Surreal Numbers (Paperback)

~ (Author)

Editorial Reviews

Product Description

Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E. Knuth, in appreciation of this revolutionary system, took a week off from work on The Art of Computer Programming to write an introduction to Conway's method. Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness. The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."...It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory.Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19 Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created. 0201038129B04062001

From the Back Cover

Nearly 30 years ago, John Horton Conway introduced a new way to construct numbers. Donald E.Never content with the ordinary, Knuth wrote this introduction as a work of fiction--a novelette. If not a steamy romance, the book nonetheless shows how a young couple turned on to pure mathematics and found total happiness.

The book's primary aim, Knuth explains in a postscript, is not so much to teach Conway's theory as "to teach how one might go about developing such a theory." He continues: "Therefore, as the two characters in this book gradually explore and build up Conway's number system, I have recorded their false starts and frustrations as well as their good ideas. I wanted to give a reasonably faithful portrayal of the important principles, techniques, joys, passions, and philosophy of mathematics, so I wrote the story as I was actually doing the research myself."... It is an astonishing feat of legerdemain. An empty hat rests on a table made of a few axioms of standard set theory. Conway waves two simple rules in the air, then reaches into almost nothing and pulls out an infinitely rich tapestry of numbers that form a real and closed field. Every real number is surrounded by a host of new numbers that lie closer to it than any other "real" value does. The system is truly "surreal." quoted from Martin Gardner, Mathematical Magic Show, pp. 16--19

Surreal Numbers, now in its 13th printing, will appeal to anyone who might enjoy an engaging dialogue on abstract mathematical ideas, and who might wish to experience how new mathematics is created.

0201038129B04062001

See all Editorial Reviews

Product Details

• Paperback: 128 pages
• Publisher: Addison-Wesley Professional (January 11, 1974)
• Language: English
• ISBN-10: 0201038129
• ISBN-13: 978-0201038125
• Product Dimensions: 8 x 5.4 x 0.4 inches
• Shipping Weight: 7 ounces (View shipping rates and policies)
• Average Customer Review: 3.4 out of 5 stars  See all reviews (5 customer reviews)
• Amazon.com Sales Rank: #326,460 in Books (See Bestsellers in Books)

  Popular in these categories: (What's this?)

  #91 in	Books > Professional & Technical > Professional Science > Mathematics > Pure Mathematics > Number Theory
  #96 in	Books > Science > Mathematics > Pure Mathematics > Number Theory

Customer Reviews

Most Helpful Customer Reviews

21 of 23 people found the following review helpful:

5.0 out of 5 stars Couldn't put it down., November 12, 2001

By	Shlomo Yona (Israel) - See all my reviews (REAL NAME)

This little book, written as a "novel", actually tries to show us that each of us is actually able to be an amature mathematician, and that "pure mathematics" is not that complicated once you get down to the rules.

For readers familiar with group theory notations, this is an easy and fun read.

Byeond the superlatives given all over to the nice and simple manner in which the number system is built in front of our eyes, I would also like to add I have noticed some ideas Knuth wanted the readers to absorb by reading this book of his:

* People too much into civilization need time off to "rest".
* After a long while of "resting" people need brain stimulations.
* The joy and interest in mathematics comes with the discovery, or at least after trying the best you can. Only then can you appreciate what others did in mathematics.
* Teachers in schools would rather tell you about math, and make you takes exams, and will not encourage creativity. This results in that only in graduate school are people allowed (and demanded) to start creating things of their own.
* Solving good math puzzles or solving any problem, is satisfying, and makes you horny!
* definitions proofs to theorems and ideas should be expressed as simple as possible, and they can always be expressed in a simple way.

I could go on with more ideas Knuth wanted to pass to the readers...

I read the book in one time, not putting it down for a minute. The flow of ideas and progress in building the number system (up to the pseudo-numbers) is clear and fun. I actually felt as if I was discovering things myself.

There is a lot which can be "further probed" after readnig the book, and Knuth appeals to teachers to gives seminars based on this text, and guides them how he would want those seminars to be like.

10 of 13 people found the following review helpful:

4.0 out of 5 stars An amusing book that details an interesting subject in math, January 31, 1999

By	Adam Goode (Pittsburgh, PA USA) - See all my reviews (REAL NAME)

This book, written in Knuth's classic style, employs a unique dialog to guide the reader through the derivation of the fascinating mathematical topic of surreal numbers. Its short length and humor makes it a must for any math fan interested in the methods used for deriving new concepts in math, and the exercises included make it a useful book for math teachers interested in giving something new to their students. All said, a lovely book.

7 of 9 people found the following review helpful:

1.0 out of 5 stars An interesting mathematical exposition, made nauseating and repulsive by the contrived narrative., September 14, 2007

By	Michael F. Lamb "datagrok" (Stony Brook, NY) - See all my reviews (REAL NAME)

As a student of computer science, I began reading this book full of respect and reverence for the author. The concept seems interesting at first, to use a narrative to convey the process of researching a mathematical concept to the reader. Sure, I thought, I would love to follow along with the mind of a super-smart Don Knuth as he investigates Conway's idea for this construction of a number system.

However, I was soon blindsided by the bizarre narrative. What another reviewer critiques in a single sentence, "the dialogue itself was contrived and boring, occasionally alluding to food and sex in the midst of their mathematical orgy," I found to be so off-putting that I left the study group altogether. The extemporaneous dialogue and description of random inconsequential bits of the main characters' lives and their budding relationship (if you could call thinly veiled references to celebratory coitus for a successful math proof a "relationship") is more contrived than the worst sci-fi fan-fiction. Pornographic films have themes, relationships, and plots more believable.

I found myself reflecting more on the content of this horrible narrative than on the mathematics itself. Why would Professor Knuth torture me this way? I felt as if a grandfatherly professor of mine presented to me his lurid "romantic" fantasies about my fellow university students under the false guise of a mathematics exposition, and had the gall to expect me to appreciate his impartation of great wisdom.

Surely, Professor Knuth is one of the eminent scholars of our age, and has achieved more in his lifetime with TeX and The Art of Computer Programming alone than I or most of my peers ever will. I am no one to criticize those works. However, I stand firm and tall when I declare that Donald Knuth can NOT write romantic fiction to save his own life, nor should he EVER again attempt to do so, nor should this repulsive work ever be inflicted upon a poor student looking to obtain some knowledge of Conway's set-theoretic ideas.

Furthermore, I would consider the opinions of the reviewers who give this book more than two stars to be highly suspect.

Stay far, far away from this text, unless you're an old mathematics professor with an unhealthy interest in the sex lives of your own students. If that's the case, you can keep this one under your pillow. Students and other people looking for math plus romantic fiction should seek instead the work of Randall Munroe, who has produced the definitive work of the genre.