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Orgone is the measure of a person's connection with the cosmos. It is the conduit through which the power of the cosmos flows, focused through a sorcerer's will. Ritual practicioners must draw on this reserve of power in their souls to make a magic spell work. Spells require a constant infusion of Orgone through rituals that are performed inside a transmutation circle. These rituals require a number of ingredients and can last anywhere from 30 minutes to several hours depending on the spell. There are five types of magic that spells revolve around.

  • Enchantment Spells – These are spells designed to capture cosmic power within a crafted item, so that its power can be called upon in times of need.

  • Scrying Spells – These are spells designed to allow a user to perceive in ways that go beyond his fve senses.

  • Protection Spells – These are spells designed to ward a user, object, or location against a variety of possible harms

  • Transmogrifcation Spells – These are spells designed to fundamentally alter or control another being

  • Transmutation Spells - Changing the makeup of different materials or combining them with others to make new forms of matter.

A mage can create a familiar, creatures made purely from orgone, to assist in their rituals. They are made from a mage's soul and serve as a direct reflection of their inner self. They may have unique abilities, but their main purpose is to serve as magical batteries. They allow a mage the ability to bypass ritual circles and their ingredients to perform spells, reducing time frame from hours to literally minutes. They also make the particular spell more powerful, allowing mages to become masters of their craft. The drawback is that it limits a mage to one of the five types of spells. While these specialist mages are the most powerful individuals in their field, once they choose which form of magic to master, they lose the ability to perform the other types forever.

I need a good reason for why a familiar binds their mage to a particular type of magic. Why would it make you all powerful in one but block your access to others?

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  • 1
    $\begingroup$ you may want to Blades series by kelly McCullough, that is very close to how the magic of that world works. familiar have levels of intelligence and an elemental or magical nature that influence what spells you can use, you don't pick a familiar the familiar picks you based on your strengths and personality, nearly any magical creature is a possibility. it might be a living shadow, miniature gryphon, small elemental, undead minion, or if you are unbelievably lucky giant ancient immortal dragon. $\endgroup$ – John Dec 23 '18 at 6:34
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Access to all forms of magic is a meta-stable equilibrium, which is disturbed by familiars. Such equiliria, such as a broomstick balanced perfectly still on top of your hand or a ball balanced perfectly atop a smooth hill, are known for appearing stable in the short term but rapidly degenerating into a lower energy state. Humans, of course, are famously good at managing such equilibria. Any tight rope walker is a demonstration of this! We even manage to find tiny stable equilibria atop the metastable. Gravity Glue is my favorite artist for this. He finds the tiniest of stable configurations in rocks, where three miroscopic points form a base, right at the top of an otherwise metastable rock configuration:

Amor Fati

Of course, the price we pay for such art is that one can only make small motions. If you look at Michael Grab (the artist that is Gravity Glue) in action, it's almost... boring. He has to be in a meditative state, feeling for the tiniest of nuances in each rock as he slowly balances them. If you're into immediate gratification, balancing rocks in a metastable state is not for you!

Of course, if one moves to a point of stability, one can move as hard as one wishes. Just look at the Sith Lords, and how they move from positions based on personal power. But which position do you take? What if there are five, and you know you are going to lose access to one of them? How do you choose? And why can't you straddle them, so that you have access to more options?

Mathematicians provide fascinating options for this. Newton Basins may be the most accessible.

Newton Basin

Newton Basins map the result of applying Newton's Method to solving an equation. The one above is for an equation with 5 solutions, akin to your 5 forms of magic. The colors represent which root you end up at when you start at that point and apply Netwon's Method over and over. Note how complex it is near the fringes. If you try to find a solution in one of those areas, you can arrive at any of the answers! This prevents "straddling" to try to retain access to all magic.

Now what you do with this depends on how you want the story to go. The familiar creation ritual needs to fit in with your world. However, if I may fill in some details, I could create such an example.

A mage reaches a point where balancing all of these options gets to be too much. Such a decision can be overwhelming. Nobody likes to lose something forever, least of all an entire form of magic. The familiar is a creation embodying the act of decision. One creates a familiar to decide which of the 5 basins to strive after, and ties one's soul to the familiar, literally dragging the mage in that direction.

