Professor Paxar
Subject: Mathematics
Alignment: Phlegm
Orientation: Journeyman
Position: Chorus

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Paxar is deep, troubled and at times very profound. The other professors hint that when Paxar went out beyond the walls he met an Outsider that claimed to be his father. They also say that Paxar dispatched this man, and has never been the same since. Paxar is a stern teacher, and assigns a lot of homework, not as much as Bellona, but an awful lot.



Lesson One: Numerology


Numerology is an occult practice that looks at the implications and meanings of numbers and attributes numbers to the letters of the alphabet to "Reduce" them and thus determine their meanings in a cosmic sense. In 1533, the Kabalist Cornelius Agrippa wrote a book entitled Occult Philosophies that was based on the previous work of Pythagoras. Here is the alphabetic conversion, according to Agrippa:
1 - A, J, S
2 - B, K, T
3 - C, L, U
4 - D, M, V
5 - E, N, W
6 - F, O, X
7 - G, P, Y
8 - H, Q, Z
9 - I, R

To "reduce" a number, it is broken down into its various parts. For instance: 34 = 3+4 = 7. 526 = 5 + 2 + 6 = 13 = 1 + 3 = 4.
The same is done with words, first you ascribe their numerical equivalent.
PAXAR = 7 + 1 + 6 + 1 + 9 = 24 = 2 + 4 = 6.
1 - The symbol of unity, often being associated with God, the Supreme Being who created the universe and represents transcendential reality. Among the world's once great religions: Christianity, Judaism and Islam is was the symbol of monotheism. Keywords:the origin of all things.
2 - A number associated with division and lack of harmony. As the opposite of one, it stands apart from god and is often considered an evil number. Two is also considered to be associated with the one who follows instead of leads,; therefore it has elements of tact and gentleness although these characteristics are usually combined with indecision and hesitation. Keywords: marriage, communion/evil, division.
3 - This number is regarded as spiritual and creative. It represents the powerful Trinity (casting in which three magi work together on one spell, found most commonly in Ritual Magic). In ancient Religions, three represented the Trinity of Christianity (Father, Son and Holy Spirit); in the Kabalah it represented the three Sephiroth (Kether, Chokmah and Binah) that were said to dangle over the Abyss; in Hinduism is represented the Triad of Gods known as the Trimurti (Brahma, Vishnu and Shiva) as the vital aspects of creation. In Numerology, and indeed magic based on numbers, it is considered a perfect number, for it contains a single beginning, middle and ending. It symbolizes intelligence, vitality, artistic ability and ambition. It is also a lucky number and is popular for the use on love Charms. Keywords: the Trinity mark, wisdom.
4 - Four is associated with hard work, practicality, and also unhappiness and defeat. People who's names "reduce" to four are said to be stolid and uninspiring, but often very methodical in routine work situations. They are plodding and unadventurous and do not attain success very easily. Keywords: solidarity, permenance, foundation.
5 - The number associated with versatility, restlessness, and adventure. People who's names "reduce" to five are said to love speculation and risks and a varied environment. They are fond of travel, and resist responsibility or any other factors in their lives that might tie them down. Keywords: Justice.
6 - Six is the number indicative of love, domesticity, family affairs (as in of the alignment loyalties), and loyalty. Six consists of the first male number (three) mixed with the first female number (two), and therefore characterizes productive and harmonious balance. Keywords: creation, labour, service.
7 - Seven is a number with mystical andmagical connotations. In ancient astronomy there were seven recognized planets. The world (according to genesis) was created in Seven days, Joshua and the Israelites marched around Jericho for Seven days, each of hte moon's four phases lasts Seven days, there are seven notes on the musical scale and seven colours in the rainbow. accordingly, Seven is the number of completeness, wisdom, spiritual truth and cosmic harmony. The Seventh Son of a Seventh son is said to possess great supernatural powers, or the Seventh daughter of a seventh daughter. Rumor has it that each of the four Metatrons was chosen for being the seventh child of a seventh child. Keywords: life.
8 - Eight represents strength of character and idividuality of purpose. People who's birthdates "Reduce" to eight are said to demonstrate independance of thought, a sense of coolness in their home/personal space, and often find it difficult to express ther inhibitions. Hod is the eights sphere of the Kabalah, and stands for Rational Intellect. Keywords: fullness, balance.
9 - Nine indicates cosmic significance, as nine is the number of Ethereal Spheres in ancient cosmology. As the highest of the numbers (as ten equals 1+0 = 1), nine symbolizes spiritual achievement and initiation. Keywords: cosmic significance.
0 - Zero is the concept of nothingness,absence of good or evil, a starting and ending point. It is the point of infinity, and it is nothingness. Standing alone, zero has no power and no meaning, but coupled with the other numbers it grants immense power, especially to casting. sometimes referred to as the number Ten, which stands for completeness. Keywords: Ether.

