Gematria
By Donelle Darkefell
Gematria is the system by which hidden truths and meanings are discovered within words. Each letter of the alphabet correspodns to a number. Numerical values of words are totalled and these are said to correspond with words who share the same values. In Jewish mysticism this is a traditional system for trying to better understand the Bible. For example, one rabbi shares this anecdote:
"I noticed that in the building of the ark the ark was built not by one person or even a small group of craftsmen, but instead, everyone in the community contributed whatever they could in its construction. Thus we learn that God can dwell among us when we come together as one. To understand this further I examined the gematria of Bezalel who was the craftsman selected to head this project. The name Bezalel has a gematria of 153 which is the same as HaPesach, the Passover. From this I realized that every year at Passover we can experience the same sense of community and coming together that occured during the building of the ark..."
Magical craftsmen use gematria daily in the designs of their gadgets. It is common to choose an overidding "theme word"(in the common Gematric languages, Greek, Hebrew, or Coptic) around which the object will revolve, finding its gematria, and using those numbers or derivatives of those numbers in the design specs. For example, if I wished to design a pillow which helped people to overcome nightmares, I might choose the Greek word n EJPnrn 0EoV (OOC note: rendered as best as I could on typed format), meaning "the peace of God". The numeration of this word is 1443 and the serial is 167. I might then choose to make it 14.43 centemeters long and 16.7 centemeters wide. In gematria decimals are not used, so it is safe to insert them to make reasonable proportions and still impart the value of the word to the design. Doing this also strengthens any charms or runic enchantments later placed upon the object. This method was first used in Babylon, by kings who would create building specs with gematria that corresponded to their own names. By doing so, these kings felt they'd obtained a measure of immortality, and imposed a part of their personality on that section of the Empire forever.
In red ink: I am truly impressed Ms. Darkefell. I am glad you have enough interest to take the initiative and study a topic that has yet to even come up in class. The combination of historical references and the pillow example show you have a true grasp of the subject at hand.
Pinnacles
By Callie O'Connor
As we go through life, we experience drastic changes and events. These major life changes are examined and projected in Numerology via Pinnacles. In this system, life can be divided into 4 major phases: youth (spring), the burgeoning of family and responsibility in indpendent adulthood (summer), maturity as a person enters middle age (fall), and the richness of all experience of life which occurs in old age (winter). Pinnacles utilize a combination of numerology based upon birth date, rather than assigning values to the letters of a querantbs name (unlike soul urge, expression, and inner dreams).
In addition, the dating of the 4 phases of life is dependent upon a querantbs life path number. For the purposes of this essay, I shall use my birthdate, April 27, 1957, for the example. Thus, the life path number in use is 4+9+4 (the last 4 reduced from 22), or 1+7, thus 8.
calculate the master number of each of the four periods, the method is as follows. The resulting number reflec reflects the tenor or tone of the period, rather than an exact prediction of what major life changes will occur.
First period: Month and day of birth are added together. In this example, 4+9=13=4.
Second period: Day plus year. 9+4=13=4
Third period: First and second pinnacle are added together. 4+4=8.
Fourth period: Month plus year. 4+4=8.
In this example in particular, the numerological pattern of that date becomes clear. (4, 4, 8, 8). Note that Pinnacles usually are not so consistent in their master numerical values. Using the Life Path number (8), the pinnacles are determined to occur on the following schedulue:
First Pinnacle (spring): birth-28
Second Pinnacle (summer): 28-37
Third Pinnacle (fall): 37-46
Fourth Pinnacle (winter): 46 and on
There are two different Pinnacle numbers reflected in this analysis: 4 and 8. The 4 Pinnacle is generally associated with organization and structure, a life lived through effort and determination and the desire to achieve via hard work. The 4 Pinnacle is practical and realistic. Fittingly, the 8 Pinnacle is associated with business and capital enterprise. Like the 4 Pinnacle, this is a pragmatic number, emphasizing organizational skill and work abilities. The 8 Pinnacle is often associated with improvements in work or financial situations.
