that arise from the exercise of power and energy. Number “9” in Chinese symbolism is almost the direct opposite of its significance in Western numerology where it means a major change. In the Chinese system it represents longevity, endurance, and persisting for a very long time.
Over and above the values and meanings, which the Chinese system allocates to single-digit integers, there are certain number combinations that are thought to be very significant by Chinese numerologists who use this system. The number “99,” for example, stands for eternity, or a good thing that is everlasting. The numbers “148,” “168,” and “814” are thought to be especially lucky in China, and “168” is the number used by a chain of motels there. The personal prosperity number is “518,” which is believed to bring great success and financial rewards to those who use it. Triple prosperity is allegedly attached to “888,” which signifies infinite riches and wealth. A long and happy life verging on immortality is associated with the number “1314,” while “289” is almost as powerfully fortunate. It means always having enough, and having it throughout an entire lifetime.
Just as there are wide differences of interpretation between Western and Chinese numerologists, there are similar distinctions between both those systems and the ancient Indian system. In the Indian system, the numbers “1,” “10,” “19,” and “28” are regarded as being ruled by the sun. When their digits are added, they all reach the total of “1.” So, adding the digits of “10” together equals 1 (1+0); the digits of 19 added together come to 10 (1+9), which then reduces to 1 (1+0=1); and adding the digits of “28” also comes to 10 (2+8), which again reduces to 1 (1+0=1). Applying the system further, the numbers “2,” “11,” “20,” and “29” all represent the moon, and all add up to 2. For example, the digits of “11” add together to 2 (1+1), the digits of “20” add together to 2 (2+0), and the digits of “29” add together to 11 (9+2), which then reduces to 2 (1+1). Letters are also allocated their own special number values in this system. “A,” “I,” “J,” “Q,” and “Y” all carry the value “1,” and “B,” “C,” “K,” and “R” all carry the value “2.”
The Mayans and Aztecs were expert astrologers and calendar-makers. They achieved a highly commendable level of mathematical efficiency, which was especially evident in their amazing calendars.
Mayan calendar
They could justifiably be described as expert numerologists, but their systems varied from our contemporary Western numerology, and from Indian and Chinese techniques and interpretations.
The numerological process of adding digits to arrive at a single figure features in almost all numerological systems throughout the world, but it may not always be performed in the familiar base-10 system of Western mathematics. For example, because “9” has certain peculiarities, what is called a nonary system, or base-9, may be employed for some numerological processes. Instead of using the digits from 1–9 as in base-10, the digits 1–8 are employed; and “9” is written as “10,” signifying 1 in the nines column and no units. The columns in nonary systems are: units, 9s, 81s, and 729s, instead of the decimal system’s columns of: units, tens, hundreds, and thousands. For example, a numerologist using the nonary system would add up the digits of “578685” as 5+7+8+6+8+5=43 and then add the digits of the number “43” (4+3) to yield a single nonary digit of “7.” This is because the digits add to 39 in the normal decimal-based system, but “39” in normal decimal notation has to be written in nonary as “4” in the 9s column and “3” in the units column. This is because 4×9=36, hence the “4” in the 9s column accompanied by “3” in the units column. The same 6 digits in normal decimal notation add to 39, and the resulting 3+9 gives 12, which, in turn, can be reduced to 3 by adding the digits of 12 together like so: 1+2=3. The numerologist working in the nonary system finishes with a single digit of “7” from 4+3=7, whereas the numerologist working in decimal-base finishes with a single digit of “3” from 1+2=3. This can cause differing opinions and outcomes as the numerals “7” and “3” have very different interpretations in numerology.
The comparison of nonary and decimal systems is shown in the following table:
| Normal (Base-10) Decimal Notation | |||
| Thousands | Hundreds | Tens | Units |
| 5 | 6 | 7 | 8 |
| Nonary (Base-9) Notation | |||
| 729s | 81s | 9s | Units |
| 7 | 7 | 0 | 8 |
So what are mathematics and numerology? Scientific mathematics enables us to understand the minute mysteries of the subatomic microcosm and the almost infinite vastness of the cosmos. Mathematics is a superbly accurate number and symbol code that enables us to communicate, calculate, and solve problems.
If the numerologists are right about their mysterious fields of study, numerology might prove to be more breathtakingly exciting than scientific mathematics. Can numerology tell us about human characters and dispositions, personalities, and relationships? Can it reveal whether certain locations are favourable, while others are negative and hazardous? Can it suggest which dates and times are better than others for achieving our goals? Can it explain the immense complexity of the structure and function of plant and animal life and the mysteries of the interactions of the entire biosphere? Can it predict future events? Can it show us how to understand the mysterious influence that some numbers appear to exert over the environment?
If the mysteries of numerology could be interwoven and reconciled with pure scientific mathematics, if numerology could be shown to have a logical, rational, and scientific basis as well as a seemingly “magical” one, where would that new unified area of study take us? What if James Jeans was right in asserting that the universe is a thought in the mind of a Supreme Mathematician?
In the next chapter, we examine the long and complex history of mathematics in detail, examining in particular those areas where it comes closest to numerology.
2
History of Mathematics
The earliest artifacts relating to mathematics were various tally sticks, some dating back nearly 40,000 years. As with ancient cave paintings, which are believed to have been magical in the eyes of the early peoples who created them, the ancient mathematical tally sticks may well have had a magical numerological significance as well as a purely practical, numerical one.
The Lebombo bone is estimated to be 35,000 years old — or perhaps more. It was found in the Border Cave in the Lebombo Mountains of Swaziland in East Africa. Originally the fibula of a baboon, it has 29 distinct notches, which has led some archaeologists to believe that it was intended as a lunar calendar.
Lebombo bone
The Wolf bone was discovered in Moravia by Karl Absolon in 1937. Estimated at approximately 35,000 years old, it was found close to a Venus figurine. The bone has 55 marks carved into it. Its association with the Venus figurine suggests some kind of numerological or magical function as well as a straightforward counting or measuring function. Was this a situation in which mathematics and numerology overlapped?
The Ishango bone is rather younger, dating back some 20,000 years. It was discovered in 1960 by a Belgian explorer named de Braucourt in what was then known as the Belgian Congo, near the upper reaches of the Nile. Like the Lebombo bone, the Ishango bone was once the fibula of a baboon. At one end there is a piece of quartz, which suggests that the Ishango bone was used for marking or engraving things. It is thought that the clusters of marks cut into the bone are more complex than those on the Lebombo bone, which might indicate that the Ishango bone is something more mathematically complicated than a basic tally stick or calendar.
Mathematical historians are of the opinion that mathematical thinking started when our earliest ancestors began to form concepts of number, magnitude, and form. What precisely do we mean by number? Although there is still some controversy over whether