But one does not always have to decide. One can also leave the decision to the familiar. After balancing the familiar as best as they can between one, two, three, four, or even all five options, they let it go, and let fate and the familiar decide which basin they are pulled to forever.

There are whispers of mages who balanced between all five, and their familiar never fell into any one basin. They just remained balanced, oscillating back and forth across all magics. This, of course, is naturally unstable, but if a skilled mage were to seek stability, bouncing from form to form, they could keel their familiar from converging on one form of magic forever.

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  • $\begingroup$ Keel their familiar? $\endgroup$ – Joe Bloggs Dec 22 '18 at 18:56
  • $\begingroup$ @joebloggs - likely “keep” $\endgroup$ – Megha Dec 24 '18 at 5:00
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The soul is a metaphysical structure that both stores and focuses Orgone. In its natural state a mage's soul is malleable. It can bend in such a way as to focus any of the five types of magic using an appropriate procedure. That's what those rituals are for. They're designed to mold a mage's soul in just the right way as to make them conducive to perform the type of magic that is desired at that time.

Unfortunately this same quality of plasticity that makes the soul so versatile also precludes it from ever being optimally suited to any one task. A mage can never make it take exactly the form they want it to. As much as one tries via ritual to shape the soul in just the right way to be maximally proficient for a type of magic, it just never will. It will always bend and droop and ooze bringing it away from the design you'd want to impose on it (imagine trying to shape cookie dough into a perfect cube, without cooking or freezing it of course). To avoid this problem the soul would have to be made rigid.

At its most basic, that is what a familiar is. It is the soul (or a part of it at least) of a mage made rigid. It is a soul perfectly sculpted to serve as the optimal conduit for one of the types of magic. This is what makes spells performed using a familiar so much more powerful. This is also what allows mages to bypass the need for any ritual. There is no need to mold the soul in an arduous and time consuming process, it already is in the right shape. Indeed, it always is. The drawback of course is that as much as the familiar soul is perfectly suited to one of the types of magic, it is also permanently perfectly unsuited to the other four.

A mage must either accept that their soul will never be just right for any craft, or decide to permanently cut of the soul's ability to flow freely: reaping an enormous advantage in one area of magic but simultaneous making it impossible to perform any of the others ever again. Sad really.

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Familiar affinity to spell type produce instability on others

Each human has a small affinity over one of the spell types, a mage might note that he is quite better in one spell type that in the others, like everybody, even in magic people has preferences, talent or flaws.

Familiars are just a representation of the metaphysical soul of the person, made by orgone and part of the soul's caster. This metaphysical representation of the soul is greatly exponentiated, talents become super-strengths, while flaws become immense vulnerabilities. A familiar is greatly focused (or specialized) in one type of magic, it's whole body either physical, mental, spiritual and magical has been made for one type of spell, to produce maximums effects.

Try to cast another type of spell with the same familiar will cause instability in the familiar body, causing magical distribution, metaphysical collapse and degeneration of familiar soul, which is by extension the caster soul. Obviously, damages in souls aren't good things...

Familiar unwillingness

Maybe an extension of another idea, familiars have affinity over a type of magic, and because they are sentience creatures they can decide. If you try to cast a type of spell which isn't its affinity the familiar will greatly refuse, maybe disturb the spell, attack you or scape (no longer obey your command).

Maybe cast other spells hurts the familiars and so they are unwilling to cast them. They suffer is spells don't share an affinity towards them.

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The familiar is super enthusiastic about one type of magic. If you try to do another one, it gets surly and pissy.

Familiars are like your picky friend who only likes pizza. If there is pizza she is great company and the good times roll. The stuff she puts on the jukebox makes everyone dance in their seat - one time she busted a move and strangers got up to dance with her. She buys beers all around. If it is pizza, she is not choosy - she will feast on just about any kind of pizza. You start the night with her and with pizza and it is going to be a fun night.

