Numbers, Forbidden and Superstitious

In trying to understand the world, mankind has created many superstitions and myths that have slowly led to what we consider modern science. For example, alchemy, the attempt to change other materials into gold, helped establish important principles of modern chemistry. The same is true of mathematics.

Many mathematical theories have been proposed over the centuries. Some have become the foundation of major branches of mathematics. Others have been disproved and discarded. But like many other superstitions, some erroneous theories have unfortunately persisted even after the science of mathematics has examined and invalidated them.

The Number 13

Thirteen frequently is called an unlucky number. Many modern buildings, particularly hotels, will not have a floor numbered as the thirteenth floor because so many people consider it unlucky and wish to avoid it. Of course, any building of sufficient height does have a thirteenth floor; it is simply skipped in the numbering of floors, which will go from 12 directly to 14. But this is enough either to satisfy or to delude most superstitious people. Many airlines will skip numbering across the thirteenth row.

Similarly, some race car drivers reject the number 13 to identify their cars, and some street numbers are altered to avoid the use of the number 13. The irrational fear of the number is so common that it even has a scientific name: triskaidekaphobia. The thirteenth day of the month is considered unlucky, particularly if it falls on a Friday, a day also considered unlucky for religious and cultural reasons. Throughout history and many different cultures, superstitious meaning has often been assigned to numbers and to groups and arrangements of numbers.

The reasons that the number 13 is considered unlucky derive from various sources. Some of those reasons come from religious references, such as the Last Supper, which was comprised of thirteen people, although other references seem to predate this. Other reasons have associations with mythology and the occult. Witches are said to gather in covens of thirteen, a belief found in the Teutonic mythology of Scandinavian folklore and widespread in the Middle Ages. Indeed, the occult has embraced the number 13 and now often uses thirteen candles or other forms of symbolism based on this number.

Many other numbers are believed to hold special meaning. The number 666 was claimed by the ancient Greeks to represent the mortal mind. In the Bible the number 666 is referred to as the number of the beast and has come to be known as a symbol of Satan and the Antichrist:

Rev 13:18 Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.

The belief that there is a hidden meaning in numbers is so prevalent that special meanings steadily continue to be assigned to numbers by different groups of people with different belief systems; hence, the meanings assigned vary widely. Numerology designates meanings to all numbers from 1 to 9, as well as to some other numbers such as 11, 22, and 33. The occult assigns different meanings to these same numbers. The number 13, an unlucky number to some and a satanic number to others, represents Mary, the mother of Christ in Christian belief.

Numerology

Numerology is a belief that all things can be expressed in numbers and that numbers have special meanings because of special "vibrations" that they give off or are associated with. The ancient Greek mathematician and religious leader Pythagoras of Samos is credited with having originated this pseudo-science and is believed to have assigned numbers to letters, adding the numeric values of each letter to find the symbolism of any word.

In the process of this numerology technique, the digits of a resulting number are added together until only a single digit remains (24 yields 2 + 4= 6). Numerology claims that when a name is assigned to anything, it instantly releases occult forces expressed in numbers. Pythagoras did study music and learn important concepts about vibration and frequency from this study, but he made an unfortunate leap in forming his conclusions in regard to numerology.

Numeric Value of Letters. When adding up the values of the letters in a name or other word, the resulting "revelations" are much like the information found in a horoscope. The number 1 indicates individuality, 2 indicates balance, and 3 is said to indicate acceptance of life as it comes. The number 4 indicates dependability, 5 a desire for freedom, and 6 denotes friendship. The number 7 is said to be an indication of a deep thinker, 8 indicates discipline, and 9 is said to be governed by love. Though science considers it groundless and no scientific basis for numerology has been shown, numerology continues to attract a wide range of disciples even in current times.

Magic Squares

An interesting and novel mathematical device is often called a magic square. It is a two-dimensional array of numbers in which each row and each column, as well as the major diagonals, all add up to the same number.

The above example is a simple third-order magic square in which the sum of 15 is found in any row, column, or major diagonal. The order of the magic square is simply its size along one side. Squares of any order can be constructed. Magic squares such as this one date back as far as ancient China

in 2200 b.c.e., where legend has it that Emperor Yu first saw a magic square on the back of a divine tortoise.