Lesson Two: Geometry

Geometry is, for lack of a better word, the skill of using shapes. Different Shapes mean different things, and the ways that different objects interact has different influences on all parties involved, especially those caught in the middle of these interactions. You most commonly see this in Astrology, and certainly the majority of Circle Magic is based on these principles.
There are two types of Geometrics: Inclusive and Inducive.
Inclusive Geometry
Inclusive means that the power the shape holds takes effect on anything within the shape, whether ir be 2 dimensional or 3 dimensional. These can easily be constructed around, drawn around, or the item placed within them to have a desired effect. Some are helpful and others hindering. The forms used to affect whatever they surround are called Shapes.
Circles: Circles are the most powerful of the protective Shapes. Circles are intensified if drawn with potent materials, such as salt for purification and against spiritual attack, blood against physical attack, purified water against monsters, and sacred earth against Outsiders. (-6% to defense, -9% if draw with the appropriate sibstance.)
Squares: Squares are stabilizing, balancing out alternate elements or juxtaposed powers of planets/colours/emotions etc. (-2 damage from opposed forces that would normally increase in damage)
Pyramids: Pyramids are amplifying, projecting wishing, hopes or intentions to the universe. Pyramids, obviously need to be constructed, and can be built to align with constellations, the planets or moon to apply to certain qualities of the celestial bodies, but even a small scale pyramid crafted from stone or mirror is a powerful tool. You place the object(s) symbolizing the wish to be obtained within the pyramid and meditate on the subject as often as possible. (-3% to meditation/tactics per turn consecutively passively meditated on)
Cylinders: Cylinders are a safe Shape, protecting from tampering with other energies, as opposed to physical protection, as that of a circle. They are useful in dealing with certain monsters (such as the Hiisi) and are also good for holding parchments, scrolls, or talismans with inscribed curses or Hexes. (-2 points damage)
Moons: Moons increase and clarify hidden potentials, especially of the magical, healing or feminine persuasion. (+1 Karma for female deities or deities of the moon/+2 damage for magic casting)
Spheres: Spheres are clairvoyant, offering vision, clarity and foresight to scryers and prophets. As a rule they can contain concepts and energies, and not physical matter. (-8% on skrying, divinations, clarity of though)
Cubes: Cubes are the potent containers of physical matter. They do not offer protection to what they contain, but they do prevent whatever is put inside from getting out. Make sure that the material the cube is made of is appropriate to the object one is attempting to contain. (+10% to attempted movements or attack)
Triangles: Triangles are direction, instilling changes or alterations to the subjects they surround. They are often used in interrogations, essence fusing and transformation magics. (Breaks targeting/+8% on influencing the target)
Rectangles: Rectangles are strength, offer support and bolster existing qualities in something. If the surrounded object is strong, it will become stronger, if it is fast, it will become faster. These effects are not permenant, but temporary boosts. It cannot reverse effects that already exist, such as making a cracked breastplate stronger by mending the crack, and canoot increase qualities that are not already present in some moderate form - like installing courage into the cowardly. (-5% to repeat any skills successfully completed in the previous turn of actions.)
Ovals: Ovals, or Eggs are incubating, instilling into something a quality it did not previously possess. There is a good reason the Incubators the Technicians use are ovular in shape. It takes a great deal of organization and materials to design which qualities will be imparted, and one must be careful to research all possible imbuements before using a substance on an oval, or side effects may occur. (+5% to resist the qualities being influenced by other successful augments)

Inducive Geometry
Inducive means that the effect between two or more entities or bodies causes a form of energy or influence between them that will then affect any object caught in their path, or within their effect radius. These are most often applied to planets, stars, and forces like friction and gravity. As one becomes more adept, they can begin to spin lines of geometrics out of the essence in the surrounding world to fabricate these Inducive Geometrics. The reactions between the objects involved in Inducive Geometrics are called Aspects.
Sextile: A 60 degree interaction. Sextile is favourable, with the involved bodies in a position where the augment each other's abilities, and are found to be compatible. It promotes harmony, but it is truly only a bringer of opportunity. In order for the affects to be of use, one must act on the Opportunities Sextile opens up.
Trine: 120 degrees. the most harmonious of aspects, Trine causes energies to combine with ease, including fusing of different Essences. The lack of challenge trine causes can leave one with a feeling of unfullfilment, emptiness or cheapness to the results. It is very subtle, and it's affects never extroardinary or flashy.
Square: 90 degrees. Considered unfavourable, it represents the struggle betweent he bodies involved, usually of two forces at cross-purposes. It incenses and angers, increasing stress, and exacerbating obstacles. This opposition can inspire increased growth through concentrated effort, yeilding more durable, stalwort results in both body training and plant growth, as well as relationship ties.
Opposition: 180 degrees. Exact opposites, causing hightened awareness, stress and perception. It does not necessarily intone a disfavourable relationship, as opposites do attract, and can be complimentary to each other.
Conjunction: Forces two items to take up the same point in time and space. It gives great strength to the energies of those involved, although it can be harmonious or discordant depending on the personalities or qualities of those involved.
Orb: A moment of perfect time for a chosen action. An Orb is when the involved body is at its strongest, but influences of Aspects have fallen either before or after the chosen action. The moment in which the action is taken, and found to be perfect carries with it an aura of influence which can then in turn cause or contradict Aspects of its own accord.
Delineation: the most introspective Aspect. It does not cause or affect actions or intentions, but causes further study or thought into the actual meanings of events or Aspects. The practise of Delineation enables one to examine all possibilities that lead to and from events and actions. One can then see where a certain action will lead - such as favourable or unfortunate results, and also can make themselves aware of repercussions that may result in a change of mind or heart.


Lesson Three: Pattern & Substitution


Pattern and Substitution is a delicate and difficult art. What it entails is basically replacing an ingredient with one or many of something else to equal the same affect. For example, in cooking you can substitute mayonnaise for eggs and milk and achieve the same flavour and affect in the end product. Likewise in magic, over the years Seraphim has discovered substitutions for certain required ingredients that might be hard or expensive to come by. Not all ingredients can be susbtituted, for instance, in Alchemy there are required ingredients, and then there are the tools and other ingredients you will need. The other ingredients and tools can often be substituted as long as the qualities or properties of the ingredients are compatible. It involves extensive study, and usually advanced apprenticeship with a registered Seraphim.