Until recently, the history of computing has tended to be tied to the goals of mathematicians, as they struggled to keep up with the increasing demands of a society growing more technical. As nations began to trade with other nations, the necessity of performing computations on larger numbers very quickly forced changes in the notation. When first introduced into Europe, the modern decimal system of notation was greeted with skepticism and some hostility. However, as is nearly always the case in human endeavors, it was accepted rather quickly, as it was so much more efficient than other systems such as Roman numerals. Therefore, the history of computing devices is bound very tightly with improvements in representation, and the historical changes in notation are the topic of the first section of the book.
Ifrah does an excellent job in recapitulating the history of the notation of computation, covering the entire world, ending up with the modern notation and the efficiency of binary numbers. Nearly forty pages are devoted to explanations of many ancient numerical notations, and many figures are included. It is this approach that differentiates this book from other histories of computing. Other authors concentrate on the history of the evolving architectures of the computing devices, ignoring the necessary precondition of a compact and efficient notation. It is very difficult to imagine computing devices that could easily perform arithmetic on Roman numerals.
The second section is a two track treatment of the development of computing devices. One track covers the mathematical preliminaries and the second the mechanical advances that led to the construction of accurate computers. Most of the early improvements were done by mathematicians, and it was not until the late nineteenth century that governments started to be interested in computers. The primary event was the work of Charles Babbage, who showed that computers were possible and how valuable they could be in performing routine computations that were highly prone to error.
In many ways, this history of computing is more a history of the requisite mathematics rather than a history of hardware. This is a second way in which this book differs from other histories. One of the reasons why computers have improved so quickly is that much of the theoretical background for their actions were developed before the machines were. Ifrah explains that in great detail, describing how some of the principles of abstract mathematics have been applied to the building of computers.
The final section is very small and deals with the future of computing. This is a wise move, as this book is a history and one thing we have learned from the recent history of computers is that predicting the future is largely impossible. We know that they will get faster, have more memory and the usage will increase, but the consequences of this are difficult to predict.
If your interest is in the preconditions necessary for computers to be widely used, then this is the book for you. Ifrah covers all of the notational and mathematical background necessary for computers to be useful, for without that, they would probably have been little more than intellectual toys.
Published in the recreational mathematics e-mail newsletter, preprinted with permission.
