Surreal Numbers

Rating:
Summary: One star--the extra is for referring to John Conway as God
Review: 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. ....

Rating:
Summary: An amusing book that details an interesting subject in math
Review: 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.

Rating:
Summary: Couldn't put it down.
Review: 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.

Rating:
Summary: Couldn't put it down.
Review: 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.