The Mystery of Numbers

In The Mystery of Numbers, Annemarie Schimmel has written a modern, English "reworking" of Das Mysterium der Zahl, an apparently well-known book on number systems and numerology whose last edition was released in 1951.

The Mystery of Numbers is an interesting, rich book which draws examples from many different cultures and historical epochs. The majority of the book, some 250 pages, comes under the heading "A Little Dictionary of Numbers" where selected numbers have a broad variety of mystical and numerological properties catalogued. The numbers One through Twenty-two have their own sections, while remaining numbers of numerological importance up to Ten Thousand are grouped in sections. In the first 50 pages, the author considers "Numbers and Number Systems", "The Heritage of the Pythagoreans", and other topics to form an introduction to the volume.

Browsing through the remarkable numerological occurrences the author has assembled together is intoxicating at first. It's not clear, however, what the intended audience of the book is. The treatment of the occurrences catalogued is often too glib to construe as serious research, at the same time it assumes too much background to be meaningful to a novice reader.

Nonetheless, there is something for everyone. Our continuing "Triskaidekaphobia" (fear of the number Thirteen) which keeps us from having Thirteenth floors in buildings, Dante's use of "trinitarian symbolism," George Chapman's wedding poem about the number Five are but three illustrations of the myriad examples that make up the majority of the book. The diversity of the occurrences presented is remarkable, and I would guess important for anyone who shares the author's cultural and anthropological bent.

However, as a mathematician and mathematics educator I became troubled as I read through the book. In fact, my trouble was excellently foretold by the book's opening quote, from Willi Hartner:

The mathematical spirit is a primordial human property that reveals itself wherever human beings live or material vestiges of former life exist.

Once reminded, by this quote and the rest of the book, of the richness of life, there is little wonder that there are so many numerological incidents to report on. We are surrounded by entirely too many things that are quantified by small numbers for there not to be an endless supply of coincidences! Mathematicians even have a term for this sort of thing -- the Pigeonhole principle. Christ had to die at some hour (p. 164), on some day (p. 13; beware!), and have some number of Last Supper guests (p. 13; again!) Similarly, there had to be some number of Commandments, written on some number of tablets.

Had the author clearly admitted that these occurrences were not so much mystical as necessary, one could be left to focus on the fine cultural and anthropological aspects she has collected. Unfortunately she does not, and it is all too likely that many readers may not come see this point. Once one happens upon this realization on one's own and begins to look at many of the topics more closely, much of the content begins to seem shallow. The Pythagoreans thought of the even numbers as feminine and, imagine, female genes have Two X chromosomes (p. 26). If there were a lunar, or some other type of connection, one might be curious that he epidermis regenerates itself every 28 days (p. 239). But none is mentioned.

As I continued to read, I remembered the fable of the smallest unimportant number. If there are unimportant numbers then there must be a smallest unimportant number, right? But, by being the smallest unimportant number, it would be important, right? This must mean that all numbers are important. So where does that leave things? Well, when your mind is intent on considering cultural and anthropological issues related to number, I'd recommend The Mystery of Numbers, with the caveat that you remember that all numbers are important and the pigeonhole principle is alive and well. On the other hand, when your mind is intent on considering mathematical issues related to number and in dissolving the long held beliefs that there are important links between mathematics and numerology, I'd be more likely to recommend that you read Underwood Dudley's Numerology or, What Pythagoras Wrought.

Julian F. Fleron, Ph.D., is an Assistant Professor of Mathematics at Westfield State College. His mathematical interests include real and complex analysis, the history of mathematics, and mathematics and teacher education; hobbies include Victorian house restoration, picture framing, and beer tasting.