divisions.A lot of physics proceeded with out the any major advances in the mathematical world. For 200 years, calculus was in a different position. It was being used with great success in Physics But the mathematicians were really concerned about what it really meant. Thus there is a fundamental difference in the way of thinking of a mathematician. They tend to ask WHY rather than HOW. HOW related questions are left to domain experts, be it physicists , chemists, scientists etc Mathematicians concentrate on WHY and that opens a whole set of areas for people to work on HOWs. For example snail develops a spiral shell, mathematician will be interested in the ways a spiral is formed whereas how the snail makes the shell is matter of genetics / chemistry.
Is Mathematics about numbers, real , complex , functions, transformations, proofs, theorems etc..No , Math is about story telling. If you can take a natural phenomenon / application and can a tell an effective story using some tools, that is what Math is all about
There is a chapter titled "From Violins to Videos", which is a beautiful summarization of the events starting from the purposeless study of 1d strings on a violin to a very practical device tv. A lot of physicists and mathematicians played a role in cracking the 1d wave equation of a violin string. jean le rond d’alemert , euler, bernoulli all were instrumental in bringing about the solution for 1d waves. This was extended to the vibrations of the surface of the drum which is a 2d. Finally it showed up in the areas of Electricity and Magnetism. Michael Faraday and subsequently Maxwell came up with electromagnetic forces which was a giant leap in the advancement of scientific understanding. Visible electromagnetic waves with different frequencies produce different colors.
The book also deals with the pattern of movement. One complete chapter is dedicated to gait analysis where trot, pace, bound, walk, rotary, gallop, traverse gallop and canter is analyzed.
Chapter 8 titled – "Do Dice Play God ?" is my favorite chapter of the book. It starts off by introducing a concept called phase space which is nothing but a solution space that is obtained based on the initial conditions. The chapter’s main theme is that random movements at the microscopic level can result in deterministic movements at the macroscopic level. Also simple cause results in complex effects. One superb example that’s given to justify the theme is the half life period. One can never say that at an instant a particular atom will disintegrate or not, but one can always calculate half life period of an elements. So, one knows the half life of an elements, with out knowing which half will disintegrate..Its like the famous ad saying, I know my marketing ad budget gets me results but I do not know which half.
The last chapter is collection of 3 case studies – One , water from a tap , Two , a simulated artificial ecology example, and the final one is that of petals in various flowers. Each of the case studies is a gem that goes on tell that mathematical complexity results in simple patterns and it is well worth understanding mathematical complexity , for it is such study that creates a better understanding of nature’s patterns.
I am certain to read this book again at a later point of time