Number-Crunching

PRESENT DAY
In the Introduction I mentioned that we will often use a computer in this book. Indeed, modern computer software is a powerful tool for mathematical physicists, and in this first chapter I want to give you a simple illustration of this.(I have strong personal views on the usefulness of computers in society in general, and not just as a tool for mathematical physicists. In Chapter 8 of this book are illustrations of some of those views using the device of short fictional stories published more than thirty years ago.) As the epigraph to this chapter suggests, my example involves both Feynman and the famous Last Theorem of Fermat. Now, I also told you in the Introduction that physicist Feynman was a highly skilled mathematician, and to illustrate that claim, let us consider the following amusing tale.

Every year the best college undergraduate math students in America compete (as multiperson teams representing each participating school) in a national test called the Putnam Exam. In addition to naming the top school teams, the five top scoring individuals are awarded the title of Putnam Fellow. The Putnam Exam is very difficult, with a median individual score in some years being 1 (yes, one) out of a possible 120. That means an awful lot of people get zeros!

The Putnam was in its second year of existence when Feynman was a senior physics major at MIT in 1938–39. When the MIT math department discovered, to its horror, that it didn’t have enough good math majors to complete its team, the department turned in desperation to Feynman (who, you won’t be surprised to learn, already had a reputation). Happy to help, Feynman joined the team and took the exam (indeed, he turned his paper in before the allowed time was up)—and was soon after named a Putnam Fellow. (The MIT team placed second, behind Brooklyn College, and it’s clear that Feynman did his part.) The math people at Harvard were sufficiently impressed that they offered a graduate scholarship in mathematics to Feynman, but he had already committed to starting a Princeton PhD in physics. Still, while first a physicist, Feynman always remained an imaginative fellow with his mathematics, too, as you’ll see by the end of this chapter.

Copyright © 2011 by Princeton University Press

Time Travel

In an editorial published in the November 1926 issue of Amazing Stories (“Plausibility in Scientifiction”), Hugo Gernsback wrote:

[E]ven in the best-written fiction stories you will notice the characters converse in rather extraordinary language.  This is the so-called fiction language and is not generally used in real life.  Open almost any first-class magazine and, if you stop to think a second, you will realize that human beings do not use the flowery language that the characters do in fiction.  This same is true of scientifiction in another respect, where authors often take poetic license, sometimes disregarding true scientific facts, although retaining enough scientific accuracy to make the plot or story seem probable and at the same time interesting.

I don’t believe any good science fiction editor today would allow a writer to ignore “true scientific facts” (with the exception of an obvious spoof), and certainly no writer who hopes to sell his or her work should believe it’s OK to write dialogue in “fiction language.”  One of the goals of this book is to help you tell your time-travel tales without resorting to “fiction language.”

Time machines and time travel are certainly radical topics that demand a skeptical reaction.  Even if physics should one day establish these topics on firm scientific and experimental grounds, I think many people will persist in thinking of them as fantasy (just as physicists who understand the optical properties of water droplets still stand in awe at the appearance of a rainbow).  In 1979, the science fiction grand master Lester del Rey wrote in his The World of Science Fiction: 1926-1976 that time travel is one of the genre’s conventions that “seems clearly impossible.”

Del Rey’s position was nothing new among science fiction critics, because, as early as 1960, writer-critic Kingsley Amis wrote in New Maps of Hell that “time travel is inconceivable.”  And even then the view wasn’t original, as in 1953, the respected anthologist Groff Conklin wrote the following as an introduction to Murray Leinster’s time-travel story ”The Middle of the Week After Next” (in Science Fiction Adventures in Dimension): “In this tale we meet our first Mad Scientist.  Just as in reality the thoroughly cracked pots used to be found inventing perpetual motion machines, so in science fiction we find the lunatic fringe more often than not trying to perfect time-travel mechanisms.”

And finally, as long ago as 1940 a writer in the British pulp Tales of Wonder wrote words that many (but not all) physicists today might agree with: “Of all the fantastic ideas that belong to science fiction, the most remarkable – and, perhaps, the most fascinating – is that of time travel…indeed, so fantastic a notion does it seem, and so many apparently obvious absurdities and bewildering paradoxes does it present, that some of the most imaginative students of science refuse to consider it as a practicable proposition…”

© 1997, 2011 Paul J. Nahin