Читать книгу Mysteries and Secrets of Numerology - Patricia Fanthorpe - Страница 8

Our broad understanding of mathematics is that it is a system of communication, calculation, and problem solving involving the use of numbers and allied symbols that represent processes such as addition, subtraction, multiplication, and division. It may be described as a language or code. Its more advanced concepts include the measurement of single linear dimensions, areas, volumes, structures, and changes. Further extensions of its definition include special fields such as algebra, trigonometry, statistics, and calculus. Mathematicians look for patterns and then base conjectures on the patterns they have observed. Mathematics lies at the heart of understanding the amazing complexities of the universe, from subatomic particles to the unimaginably vast spaces between the galaxies. Sir James Jeans once suggested that the universe is a thought in the mind of a great mathematician.

In their earliest days, mathematics and numerology were practically indistinguishable. The power of numbers, and the power of those who understood more about numbers than most of their contemporaries, seemed close to magical. Numerology may be regarded as the fundamental idea that numbers, mathematical symbols, quantities, measurements, and statistical analyses have yet further powers than those which they display when we use them to solve mathematical problems. Inside their straightforward mathematical box, numbers and symbols answer questions that have been posed in numbers and symbols. Outside their mathematical box, numbers and symbols are believed to have powers far beyond mere calculating. Numerology suggests that certain digits can affect the universe around them and can influence human behaviour, success, and failure. To the mathematician, numbers and symbols solve problems of quantity, measurement, and numerical changes. To the numerologist, numbers and symbols are like the words of magical liturgies and the ritual movements of enchanters, sorcerers, and magicians. To the numerologist, numbers and symbols have the power to influence people and things in paranormal ways. They also have the power to predict likely outcomes.

The Greek word μάθημα (mathema), from which the English word mathematics is derived, originally meant “knowledge, learning, or study.” Having studied patterns and derived conjectures from them, mathematicians look for proofs of their conjectures. There are several forms of mathematical proof, and a very basic example of the type called “direct proof” can be seen in the fact that the sum of any 2 even numbers will always be another even number. The term integer is used in mathematics to define a whole number with no fractional parts attached to it. Integers can be positive or negative: -3, -2, -1, 0, 1, 2, and 3 are all integers. The proof begins by calling any 2 even integers “x” and “y.” Because they are even — that is, they can be divided by 2 — it can be argued that x=2a and y=2b. Putting a number next to a letter in mathematics signifies that the number multiplies the letter adjacent to it. So, if x and y are both even, each of them will be made up of 2 other integers, which we call “a” and “b.” Suppose that we decide that x=8 and y=12. Then 8=2×a and 12=2×b. This means that a must be equal to 4 (8=2×4) and b must be equal to 6 (12=2×6). This then leads to the next step in the proof, which is the following equation:

x+y=2a+2b or 8+12=2(4)+2(6)

This can be written as 2(a+b), or 2(4+6). The “2” outside the bracket multiplies everything inside the bracket. What has been done so far shows that x+y has 2 as a factor, and the definition of an even integer is that it can be divided by 2. This then constitutes the mathematical proof that the sum of any 2 even integers is another even integer.

It is an essential part of mathematics to set out to prove or disprove mathematical conjectures by using mathematical proofs like the one above. Unlike that basic example, it can sometimes take many years to establish an advanced mathematical proof.

Two very great philosophical mathematicians, Giuseppe Peano (1858–1932) and David Hilbert (1862–1943), made outstanding contributions to mathematical proof theory and mathematical logic.

Of even greater mathematical stature than Peano and Hilbert was the outstandingly brilliant Johann Carl Friedrich Gauss (1777–1855). He was justifiably known as Princeps mathematicorum, a Latin title meaning “Prince of Mathematicians” or “Foremost Mathematician.” Gauss was also known in his own day as the greatest mathematician since antiquity, and he himself referred to mathematics as “the queen of sciences.” He spread his academic and intellectual net widely,

making massive contributions to astronomy, statistics, number theory, geophysics, and electrostatics. Gauss’s theories are at the forefront of the debate about whether mathematics is a science, and so much of that debate hinges on the definition of what constitutes a science as opposed to a field of knowledge.

Sir Francis Bacon (1561–1626) combined philosophy with statesmanship and a deep knowledge of legal matters, but his contribution to science and the scientific method may be reckoned as his most worthwhile memorial.

The Baconian method of studying science aimed to investigate the cause of a phenomenon, especially what made it different. He advised researchers and investigators to make lists of where the phenomenon occurred and where it did not occur. The lists were then ranked in order according to the strength of the influence of the phenomenon being studied. From Bacon’s underlying principles came the idea of natural science as distinct from other fields of knowledge and the various methods of making progress within them. The natural sciences were closely concerned with experimental procedures, and this gave rise to the controversy over whether mathematics could be classified as a science if it was capable of functioning without a reliance on experimentation. Einstein, who had an amazing gift for summarizing major facts succinctly, said that when mathematical laws referred to reality, they were not certain, and when they were certain, they didn’t refer to reality.

