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The Kingdom of Infinite Number: A Field Guide

Bryan Bunch
W. H. Freeman
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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Numbers are such flexible creatures that any attempt to classify them beyond the standard ones such as integer, rational and irrational are both subjective and incomplete. However, that is hardly the point. Working with numbers and learning new ways to classify them is a fascinating, thoroughly enjoyable exercise. That is what the author has done here, and it is clear that he had a lot of fun doing it. Borrowing from the biologists, the numbers are split into taxonomic classifications. The two Kingdoms are Kingdom Number and Kingdom Infinite. The Number Kingdom is further "subdivided" into the Natural, Integral, Rational, Real and Complex Genera. While this is not all that exciting, the explanations of the members is where the fun begins, and it does not stop until the end of the book.

When a number is listed, the name is also given in French, German, Spanish, Latin and Greek. The inclusion of the two languages of ancient scholars was a nice touch, although it would have been good to include the Arabic as well. Modern mathematicians owe a great deal to the Arab scholars who were the only real point of mathematical advancement and archiving in the Western World for almost a thousand years.

The listing of the properties of the numbers sometimes leans towards the mystical without actually crossing the line. As someone who has little time for the absurdity of numerology, I was a bit taken aback when I saw a section in the description of the numbers headed Personality. This word in association with numbers set my warning buzzers off. Numerologists often assign human character traits to numbers and I was prepared to stop reading immediately. However, my initial concern was unjustified, as the term is used more as a descriptor of what fundamental properties the number defines.

Those properties are often numeric, but sometimes are historical, other times mystical, but always interesting. While I yield to no one in my disdain for numerology, it is a fact that there are reasons to think more highly of some numbers than others. Since we live in a universe that is on the surface three dimensional, it is natural that there would be something special about three in this context. It takes two to make a child, so it is natural that two would be a special number. Other physical conditions of the universe such as the number of forces in nature can help raise serious questions. Is there a fundamental requirement of a certain number or is it a simple accident of how things coalesced after the Big Bang erupted? Those are serious questions with the only current answers being more mythological rather than scientific.

I thoroughly enjoyed the sections where the ancient and mythological references to numbers were given. The choice of which number to use in the explanation of an unknown phenomena tells us a great deal about how ancient minds approached things. Which really is a description, albeit a bit altered over time, of how our minds work today.

The enjoyment of numbers is one thing that unites all mathematicians, regardless of area of expertise, nationality or personal appearance. If you are looking for a light book describing these creatures of your affection, then you will enjoy this one.

Charles Ashbacher is co-editor of Journal of Recreational Mathematics, a part-time instructor at Kirkwood Community College and President/CEO of Charles Ashbacher Technologies. He can be reached at

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