Magic squares have been a mathematical curiosity since then, and creation of larger order magic squares is an interesting diversion. In some cultures magic squares have been linked to spiritual or supernatural powers. They have been applied to astrology, which claims to be able to predict the future based on the positions of stars and celestial objects, asserting that a mysterious life energy originates in the cosmos and is controlled or filtered by nine stars. Magic squares also show up in some forms of the Oriental practice of Feng Shui, in which objects are arranged in a certain way to produce a mysterious "energy flow."

The Golden Ratio

In addition to the integers and rational numbers, mathematics includes many interesting irrational numbers. Pi (π), the ratio of the circumference of a circle to its diameter, is perhaps the best known. The letter e, used to represent 2.71828182845…, is another; it is the base of the natural logarithm and its inverse, the exponential function. Logarithms based on e have much more practical use than common logarithms built on a number base of 10 because the value e shows up in many real world rates of change. Another irrational number that has interested many cultures over the centuries is the irrational number Phi, also known as the golden ratio. The golden ratio can be illustrated by a line that is cut into two segments, A and B, in such a way that the ratio of the entire line to segment A is the same as the ratio of segment A to segment B.

Phi is the only positive number from which 1 can be subtracted to get its own reciprocal. This phenomenon is also seen in the Fibonacci sequence, or any similar sequence: If one adds any two numbers to produce a third, adds the second and third to produce a fourth, and the fourth and fifth to produce a sixth, and so on, the ratio of each pair of adjacent numbers approaches the golden ratio.

There was much interest in Phi during the Renaissance, and since that time a considerable amount of literature has been written about it. Many misconceptions about the golden ratio have arisen. Probably the most repeated one is that it is the most pleasing ratio for a rectangle. While some modern architecture and art have been based on this statement, there seems to be no basis for it. Blind studies have, in fact, shown that when large numbers of people are asked to pick the most pleasing rectangle from a group of rectangles, those rectangles based on the golden ratio are selected no more often than other similar rectangles.

Some have tried to establish Phi as a basis of the works of Leonardo da Vinci, but there is no real evidence that Leonardo da Vinci used Phi as a basis for any of his works. Similarly, claims that the pyramids, the sphinx, and other ancient structures are based on the golden ratio cannot be confirmed. Some measurements taken to substantiate these claims may have come close to this ratio, but in those cases it seems more likely that those people who were trying to validate the claim were too willing to give unwarranted significance to the measurements.

Dangers of Superstitious Numbers

While there is no evidence that the numbers 13, 666, or others are unlucky, the belief that numbers have special metaphysical influence has affected math and science in very unfortunate ways. Galileo was put on trial twice by the Catholic church during the Inquisitions and forced to recant what he had learned of the solar system. The Catholic church was primarily upset that he contradicted their teaching that the Sun revolved around the Earth.

Another of Galileo's "transgressions" was his discovery of several moons of Jupiter, thus increasing the number of known observable objects in the solar system from seven to eleven. The church insisted that there had to be seven such objects because seven was a mystical number. While Galileo was able to retract his statements, others were not so lucky and were executed.

see also Fibonacci, Leonardo Pisano; Golden Section; Pythagoras.

Harry J. Kuhman

Bibliography

Gardner, Martin. Weird Water & Fuzzy Logic. Amherst, NY: Prometheus Books, 1996.

Guiley, Rosemary Ellen. Harper's Encyclopedia of Mystical & Paranormal Experience. New York: Harper Collins Publishers, 1991.

Hitchcock, Helyn. Helping Yourself with Numerology. West Nyach, NY: Parker Publishing Company, 1972.

New Age Collective and Lisa Lenard. The Complete Idiot's Guide to New Millennium Predictions. New York: Alpha Books, 1998.

Pappas, Theoni. The Joy of Mathematics. Tetra: World Wide Publishing, 1989.

Shermer, Michael. Why People Believe Weird Things. New York: W.H. Freeman and Company, 1997.

LUCKY 13?

Though the number 13 has many unlucky connotations, it is considered lucky to be born on the thirteenth day of the month. A child born on the thirteenth is expected to prosper in anything he or she begins on that day later in life.