Francis Bacon

Sir Karl Raimund Popper (1902–1994), undoubtedly one of the greatest philosophers of science of all time, argued that mathematics was much closer to the natural sciences than it seemed. The outstanding physicist John Ziman (1925–2005) held the view that science is best defined as public knowledge, and must, therefore, include mathematics. Different philosophers and scientists hold varying views, but the weight of evidence, and the increasing importance of experimental mathematics, would favour the idea of including mathematics among the sciences. It is undeniable that it forms the solid rock foundation upon which many sciences are built, especially physics and chemistry.

Mathematics and numerology can be thought of as originating rather like a pair of conjoined Siamese twins, but they have separated over the millennia. Just as academic mathematics can be seen to belong in the vicinity of the natural sciences, so numerology belongs in the vicinity of magic. Magic can be defined and described as what are believed to be methods of altering and manipulating the environment (people and things) by supernatural means. These so-called supernatural means can be thought to include knowledge of occult causes and effects that are unknown to science. It is an essential part of science to rely on observation and logical analysis; it is an essential part of magic to believe that there are inexplicable forces beyond logical cause and effect.

There are ways in which magic resembles religion. Although heavily criticized by later thinkers, Sir James George Frazer (1854–1941), author of the monumental work on anthropology The Golden Bough (1890), worked out a succession in which the earliest peoples tried to control nature by using magic, which gave way first to religion and then to science. Fundamentally, Frazer argued, humanity had attempted to control the environment by using what were believed to be the inexplicable and illogical powers of magic. When these palpably failed so frequently, and were clearly seen to be ineffective, our remote ancestors turned to religion. When their magical activities — rituals, liturgies, spells, and incantations — did not control the environment, they thought that they must appeal to the gods to help them. In due course, as millennia passed, it became clear that appealing to the gods was also ineffectual. Along with the decline in religious belief came the realization that science could succeed far more often than either magic or religion. If making magical gestures and reciting curses failed to kill the enemy, and if prayers to divine beings also failed to halt the advance of the foe, then the invention and employment of superior weapons based on scientific principles would bring an opponent down. Where magic and prayer had failed to accomplish the desired results, scientifically designed Gatling and Maxim guns could cut the enemy down very effectively.

There are contemporary magicians — numerologists among them — whose theory of magic regards it as some strange kind of bonding with largely unknown universal powers. They believe that if some magical act is performed, through manipulating numbers, reciting incantations, making magical passes with the hands, or flourishing a magic wand, then a result will occur elsewhere in the universe. If it is benign white magic, the magician believes that a sick person will recover, or a lost person will be found alive and well. If it is dark, negative magic, the black magician believes that someone will suffer financial loss, a healthy person will become ill, a sick person will die, or someone previously honest and well-balanced will delve into criminality, vice, or drug misuse. Another view of magic held by some contemporary magicians is that it is not itself a controlling or directing phenomenon, but a way of contacting powerful spirit beings who will carry out the magician’s will when asked to do so.

Numerology can also be thought of as the search for a link between some measurement, or counting process, and life itself — a link that numerologists believe can be used advantageously. The number may be thought to control the environment, or individuals within the environment, or to predict what has been revealed by the supposed environmental link. Put in its simplest and most basic form: the number “7,” for example, may be thought to cause good things to happen, or it may be thought to predict the good things that are about to happen without having any causative influence over them. Theory number 1, the causative theory, likens the magical, influential number to a hand and arm that can manipulate events. Theory number 2, the predictive theory, likens the magical number to an eye that can see and predict, but cannot influence or manipulate events.

In his book, Numerology: Or What Pythagoras Wrought, highly analytical mathematician Underwood Dudley discusses the Elliott Wave Principle used for analyzing the behaviour of stocks and shares. The Wave Principle was the creation of a professional accountant, Ralph Nelson Elliott (1871–1948). It’s a form of technical analysis that investors can use to analyze cycles in financial markets, and so make substantial gains by buying and selling at appropriate points in those stock market cycles. Market trends can be analyzed by studying investor psychology and the ways in which stock market prices change. Elliott’s book, The Wave Principle, came out in 1938. A later book, Nature’s Laws: The Secret of the Universe, appeared in 1946, just 2 years before Elliott’s death. In it he argued that humanity was rhythmic by nature and human behaviour was therefore also rhythmic and cyclical. From this basic idea Elliott deduced that human behaviour could be predicted with remarkable accuracy, and that those who knew how to understand and use this wave information could make a success of buying and selling on the stock exchange.

