Erickson delves into the nature of numbers, what they are, how we have formulated them throughout history, where we’ve gone wrong and how we can fix it.
In this numeric exploration, Erickson exposes inconsistencies in the way the real number system has been structured. Starting from the nature of real numbers together with their basic operations such as subtraction and multiplication of signed numbers, Erickson finds that there are flaws in how we view negative numbers; their roots lie both in our structure of the number line and the notion that the removal of a deficit is equivalent to giving a gift. To resolve these issues, the author presents his own number system, what he terms the “veritable” number system. Common operations such as subtraction, logarithms and trigonometric functions no longer work as they used to, and Erickson spends much of the remainder of the book showing us how to do these operations using his veritable numbers. But since essentially all of mathematics and the sciences are rooted in the real numbers with their own (different) laws, functions and operations, the author’s new number system is not particularly practical. Erickson rounds out the book discussing a few other topics, such as polar coordinates and Hamilton’s discovery of the quaternions. The author’s ideas and reasoning are compelling, and his discussions about imaginary numbers and how he unifies them via the use of both the real numbers and his veritable numbers, together with his desire to remove the “mystery” behind these concepts, should carry the interest of most mathematically inclined readers.
A fascinating look at some of the underlying issues behind numbers—negative numbers in particular—though perhaps more as a curiosity than for practical application.