For this particular reading, the 4 pinnacle for the First Periods can be seen as indicative of hard work, often relating (given its first phase), to heard work in school, often at the expense of the usual schooltime hobbies, or economic need (such as having a summer job to help pay bills). In the Second Period, the 4 pinnacle is indicative of steady and continued growth as one becomes an adult and enters the workforce and the prime of life. Switching to the 8 pinnacle for Periods 3 and 4, we see continued job growth, perhaps having- at this later stage of life- reached the top of the career ladder, ambition and success being major motivators. By retirement age, the person with an 8 pinnacle has not, in fact, retired, too enmeshed in work to do so. They occupy a position of status and power, having spent their lives building their success.
Again, the Life Pinnacles are not an exact predictor; they use the power of numerology to give a sense of direction, of motivation and drive, of the forces at play. They are neither a blueprint to be followed nor a warning to be heeded, but rather can help us make decisions and see the forest for the trees. In this, they are an excellent tool.
In red ink: Certainly up to the expected level Ms. O'Connor. Pinnacles are a truly difficult subject, and of the level suited for a student only a year from NEWTs. Excellant work, and evaluating your own numbers shows that you truly grasp the subject at hand.
Life Path Numbers
By Christopher Evans
Doing research into Numerology I found three different methods for determining a persons Life Path Number. One involved the date of a persons birth and the other two were different ways of determining the number through a persons name. I have broken my report up into each of these methods, the numbers I got and what they mean.
My life path number that I determined though the date of my birth, January 28, 1957, was 6. That was gotten by adding 1+28+1957=1986 then 1+9+8+6 = 24 and finally 2+4 = 6. The possible out come numbers for this method are 1 - 9, unlike the numbers give though names. The designation of a 6 bears with it the title of The Romantic. It is said that 6's are idealistic and need to feel useful to be happy. A strong family connection is important to them. Their emotions influence their decisions. They have a strong urge to take care of others and to help. They are very loyal and make great teachers. They like art or music. They make loyal friends who take the friendship seriously. 6's should learn to differentiate between what they can change and what they cannot. This is, I feel, very accurate to my personality, especially the last part for I don't believe there is anything that I can not change if I put my mind to it.
The next method I attempted was the Chaldean method, which assigns a number to the letters making up a persons birth name. Chaldean numerology was originally developed in Ancient Babylon, and combines Kabbalistic name interpretation with aspects of astrology. The 9 is considered holy and therefore is kept apart from other vibrations, except when it results as the sum of vibrations. In Chaldean numerology, compound numbers always used. Single digits represent the outer aspects of a person, while double digits reveal inner influences. Using my birth name, Christopher, I arrived at the number 9. I got this number by: Christopher = 3+5+2+1+3+4+7+8+5+5+2 = 45 then 4+5 = 9 The number nine is, as stated above, considered to be a holy number and gives the title of The Performer. It says 9's are natural entertainers. They are very caring and generous, giving away their last dollar to help. With their charm they have no problem making friends and nobody is a stranger to them. They have so many different personalities that people around them have a hard time understanding them. They are like chameleons, ever changing and blending in. They have tremendous luck, but also can suffer from extremes in fortune and mood. To be successful they need to build a loving foundation. This reading, while it does contain some of my characteristics, isn't as accurate as the number 6.
The last method I used was the Pythagorean which, like the Chaldean method, assigns numbers to the letters of a persons birth name. Unlike the Chaldean method the number 9 is in the calculations and the letters are more evenly distributed. The Pythagorean method was developed by Pythagoras, a Greek mathematician and metaphysician who lived during the 6th century BCE. Similar to above I did: Christopher = 3+8+9+9+1+2+6+7+8+5+9 = 67 then 6+7 = 13 then 1+3 which gave me the number 4. The number 4 has the title of The Conservative. 4's are sensible and traditional. They like order and routine. They only act when they fully understand what they are expected to do. They like getting their hands dirty and working hard. They are attracted to the outdoors and feel an affinity with nature. They are prepared to wait and can be stubborn and persistent. They should learn to be more flexible and to be nice to themselves. This reading I don't agree with at all.
