Einstein's Heroes: Imagining the World through the Language of Mathematics

by Robyn Arianrhod

Overview

Imagine you are fluent in a magical language of prophecy, a language so powerful it can accurately describe things you cannot see or even imagine. Einstein's Heroes takes you on a journey of discovery about just such a miraculous language—the language of mathematics—one of humanity's most amazing accomplishments.
Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. Robyn Arianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a new and radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of the radio wave, teasing it out of the mathematical language itself.
Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.

Product Details

ISBN-13:	9780195308907
Publisher:	Oxford University Press
Publication date:	07/20/2006
Edition description:	New Edition
Pages:	336
Product dimensions:	5.38(w) x 7.90(h) x 0.61(d)

About the Author

Robyn Arianrhod is a writer and mathematician whose passion for both literature and mathematics reflects her love of language. She teaches mathematics at Monash University, where she is also an Honorary Research Associate.

Table of Contents

	A Seamless Intertwining	1
	A Reluctant Revolutionary	8
	Beetles, Strings and Sealing Wax	14
	The Nature of Physics	29
	The Language of Physics	42
	Why Newton Held the World in Thrall	51
	Rites of Passage	83
	A Fledgling Physicist	96
	Electromagnetic Controversy	104
	Mathematics as Language	130
	The Magical Synthesis of Algebra and Geometry	172
	Maxwell's Mathematical Language	195
	Maxwell's Rainbow	229
	Imagining the World with the Language of Mathematics: A Revolution in Physics	248
	Epilogue	274
	Appendix	282
	Notes and Sources	284
	Bibliography	307
	Index	316

Editorial Reviews

This deeply resonant book is about Albert Einstein's intellectual heroes: Sir Isaac Newton, Michael Faraday, and most especially James Clark Maxwell. As author Robyn Arianrhod argues brilliantly, Maxwell was the first physicist to embrace deliberately the ambiguous relationship between language and reality; the first to accept that in a very real sense, language is reality. Maxwell showed that the structure of mathematical language seems to reflect hidden physical patterns, thus setting the stage for counterintuitive insights into our universe.

Admirably sketching the battle lines currently staked out over the idea of objective truth, a Cambridge professor of philosophy makes his subject lively and accessible even as he parts some of its deepest waters, with absolutists-traditionalists-realists on the one side and relativists-postmodernists-idealists on the other. The absolutists believe in "plain, unvarnished objective fact"; the relativists say with Nietzsche, "There are no facts, only interpretations." Blackburn scrutinizes the claims of both sides with a collegial but critical eye, carefully distinguishing positions and identifying places where the two sides are speaking past each other, covering, among others, Protagoras, Plato, Hume, James, Nagel, Wittgenstein, Locke, Rorty and Davidson. He constructs a simple diagram that makes sense of four contrasting attitudes toward truth: eliminativism, realism, constructivism and quietism. Out of this inquiry emerges a middle position: truth is real if accepted in a minimalist way; relativism is not necessarily incoherent; and we can respond to science with "well-mannered animation" that is indistinguishable from belief. As Blackburn recognizes, this solution will not please everyone: absolutists may find it treasonous, relativists too conservative. But the overall result is to salvage a plausible version of truth. Blackburn considers truth "the most exciting and engaging issue in the whole of philosophy," and, with wit and erudition, he succeeds in proving that point. (Aug.) Copyright 2005 Reed Business Information.

Publishers Weekly

Dealing with physics history at several different levels, Australian mathematician Arianrhod offers an intriguing blend of science, history, and biography. Noting that the widely admired Albert Einstein had his own scientific heroes-Isaac Newton, Michael Faraday, and James Clerk Maxwell-she explains the reasons for the great physicist's esteem. She especially pays detailed attention to Maxwell and his famous set of four equations that summed up the essence of electricity and magnetism and revealed that light itself is an electromagnetic phenomenon. Using the marvelous eventual success of Maxwell's equations, the author then reflects on the uncanny usefulness of mathematics in building models of physical discoveries and in predicting physical facts not yet revealed by experiments. (E.P. Wigner, a great modern physicist, has referred to the "unreasonable effectiveness of mathematics in the natural sciences.") Arianrhod's well-written, fascinating discussion of intertwined topics not usually presented in one book aimed at general readers is highly recommended for academic and public libraries.-Jack W. Weigel, Ann Arbor, MI Copyright 2005 Reed Business Information.

Library Journal

"Arianrhod is an infectiously enthusiastic writer, keen for her audience both to admire Einstein's heroes and to understand their contributions to fundamental mathematical physics."—Physics Nature

"Arianrhod's achievement is to so masterfully combine history, biography, and mathematics as to absorb and enlighten even the mathematically maladroit."—Booklist

"A magnificent saga...well worth reading.... For those who are interested in scientific subjects but have no experience with math or physics, the author takes particular care to include simple descriptions and drawings to illustrate the ideas. Thus this really is a book for all who would like to know the essentials of a key part of modern science."—American Scientist

"An intriguing blend of science, history, and biography.... Arianrhod's well-written, fascinating discussion of intertwined topics not usually presented in one book aimed at general readers is highly recommended."—Library Journal (starred review)

"A thrilling story.... Arianrhod is an easy author to like, and not simply for the clarity of her narrative. She brings out the human side of the scientists. She also is a student of imaginative prose: Her explication of a novel by the Australian David Malouf helps introduce ideas about mathematics, and she quotes the poet William Blake to crystallize a thought about Maxwell.... Scientists' quest for knowledge is exhilarating to Arianrhod, and she conveys that to the reader."—bloombergnews.com

"Offers readers an engaging intellectual exercise combining physics, language, mathematics, and biography."—Science News

"On one level, Robyn Arianrhod's Einstein's Heroes is about the crowning achievement of classical physics—James Clerk Maxwell's understanding of electricity, magnetism, and light. But on another level, Arianrhod adeptly examines a much deeper idea: why is mathematics the language of nature and how do physicists tap the hidden power of numbers to understand the physical world? Einstein's Heroes does an admirable job of explaining the strange allure that mathematics holds over the scientists who so dramatically altered the way we look at the universe."—Charles Seife, author of Zero: The Biography of a Dangerous Idea

From the Publisher