Customer Reviews

Surreal Numbers

5 star:		(3)
4 star:		(1)
3 star:		(0)
2 star:		(1)
1 star:		(2)

 

 

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.

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.

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.

Stanford mathematician D. E. Knuth, in his slim volume Surreal Numbers, attempts to impart to the reader the notion of surreal numbers by way of a very unusual tactic: the dialogue. The book has two characters-a man and a woman-that, as a couple, have left Western society to find peace and their inner selves on a beach in India. After several months of swimming and picking berries, their intellectual needs begin to weigh heavy on them. In other words, they become bored. As luck would have it, their boredom is halted by the discovery of a stone tablet on the beach near their camp. The tablet reads, in Hebrew, "In the beginning, everything was void, and J. H. W. H. Conway began to create numbers." The tablet continues, giving the basic axioms that serve as basis for the creation of surreal numbers. The rest of the dialogue consists of our lovely couple discovering theorems and properties of surreal numbers using the axioms from the stone tablet. We see them take many wrong paths in their journey, only to realize and correct their errors in moments of sudden and poorly explained revelation. ....

To the math buff, I recommend studying up on these magnificent numbers. However, I do not recommend you use the present text to do so. It does little justice to the beauty of surreal numbers, and does even less in its explanation of their properties. The intention of the author, as he states in the postscript, is to present a math text in such a way that the reader not only learns of the topic discussed, but participates in its development. He sees the common math text as a dry conveyer of theorems and proofs that hides the intriguing and moving path of discovery that resulted in these theorems and proofs. He seeks, in Surreal Numbers, to write a sort of antithesis to this type of book. A grand goal, and one he does not achieve. In order to allow, or force, discovery by the reader, he avoids giving the details of many of the proofs. Often, his two characters just intuit the proofs in some moment of great inspiration. By the end, the characters seem like math protégés, whipping theorems out right and left without caution. True, the lack of proof does urge the reader to find the reasoning himself, but it is too tempting to just accept their theories in passing so you can get through that particular chapter. I really like math, but I was left utterly uninspired to fill in the gaps. In the author's defense, he does recommend this text be used as a supplement to another text or class. As such, you might find reason to attempt to complete the ideas, but most of the motivation would have to come from the instructor, as the book just does not make you care. Essentially, his goal would have been more easily reached-and probably bettered-if he forsake this confused dialogue for simply the following: "Here are the axioms for the surreal numbers:... Have fun!"

I do not wish to bash the use of dialogue to convey ideas. This form is not unprecedented in the world of mathematical literature .... To those who don't love math, nothing is going to work. He fell into a hole that many others who analyze different pedagogies of math fall into; he believes that everyone can see the beauty of math. ....

The dialogue itself was contrived and boring, occasionally alluding to food and sex in the midst of their mathematical orgy. Why even bother? Without further exploration, these side comments are just annoying and obviously just tacked on. In his postscript, the author states that an interesting topic to consider would be the differences of the personalities of his two characters. I don't see much to discuss here. Certainly, you can vaguely make out different approaches to math problems between the man and the woman, but there is not enough development to have more than about a five-minute discussion. He could have asked me to describe the conflicting ambitions of a triangle and a square, and I would have had more to say.

Though I admire Dr. Knuth's efforts, I just cannot recommend the present text. ....

First of all, a word of advice for the future readers of this book. Do not read it for its story. From the literary point of view, it's bad. Perhaps the only type of reader that will benefit or enjoy this book is the mathematical one.

In this book, you will find an exposition of a construction of a special number system (formally, a proper class of number systems). However, this exposition does not follow the formal or even traditional method employed in most mathematics books. It is told in form of a story. Two characters find a stone inscribed with the axioms of the construction of some "surreal numbers" and spend the whole book thinking what these axioms mean in some intuitive way.

In a mathematician's perspective (rather, my own), it is very entertaining. The characters' point of view is just as that of two mathematicians talking about some problem. And the construction is very interesting from a mathematician's point of view. So, yet again, for a mathematician, it will be like listening to two colleagues talking about some problem. It also has another element cooked for mathematicians: it has a small discussion about the fact that mathematical thinking is not taught until graduate school.

In conclusion, this book is a book about advanced mathematics written in a funny style. Do not expect the story to be good in a literary sense.

I've loved this novel ever since I was a math-loving kid of 14 or so. Here we have a nice American couple of kids out on an island in the Indian Ocean....perhaps the LOST island? Anyway, they're bored, find a mysterious tablet, and spend the rest of the book talking about math, philosophy, sex, theology, coconuts, math, fish and sex. Alice is the analytic one, Bill more intuitive, and it's true, the erotic content is a trifle dated these days...but in a good way, I think, it helps to leaven the discussions, the same way that the Marquis de Sade's (sorry, Dr. Knuth, it's the only comparison that springs to mind) dialogues are unreadable without the "other" material (whether you're referring to the politics or the sex, is your choice.) Anyway, hats off to a fun book!

The concept of surreal numbers is irritating enough without them being cutesified by a sycoophant.