Customer Reviews

Realm of Numbers

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"The number sense is not confined to the human race." This is the first sentence in "Realm of Numbers," written by Isaac Asimov.

He goes on to explain that animals can recognize the differences in numbers (I think as a kind of encouragement to those humans who have problems dealing with numbers and mathematics or are clearly math phobes like me.)

Even a math phobe is able to recognize patterns of numbers on the faces of playing cards. As another example of pattern recognition, he gives the situation of Mr. Caveman peering into the cave to check on his two children. However, as the pattern increases, he needs some way to communicate this and so creates names for numbers.

Mr. Caveman has a rack of stone axes--four to be exact, but the pattern shows one is missing. He goes to his neighbor and asks if he borrowed one. Just this simple mathematical problem shows us the necessity of naming numbers.

Now Mr. Caveman must move beyond counting on his fingers to creating and using an abacus. However, Mr. Caveman has Dr. Isaac Asimov to explain the maneuvers to him.

Here are some of the chapter titles to give an idea of Asimov's Big Brain in action:
*Nothing--and Less than Nothing
*By-Passing Addition (make sure you read this line correctly!!)
*Broken Numbers
*The Shape of Numbers (why is he including erotica?--just kidding to see if you are paying attention!)
*Digging for Roots
*The Very Large and Very Small
*Endlessness (what math seems to have to me!)

In the 1950's this book must have been a best seller because my copy is from the 8th printing. Wow!

Honestly, anyone who opens this book to get some help will enter the "Realm of Numbers" where "a clear, imaginative approach to mathematics" can be as easy as 1-2-3. If anything is unclear in this review, blame it on math, not the reviewer.

Note: Any biographical sketch about Dr. Asimov will state that he was a prolific writer who wrote in nine of the ten Dewey Decimal categories. This is my third Asimov review. The first book belonged to the world of science (Dewey 500s) in that it was a book of science terms. The second book is about the meanings of map names and places and their etymologies (Dewey 400s or 900s). This book is about making the use of numbers easier--another 500s category.

In this book, Asimov takes you through the development of numbers, from the initial set of positive integers through the transfinite alephs. The progression is logical, he first establishes the infinitude of the positive integers and then explains the reasons why negative numbers are needed. Along with the negative integers, he explains the basic rules of addition, subtraction, multiplication and division as applied to integers. Subtraction is used to justify the need for negative integers and then division to explain the need for fractions. Asimov uses the applications for commerce to describe how negative numbers and fractions came to be accepted.
At one point, he argues that the most powerful force driving the development of early mathematics was the need for the rulers of civilization to assess the values of land and collect the appropriate taxes. Interesting thought, and quite likely true. Negative numbers no doubt have their origin in the computation of back taxes and plane geometry and fractions arose from the need to measure and subdivide land. The more complicated computations of the areas of non-rectangular regions also led to the development of a great deal of geometry.
After fractions are covered, he then goes on to explain infinite decimals, starting with those that repeat and then to the ones that do not. Complex numbers are next, although here, he is somewhat limited in the explanation of the details in how arithmetic is done on complex numbers.
Written at the level of the middle school student, Asimov is once again at his best, explaining the various categories of numbers and showing why they are needed in the modern world. This book is very suitable reading for students at that level.

Asimov as usual turns the complex into the easy. This book starts with the first thoughts of math and how it logically evovled. A must for anyone who lacks number sense. Invaluable for the elementary school teacher.

I received the book well packed, in due time and according to the description, a satisfactory purchase.

Hello, I'm a Pima Community College student. I choose this book to read to junior high students. This book reads a lot like an old text book, it was very dull and boring. I found it very hard to read and I also found it hard to keep the attention of the 7th grader that I read the few chapters to.