Ian Stewart's Nature's Numbers: The Unreal Reality of Mathematics (New York: Basic Books, 1995) is a book that lets us see nature from a mathematician's point of view, changing the way we view the world. The book begins off with an introduction of patterns that we can observe in nature. Numerical patterns, patterns of form, movements (translation, rotation, reflection) and shapes are so widespread in the nature that it is difficult not to notice them. Stripes on zebras and tigers, spots on leopards and hyenas, movement of stars across the sky, number of seeds in the head of a sunflower, the shape of a snowflake and even colored arcs of light adorn the sky in the form of rainbows all happen based on a pattern.
Ian Stewart also emphasizes that mathematics it's not with regards to numbers, however additionally concerning operations (also referred to as functions or transformations), concerning the logical relationships between facts, and concerning proof. He provides a decent example of the method of finding a symptom. There's additionally a motivating section on the "thingification of processes" as a basic mathematical operation.
Here it's created clear what a universal abstraction method this can be, not simply in arithmetic. Painting pictures, sculpting sculptures, and writing poems are valid and vital ways to express our feelings about the world and about ourselves. There is a little of all these instincts in all of us, and there is both good and bad in each instinct. The scientist's instinct is to try to understand it to work out what's really going on. The entrepreneur's instinct is to exploit the natural world. The mathematician's instinct is to structure that process of understanding by seeking generalities that cut across the obvious subdivisions. Communing with nature does all of us good: it reminds us of what we are.
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I enjoyed reading his book because it is truly interesting, informative and educational in a way that he presented and provided evident examples of mathematics in our nature and he writes with clarity and precision. We don't pay attention to those patterns but because I've read the book, I realized that it really exists and we just ignore them.
I have also learned that patterns of form and motion reveal deep regularities in the world around us specifically the sixfold symmetry of snowflakes which led Kepler to conjecture that all matter is composed of atoms; patterns of waves and dunes give clues to the laws of fluid flow; and tiger stripes and hyena spots give a key to understanding the processes of biological growth. It's like science and mathematics is connected in some ways.
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 how's. It was being used with great success in Physics but the mathematicians were really concerned about what it really meant. They tend to ask why rather than how. Thus, there is a fundamental difference in the way of thinking of a mathematician. A lot of physics proceeded without any major advances in the mathematical world. For 200 years, calculus was in a different position.
I'm not really fond of reading books with no pictures in it. But this book is an exception. I was amazed when I read Chapter 5. I had no idea that a simple violin string vibrating caused a chain of thinking and discoveries that lead to the birth of television. I didn't consider the thought that a simple vibration of a linear object may come up with the invention of something which is way different than that object.
A lot of physicists and mathematicians played a role in cracking the 1D wave equation of a violin string. Jean Le Rond d'Alembert, Leonhard Euler, Daniel Bernoulli were all instrumental in bringing about the solution for 1D wave.
This was extended to the vibrations of the surface of the drum which is 2D. Finally, it showed up in the areas of Electricity and Magnetism. Michael Faraday and subsequently Maxwell came up with electromagnetic forces which were a giant leap in the advancement of scientific understanding. Visible electromagnetic waves with different frequencies produce different colors.
But vibrations of a linear object are universal-they arise all over the place in one guise or another. It may come from a spider struggling in the spider web that led to the discovery of electromagnetic waves. The point is in order to have an epic discovery; it has to start with something simple. Mathematics reveals the simplicities of nature and allows us to generalize from simple examples to the complexities of the real world.
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