is a tradition that the first so-called “magic square” appeared in China about 4,000 years ago. In the legend it appeared on the shell of a turtle that had been sent by the river god to assist the emperor. The essence of these numerological magic squares is that all the columns and rows in the square, as well as the diagonals, add up to the same number. Chinese traders who visited India with spices also seem to have carried numerological concepts with them. According to the form of numerology that developed in India, every person is endowed with 3 numbers. The first of these is the psychic number, which is related to the person’s date of birth. Anyone born on a date from the first to the ninth day of a month has a psychic number between 1 and 9. Someone born on the fifteenth of the month, for example, has a psychic number of “6” (1+5). A birth date on the twenty-ninth works in 2 stages: first, the numerals in the number 29 are added together (2+9=11), then, the numerals from whatever the sum of the first equation was, are added together (1+1=2).
The next number is referred to as the person’s destiny number. This is found by adding the sum of the numerals for the year of their birth to the sum of the numerals for the day and month of their birth. For instance, co-author Lionel was born on 9/2/1935. Since the numerals for the day and month (9 and 2), are singular, we leave them as is. The year, however, needs to be calculated into a number below 10 using the reduction method we have previously demonstrated. So, first we add together the 4 numerals of the year (1+9+3+5), which comes to the sum of 18. We then add together the numerals of this sum, 18, which equals 9 (1+8). We now can add the 9 (representing the year of Lionel’s birth) to the numerals representing his day and month of birth: 9 (day)+2 (month)+9 (year)=20. Finally, we add together the numerals of the sum 20 (2+0). This comes to 2, whereas his psychic number is “9.” The destiny number refers to the way that other people see you, whereas the psychic number represents who you actually are. The third number, known as the name number, is rather more complicated.
There are several ways in which the name number can be calculated. The simplest and best known technique is to use a number for each letter, but different numerologists would tend to allocate different numbers. One school of numerologists might say: A=1, B=2, C=3, and so on until I=9; but that would mean J=10, so the reduction of 10 (1+0) reverts to “1” again, like the “A.” The next letter, “K,” becomes “11,” which is reduced to “2” — the same number as allocated to the letter “B.” There are also complications about which name the person prefers, and which name he or she is best known by. This again distinguishes between the introspective self and the public self. In some systems the capital letter with which the name begins may be allocated additional weight and numerical value. Therefore, 2 equally well-qualified and experienced numerologists working with slightly different systems could reach very different conclusions.
In the sixteenth century, Albrecht Dürer (1471–1528), the mathematician, painter, and engraver, brought the old Chinese art of
magic-square-making to its zenith. In his engraving entitled Melancholia, which he completed in 1514, there is a magic square in the top right-hand corner. The theme of the engraving is a proto-
scientist, an alchemist in all probability, who is surrounded by unused equipment. His posture and the position of his head suggest that he is deep in melancholic thought.
| 16 | 3 | 2 | 13 |
| 5 | 10 | 11 | 8 |
| 9 | 6 | 7 | 12 |
| 4 | 15 | 14 | 1 |
The magic square that he has created contains each of the numbers from 1–16. When added vertically, horizontally, or diagonally, they total 34. This has the numerological significance of “7,” which is found by adding the numerals of the sum 34 together (3+4). Each of the 4 corners adds to make 34 as well, as do the 4 centre squares. Dürer has even managed to incorporate the date of his work, 1514, by placing the numbers “15” and “14” together at the bottom of his magic square. It is a truly amazing piece of numerology.
Basque numerology has significant contributions to make to the general history of the subject. Their language is not related to the old Indo-European, and their ancient origins are the subject of much speculation. Were the Basque people the original inhabitants of Europe prior to the arrival of the Indo-European peoples? Or were they from Chaldea? Interestingly, “11” has special significance in the Chaldean system. The Basques were certainly written about in Roman times. There are numerological references that suggest that the number “11” was of great significance in Basque numerology. In the Basque language, “11” is hamaika; “7” is hazpi, and “3” is hiru. Their interest in “11” as having special numerological significance relates to “11” being the first number that cannot be counted with the hands alone. In the sequence of prime numbers, it is the fifth: 2, 3, 5, 7, 11. There are some very strange calculations connected with the number “11.” For example, to check whether a number is exactly divisible by 11, add every alternate digit, then add the remaining digits and subtract one total from the other. If the answer is “0,” or a multiple of 11, the large number will divide by 11. For example, consider 2,592,821. Consider the equation 2+9+8+1=20 followed by 5+2+2=9. Subtract 9 from 20, resulting in 11. This reveals that the large number 2,592,821 is divisible by 11. When the division is done, the answer is 2,592,821÷11=235,711 — an answer that consists of the first 5 prime numbers.
A polygon with 11 sides is called an “undecagon” or a “hendecagon,” and has special significance for numerologists. A regular hendecagon can have a spindle placed through its centre, so that it can be used as a spinner — the equivalent of a miniature roulette wheel. The numbers 1–9 are marked on 9 of its sides, and two extra “1”s fill the last 2 sides to represent “11.” When the undecagon settles on any of the “1”s it is considered to be very positive and to bring good fortune to the person who spun it. If this occurs on 3 consecutive occasions, it is thought to bring either great fortune or deep and lasting romantic fulfilment.
There are points throughout the history of numerology at which numerology blends into general magic involving spells and charms: so many movements of the hands, so many repetitions of an incantation, so many portions of each ingredient, the dates and times at which the spell can be enacted with the greatest likelihood of success. The same is true of the interaction between alchemy and numerology: for the alchemical processes to work, the alchemist believed that a particular blend of ingredients had to be assembled, and that the numbers of each, and the temperatures reached, were all significant for the work.
The history of numerology, with its global ramifications and its intertwining with scientific mathematics, is a difficult path to follow, but it can be summed up as the route that perceptive and thoughtful numerologists have followed in order to reach the interesting forms of numerology that are practised today.
4
The Mysterious Fibonacci Numbers
and the Golden Mean
Two of the most intriguing sets of numbers that are of interest to scientific mathematicians as well as numerologists are the Fibonacci numbers and the golden mean, which are closely bonded to one another.
The brilliant Italian mathematician and numerologist generally known as Fibonacci was born in 1170 and died at the age of 80 in 1250. His full name was Leonardo Pisano Bigollo, and he was referred to by a few different names, including Leonardo of Pisa, Leonardo Fibonacci, and Leonardo Bonacci. Historians of numerology and mathematics regard him as the outstanding genius of the Middle Ages in those allied fields.
Fibonacci’s father, Guglielmo Fibonacci, was a very prosperous Italian merchant who was in charge of a busy trading post in Bugia, which was then a port belonging to the Almohad Sultanate in what is now Algeria. Bugia is currently known as Bejaia. As a youngster, Fibonacci travelled with his father to assist him with the demanding work of the trading post, and in the process, the young and gifted mathematician learned all about the numerals used by Hindus and Arabians. He saw almost immediately that these were much easier to manipulate than the Roman numerals that he had grown up with in Italy.
Captivated by the relative ease and simplicity of using the Hindu-Arabic numerals, young Fibonacci went in search of the top mathematicians and numerologists in the whole of the Mediterranean area. In his