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See Article History Number symbolism, cultural associations—including religious, philosophic, and aesthetic—with various numbers. Humanity has had a love-hate relationship with numbers from the earliest times. Bones dating from perhaps 30, years ago show scratch marks that possibly represent the phases of the Moon. The ancient Babylonians observed the movements of the planets, recorded them as numbers, and used them to predict eclipses and other astronomical phenomena. The priesthood of ancient Egypt used numbers to predict the flooding of the Nile. Pythagoreanism , a cult of ancient Greece , believed that numbers were the basis of the entire universe, which ran on numerical harmony. Numbers were associated with names for magical purposes: More recently, cranks have sought the secrets of the universe in the dimensions of the Great Pyramid of Giza , an aberration so common that it even has a name—pyramidology. Millions of otherwise rational people are terrified of the number 13, to the extent that hotels omit it from their floors, airplanes do not have a row 13, and the numbers for Formula 1 racing cars skip from 12 to 14 so that, for example, 22 cars would be numbered from 1 to Learned tomes are written about the significance of such stalwarts as the golden number 1. Mathematics is the study of numbers, shapes, and related structures. Number mysticism belongs elsewhere and is generally categorized as numerology. Numerology sheds light on the innermost workings of the human mind but very little on the rest of the universe. Mathematics, meanwhile, sheds light on much of the universe but, as yet, very little on human psychology. Between the two lies fruitful scientific ground, yet to be cultivated extensively. Numerals and numerology Numerical coincidences abound, and they are often so remarkable that it is difficult to explain them rationally. Not surprisingly, many people become convinced that these coincidences have irrational explanations. What, for example, should be made of the following similarities not all of them numerological between U. Presidents Abraham Lincoln and John F. Lincoln was elected president in , Kennedy in Both were assassinated on a Friday. Both were succeeded by Southern Democrats named Johnson. Andrew Johnson was born in , Lyndon Johnson in Booth shot Lincoln in a theatre and fled to a warehouse; Oswald shot Kennedy from a warehouse and fled to a theatre. The first public suggestion that Lincoln should run for president proposed that his running mate should be John Kennedy. John Pendleton Kennedy was a Maryland politician. One explanation for coincidences of this kind is selective reporting. Anything that fits is kept; anything that does not is discarded. Thus, the coincidence of day of the week for the assassinations is emphasized; the differences in month and number of day in the month are ignored. Lincoln was assassinated on April 14, Kennedy on November More subtly, only one choice is made from many possibilities, the one that maintains the numerological pattern. Sometimes the date of birth is used, sometimes the date of election. If those do not work, how about the dates of college graduation, marriage, firstborn child, first election to office, or death? The correct birth date for Booth is now thought to be , not , and Booth actually fled to a barn. It is common for coincidences to be exaggerated in this manner. And once one starts looking…Lincoln had a beard. No, he was clean-shaven. Do not mention beards, then. Many of the coincidences listed here are exaggerations, lies, elaborations chosen from an infinite range of potential targets, or the result of a hidden selective process. Still, a few of the coincidences are quite startling. Although rational explanations exist, a true believer cannot be convinced. It is in this fertile territory that number mysticism thrives. Words become numbers when their letter values are added together. The significance is clear: But who is the beast? Two 16th-century numerologists were Michael Stifel and Peter Bungus. Not coincidentally, Stifel was a Protestant theologian and Bungus a Catholic. The name of Jesus in Greek has the numerological value , three repetitions of the number 8, which is often considered auspicious. Many people have discerned numerical patterns in the Bible. For example, consider the King James Version. The phrase Old Testament consists of two words, one with three letters, the other with nine. Concatenate the two digits to get 39, the number of Old Testament books. Methuselah is said to have lived years. This number is a palindrome , meaning that it looks the same when reversed. It is also the 17th tetrahedral number, meaning that if you pile up spheres so that successive layers form the triangular numbers 1, 3, 6, 10, and so on, by layer 17 the total number of balls will be Does 17 have any other significance? According to John The Bible contains so many numbers that such games can be played indefinitely; the question is what conclusions if any should be drawn from them. Pythagoreanism The earliest known systematic cult based on the rule of numbers was that of the Pythagoreans. Pythagoras was a Greek who thrived in the 6th century bce. Little is known of his life, and in fact he may be a composite figure to whom the discoveries of many different people have been attributed by his followers. It is not even known whether the Pythagorean theorem in geometry was actually discovered by him. The Pythagoreans invested specific numbers with mystical properties. The number 1 symbolized unity and the origin of all things, since all other numbers can be created from 1 by adding enough copies of it. All even numbers were female, all odd numbers male. The number 4 represented justice. This number symbolized unity arising from multiplicity. Moreover, it was related to space. A single point corresponds to 1, a line to 2 because a line has two extremities , a triangle to 3, and space to 4. Thus 10 also symbolized all possible spaces. The Pythagoreans recognized the existence of nine heavenly bodies: So important was the number 10 in their view of cosmology that they believed there was a tenth body, Counter-Earth, perpetually hidden from us by the Sun. Some Pythagorean speculations were mathematical. They represented numbers by arrangements of dots. The square numbers 1, 4, 9, 16,… were arranged in squares, and the triangular numbers 1, 3, 6, 10,… were arranged in triangles see figure. This terminology remains in use to the present day. The Pythagoreans were especially fascinated by the presence of numbers in the natural world. Perhaps their most spectacular discovery was that musical harmony is related to simple whole-number ratios. A string such as that on a violin produces a note with a particular pitch ; a string one-half as long produces an extremely harmonious note to the first, now called the octave. A string two-thirds as long produces the next most harmonious note, now called the fifth. And one three-fourths as long produces the fourth, also very harmonious. The Pythagoreans discovered these facts empirically by experimenting with strings of different lengths. Today these harmonies are traced to the physics of vibrating strings, which move in patterns of waves. The number of waves that can fit into a given length of string is a whole number, and these whole numbers determine the simple numerical ratios. The full story is more complex, involving what the brain becomes accustomed to, but there is a definite rationale behind the Pythagorean discovery. Cultural associations of some numbers The enormous range of symbolic roles that numbers have played in various cultures , religions, and other systems of human thought can be gauged from a brief sample. Therefore, in monotheistic religions, it often symbolizes God or the universe. The Pythagoreans did not consider 1 to be a number at all because number means plurality and 1 is singular. However, they considered it to be the source of all numbers because adding many 1s together can create any other positive whole number. In their system, where odd numbers were male and even numbers female, the number 1 was neither; instead, it changed each to the other. If 1 is added to an even number, it becomes odd; similarly, if 1 is added to an odd number, it becomes even. Although 2 was female to the Pythagoreans, other numerological schemes viewed it as male. The yin and yang symbol suggests the two opposite principles or forces that make up all the aspects of life. Some religions are dualistic, with two gods in place of the one God of monotheism. The number 2 is often associated with negatives, as in the words duplicity and two-faced. Northwest Coast Indian s required the parents of twins to observe various taboos because they believed that supernatural powers would bring the wishes of twins to fruition. Similarly, there were three aspects to the Egyptian sun god: Khepri rising , Re midday , and Atum setting. Plato saw 3 as being symbolic of the triangle , the simplest spatial shape, and considered the world to have been built from triangles.
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