Having looked through all three menthes I got 6, 9, and 4. Of the three numbers I find my self most compatible with the reading given by the birth date analysis of 6, but the Chaldean method that gave me the number 9 was also good. Based on these results I would have to say that the best method of deriving ones personal life path number is using one's date of birth. This ties in closely with astrology as well as the Chinese Zodiac. The closeness of both numbers, however, lead me to believe that we are partially shaped both by the time of our birth and the names placed upon us at our birth.
In red ink: While this is a decent essay Mr. Evans, you are going into NEWTs next year, and this is a fairly basic level topic. Also, a better explanation of the difference between the Chaldean and Pythagorean methods would have been an improvement. Keep in mind that most often, such numbers are obtained with the full birth name, first, middle and last. Also, such methods are more commonly considered to obtain what is now called the expression number, with life path being generally accepted as attained through the birth date. While these methods are historically accurate, it bears mentioning.
Geometric Series
By Vivian Barlow
In 1956, Argus Eliot derived a certain geometric series contributing to the greater predicting power of the Arithmanic method. Since then, there have been refinements to his system, but the essence of the system has remained the same.
But, to explore this series, first some definitions should be explained. A series consists of a sequence of values added together. If there is an infinite number of values added together, this is called an infinite series. These are written in summation form using the Greek letter epsilon to indicate the operation; the summation is bounded by the numbers below and above the letter, increasing by 1 each time for each loop. For example,
5
\ 2 = 2 + 2 + 2 + 2 + 2 = 10
/_
n = 1
5
\ 2n = 2(1) + 2(2) + 2(3) + 2(4) + 2(5) = 2 + 4 + 6 + 8 + 10 = 32
/_
n = 1
In particular, a geometric series is a series where each succeeding term is multiplied by a value. For example,
1 + 1/3 + 1/9 + 1/27 = 40/27
That series could be written in summation form as,
3
\ 1 * (1/3)^n = 40/27
/_
n = 0
However, if one uses an infinite geometric series, there may be a special formula to calculate the value. In general, an infinite geometric series resembles,
Infinity
\ a * r ^ (n - 1)
/_
n = 1
(a and r are real numbers)
However, if |r| < 1 then the exact value of this series can be calculated as -
a / (1 - r)
If this is the case, then the series is considered convergent, because it 'converges' to a single number. Otherwise, if |r|> 1 or |r| = 1 the series is divergent, because it continually adds up to approach infinity.
In particular, then, Mr. Eliot figured the importance of this series to divination. The variable a is significant as the Chaldean life path derived from birthdate. And the r is important as a determination variable, which varies depending on circumstances. For example, the "chance of success in common projects" is defined as -
r = |10 / age + q|
Where q is called the individual constant. This constant requires a complex formula to determine, that is far beyond easy determination and varies with situation. In this case, it depends on individual skill.
However, at the end of this divination, different conclusions can be drawn based on whether the resulting series diverges or converges. If the series converges, then significance can be drawn from that answer. The fifth edition of The Geometric Series Reference written by Eliot himself explains these numerous circumstances. For example, let us examine divination for a quidditch game.
Let,
a = 6 (the author's life path)
r = |e + age/10 - q| = 1.2 (approximately, e estimated as 2.71)
q = 3.21 (courtesy of the included magical calculator with the reference book and depends on team skills. This divination considers Ravenclaw v. Gryffindor)
Infinity
\ 6 (1.2) ^ (n - 1)
/_
n = 1
This example diverges, suggesting that, indeed, Ravenclaw will lose. If it had converged, further interpretation would be required to determine if there was still a loss and, if so, by how many points. The great flaw in this original idea is that it relies on the individual life path. Later formulas which are more complicated use 'a' values that better reflect true circumstances.
In conclusion, this method is rather complex, but can be fascinatingly truthful. It is among the more accurate methods, but requires significant computation time. This essay has only addressed the simplest form, but the more accurate and more useful forms are far too complex to attempt for those who have not pursued higher level mathematical and arithmatic studies.
Works Cited:
Eliot, Argus. Muggle Mathematics and Divination. Haunted Press: New York, 1956.
In red ink: I am truly, truly impressed Ms. Barlow. This essay not only shows an impressive grasp of the uses and interpretations of arithmancy as a form of divination, but also and AMAZING grasp of mathematics. If you are not already planning on receiving a NEWT in Arithmancy, I suggest you do so.