In the hands of the right person, an intriguing idea can be nurtured into an innovative new philosophy. Such is the case with Chibamba Mulenga’s The Fundamental Principle of Digits of a Number: d = 9k, a speculative take on the well-known mathematical Rule of Divisibility by 9.
Mulenga patiently builds and defends his principle one brick at a time. He embarks in Chapter One with basic definitions of integers, digits, and numbers—terms that are often incorrectly used interchangeably. He also refreshes readers as to the divisibility rule he references.
Once basic concepts are clarified, he makes his case for his principle on the basis of two ideas. The first is that the permutation of digits of any number contains the same digits and same number of digits as the given number. (For example: two of the permutations of the number 7182 are 1827 and 8271). The second is that the difference between two permutations of said digits is governed by his defined principle, which guarantees that the difference is divisible by 9 (example: 8271 – 1827 = 6444 which divides neatly by 9 to equal 716.)
Once the reader has grasped these two propositions, the remainder of the book is simply a series of concepts built upon familiar mathematical views of number patterns, sequencing, ordering, permutation, and combination — all using fundamental mathematics familiar to those who have mastered first-year algebra.
Although the mathematical concepts on which Mulenga relies are rudimentary, some may need to slow their normal reading pace, since the book lacks chapter sub-divisions that usually aid in organization. This does not diminish the quality of the read, however, and the overall experience is satisfying, rather than a frustrating challenge.
A missing puzzle piece here is the practical application of the principle, but overall this book is highly absorbing, and those who appreciate delving into abstract theories will find it appealing.