An interesting suggestion regarding wider and deeper aspects of numerology follows from this preliminary look at the Elliott Wave. Scientists recognize that series, cycles, and rhythms are part of natural life, including human life, and that they are also susceptible to numerical analysis. Series, cycles, and rhythms can also be observed and recorded. It could perhaps be suggested that where numerology appears to produce positive results it is because the numerologist has linked up, either knowingly or unknowingly, with a natural rhythm, series, or cycle. Examples include circadian rhythms and the so-called “body clock.” These biological mechanisms control human times of activity and inactivity. Scientific and medical research has observed that these body clocks and circadian rhythms operate on an approximate period of 24 hours. Reflection on our own physical and mental experiences indicates that there are times in the 24-hour cycle when we feel alert and energetic, while at other times in the cycle we feel sleepy and lethargic. For many self-observers, there are perceptible high points of mental alertness between 8:00 and 10:00 in the mornings and again between 8:00 and 10:00 in the evenings. Physical strength and energy peaks later than the mental summit in the mornings — on average, about an hour later. In the evenings, however, the peak of physical strength and energy comes an hour or so before the mental peak is reached.

Medical scientists and expert neurologists have located an area in the hypothalamus containing approximately 20,000 neurons. This is known as the SCN, or suprachiasmatic nucleus, and acts as the body’s super-clock, or biological pacemaker. The external stimuli, which appear to stimulate its activities, are generally thought to be associated with sunlight or bright daylight. As light decreases at the end of the day, the eyes and associated visual system transmit messages to the suprachiasmatic nucleus, which signals another gland to produce more melatonin. This, in turn, produces a feeling of tiredness and sleepiness. Lengthy experiments with subjects being deprived of light tend to indicate that without the natural 24-hour light and darkness cycle the body clock moves to a 25-hour cycle. Numbers and time measurement are at the core of any understanding of circadian rhythms, and this can provide essential data for numerologists.

The seasons of spring, summer, autumn, and winter are a major example of a natural cycle that can be assessed and analyzed numerically. Rather less obvious than the cyclic nature of the 4 seasons are the biogeochemical cycles, yet they are very real and are subject to numerical, scientific analysis. Some of these cycles are gaseous and others sedimentary. Gaseous cycles store the element that is being analyzed and followed in the earth’s atmosphere. Sedimentary cycles store the element that is being tracked within the earth’s crust. The carbon cycle provides an important example. Plants absorb carbon dioxide from the air. Herbivores, such as rabbits, eat the plants. The carbon absorbed from the plants creates tissue for the herbivore. Carnivores then eat the herbivores, and use the carbon they have ingested. Carbon dioxide is returned to the air when the animal breathes, and to the earth when the animal dies and decomposes. Plants can then take carbon from the soil and the whole cycle continues. The carbon in the cycle can be weighed and measured, and therefore is subject to numerical analysis.

The water cycle provides another useful example of a natural cycle that can be analyzed numerically. Water evaporates from the surfaces of lakes, seas, and oceans and forms clouds. When the meteorological conditions are right, it falls again as rain, sleet, hail, or snow. It is then evaporated again, and so the cycle continues. Precipitation and evaporation can be weighed, measured, and analyzed numerically.

Later chapters will deal in full with the meanings of different integers as understood and used by numerologists. At this early stage, however, it will be useful to give a broad interpretation of the basic meanings assigned to numbers, as this allocation of meanings marks a clear distinction between scientific mathematics and the “magical” aspects of numerology. The “0” is one of the most powerful of all numerological symbols. It can represent everything from the entire universe to nothingness. It can signify ascent and descent. The “0” is unlimited and eternal. The figure “1” stands for individuality. It can also indicate aggression and assertiveness, determination and drive. It also has a masculine aspect. The figure “2” stands for balance and unity, receptiveness and understanding. Opposite to number “1,” the “2” has a feminine aspect. Number “3” symbolizes fairness, objectivity, and good judgement. There is a sense in which numerologists regard it as the symbol of neutrality. The figure “4” represents creativity, originality, inventiveness, ingenuity, resourcefulness, vision, and inspiration, whereas “5” can be problematic. Many numerologists think of “5” as indicative of vigorous action, movement, restlessness, and an inability to find calmness and peace. “Six” symbolizes responsibility, dependability, and trustworthiness. The figure “7” is one of the very best. It means thoughtfulness, wisdom, knowledge, and insight. “Seven” can signify a careful attention to detail, consideration, and contemplation. Number “8” stands for power, but can also entail sacrifice. “Eight” is sometimes thought of as a heroic number; it signifies gallantry and noble courage. The “9” signifies change of a major type: movement from one lover to another, from one religious faith to another, from one philosophical persuasion to another.

It should be noted that numerology is known and practised globally, and the list of numbers and their meanings can vary considerably from one location to another.

One important Chinese system is associated with the sounds of certain letters and numbers. In this system, “1” represents certainty; “2” is ease, comfort, facility, and simplicity. Number “3” is life, self-awareness, and existence, whereas “4” is associated with water, which is considered to bring wealth and good luck. In a different Chinese system, however, “4” is thought to be a warning of impending death. The number “5” is the self, the individual, the person, the self-conscious entity. In this system, “6” is thought of as a stronger version of “2.” It represents ongoing easiness and smoothness, a situation that is pleasant all the way, and enduring happiness. Whereas “7” is a supremely good number in Western numerology, it is regarded as being negative, crude, and vulgar in this Chinese system. The “8” has some similarities in both systems. Here, it symbolizes the prosperity and good fortune 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.