As Galileo has famously said, "Mathematics is the language with which God has written the universe."
In a recent book, The Mathematical Mechanic, Mark Levi - professor of mathematics at Pennsylvania State University - has surprised the reader by undercutting Galileo's maxim. The book is a collection of mathematical theorems validated by means of thought experiments and physical reasoning. For example, he gave several explanations based on physical laws that justified the Pythagorean Theorem; the most stunning of which was a simple fact that the kinetic energy of an object is proportional to the square of that object's speed. Mathematical theorems are known to have a tendency to reappear in unexpected places - mathematical fields to which the theorems had originally no relevance. That many a theorem had an underlying physical phenomena to explain their validity, came through as a stunning revelation.
Now Mark Levi came up with a second book, Why Cats Land on Their Feet where, at first sight, he does right by Galileo setting up mathematics as a mechanism to describe physical phenomena and as a tool to help solve physical problems.
But what problems! The new book is a collection of physical puzzlers, often with counter intuitive manifestations, which, for all that, admit rigorous explanation supported by physical intuition.
Say, you are in a spacecraft orbiting a planet. You turn your jets on for a short while to propel the ship forward. Will it now go faster?
In another experiment, is it possible to turn an open jar half-full with molasses upside-down without spilling the contents?
And, of course, their is the question of cats landing on their feet. How do they do that? How do they manage to circumvent the conservation law of the angular momentum?
Both books are hugely entertaining and provide hours of brainy activities. But there may be an extra message that parents of young children should try to absorb. In both books, Levi credits his father with fostering his interest in physical puzzles and the interplay between physics and mathematics. Levi's father encouraged him to document his discoveries, and, by doing that, helped him develop his natural curiosity and sharpen his power of observation. Many of the puzzles are the author's invention; some have occurred to him while he was doing the dishes ...
It is often said that "mathematics is all around us"; naturally so is physics. You may pass by and miss the excitement, or you can sharpen your focus on what is going around and, perhaps, notice how it all (or a part of it) works. Besides offering practical and thought experiments that would test one's intuition and knowledge of basic physical laws, the latest book entices the reader to keep eyes and mind open - this may become a worthy habit too.
- M. Levi, The Mathematical Mechanic: Using Physical Reasoning to Solve Problems, Princeton University Press, 2009
- M. Levi, Why Cats Land on Their Feet and 76 Other Physical Paradoxes and Puzzles, Princeton University Press, 2012