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A philosophical journey through some classical equations,
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This review is from: A Brief Guide to the Great Equations (Paperback)
The Great Equations: The hunt for cosmic beauty in numbers, by Robert C. Crease, W.W. Norton, New York, 2008; Constable & Robinson, London, 2009, 318 ff.
A philosophical journey through some classical equations
By Howard Jones
The author of this fascinating book is Professor and Chairman of the Department of Philosophy at Stony Brook University in New York, a man who has written many other books and articles. The book is about the journeys that we make in our increasing understanding of the world through the mathematical equations that represent some of the fundamental laws of physics . . . and therefore the laws of Nature. Crease makes the point that science is about the search for greater understanding of the way the universe works and that the equations are simply beautiful, but shorthand, expressions for some of the regularities we find.
The presentation begins, perhaps unsurprisingly, with the relation we know from high school as Pythagoras' Theorem, though how much Pythagoras himself had to do with it we don't know. There's an interesting philosophical aside in this first chapter about Meno's Paradox on the nature of learning, which Plato presented in one of his dialogues. This is intended as an allegory of the utility of mathematics. Each chapter is followed by an Interlude that gives additional commentary on the preceding chapter.
Chapter 2 takes us into physics with Newton's Second Law of Motion that defined the concepts of force, acceleration, and this strange quantity `mass' and gives us the relation between them. Newton was the first to introduce the ideas of `force' and `mass'. This treatment is followed by Newton's Law of Gravitation that illustrates the force that keeps the planets in orbit around the sun.
It may seem a strange thing to say about a book about equations but there is very little maths in this book at all, and certainly none that should deter readers. However, in Chapter 4 we do meet the first equation that we could describe as more advanced mathematics, and that is Euler's Equation. This concerns a relation between the base of natural logarithms (denoted by `e'), the unit of imaginary numbers (denoted by `i'), and the ratio of the perimeter to the diameter of a circle (denoted by pi), all symbolic notations that Euler created or standardized.
And so on in the remaining chapters, through the Second Law of Thermodynamics, Maxwell's Equations for Electromagnetism (these do look a bit scary, but the explanation in the chapter is easy to follow), Einstein's Mass-Energy and Relativity Equations, and Heisenberg and Schrödinger's basic equations of quantum physics (again, a bit challenging, but lucidly explained). Crease also brings their authors to life!
This book is accessible to anyone who has a curiosity about the fundamental relationships of physics and how these relations are expressed symbolically. It is 99% prose and 1% mathematics, so don't let a few symbols intimidate you! The description of each relation is both enlightening and intriguing. And if the background to each equation in each chapter is still not enough for you, there are 26 pages of Notes at the end of the book.
Dr Howard A. Jones is the author of The Thoughtful Guide to God (O Books, 2006), The Tao of Holism (O Books, 2008) and The World As Spirit (Fairhill Publishing, 2011)
Looking Glass Universe: The Emerging Science of Wholeness
The Arrow of Time: The Quest to Solve Science's Greatest Mysteries (Flamingo)
The Man Who Changed Everything: The Life of James Clerk Maxwell
Physics and Philosophy: The Revolution in Modern Science (Penguin Modern Classics)