But you try going for Mexican and she is quiet, sullen, wondering why you didn't go to the perfectly good pizza place right down the street where they know you and usually give you free breadsticks. She reminds you that cute waitress (Chloe!) works there and she thinks Chloe likes you. Plus she got sick on guacamole one time and threw up and it was green, then it turned dark green. Nothing can make her happy. She does a tequila shot on an empty stomach. She gives everyone the hairy eyeball and leaves early.

Pizza is good and your friend is a lot of fun when she is having fun. If you are going out and she is along, keep her happy. Go for pizza. So too your familiar. Keep it where your familiar is comfortable and things go great. Step out and suddenly your familiar is a surly jerk.

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Magic proceeds from the five Platonic solids

TL;DR: Platonic solids fits all your criteria because

  1. There are five of them
  2. They have enough fancy geometrical properties to produce appealing transmutation circles
  3. They come in pairs just like mages and their familiars

With a bit of extrapolation about how Orgone flow works, this leads to attribute the binding to a circuitry that connects edges of a Platonic solid to the faces of its dual, an actual geometrical property of those solids.

Platonic solids

To cast a spell, one must establish a flow of Orgone that fits a regular geometrical patter meeting the following criteria, sorted from most to least fundamental:

  • Orgone conservation law implies that the flow must be a closed circuit
  • Inertial principle: if not submitted to external influences, Orgone flows along straight paths, except at transmutation nodes where a mage can deviate their course => the flow must be a polygon
  • Laminar flow principle: if provided with the opportunity, Orgone will flow laminarly. That means that if two streams of Orgone cross each other, the flows will not intermix, and therefore the circuit will split itself into two disconnected circuits => no crossing allowed

    laminar flow

    Figure 1: Laminar flow crossing

  • Resonance is achieved when a high level of symmetry is respected by the nodes of the Orgone circuit. These symmetries are given by the $T$, $O$ and $I$ symmetry groups.

As it happens, 5 sets of node coordinates fit the last requirement in three dimensions. Connecting those nodes forms what is known as the Platonic solids. Each type of spell corresponds to one Platonic solid, which explains why there are five of them. They have been related to elements by Plato, also have relations to planets of the solar system due to Kepler in case either are components of your magic system.

  1. Tetrahedron - 3 triangular faces - $T$ symmetry group - associated to fire by Plato <-> Transmutation
  2. Octahedron - 4 triangular faces - $O$ symmetry group - associated to air by Plato <-> Scrying
  3. Hexahedron (cube) - 6 square faces - $O$ group - associated to earth <-> Protection
  4. Isocahedron - 20 triangular faces - $I$ group - associated to water <-> Transmogrifcation
  5. Dodecahedron - 12 pentagonal faces - $I$ group - associated to celestial bodies (or arguably to ether via Aristotle, see wikipedia) <-> Enchantment

The three other laws imply that the Orgone circuit to cast a spell must match one Hamiltonian cycle of the corresponding Platonic solid. In short, this is a closed path that visits each node exactly once, while travelling only along edges. It so happens that Platonic solids all have an associated Hamiltonian cycle. In fact there are many such paths, which sub-categorizes spells.

transmutation circles

Figure 2: Transmutation circles for some sample spells and relationship to full three dimensional form of the spell

Now, to perform the spell correctly, these paths should be drawn in three dimensions, but without any medium to draw the path out of thin air, this is rather impractical. Instead, what mages do is to draw two dimensional projections of Platonic solid on the ground, also known as transmutation circles. They then activate some edges of the graph along an Hamiltonian cycle, which triggers the flow of Orgone and casts the spell.

This form is weak, though versatile. A way to become stronger is to create a familiar.

A mage can create a familiar, creatures made purely from orgone, to assist in their rituals. [...] They allow a mage the ability to bypass ritual circles and their ingredients to perform spells, reducing time frame from hours to literally minutes.

A familiar, though it may have an outer shell corresponding to the personality of the mage, also features a geometrical core, which corresponds to one of the 5 Platonic solids. It embodies the Orgone circuit, which means the transmutation circle becomes unnecessary. It also means that the actual three dimensional resonant structure is achieved, hence the stronger performing spells. On the other hand, only one category of spell is possible, though multiple Hamiltonian cycles remain available.

They are made from a mage's soul and serve as a direct reflection of their inner self.

As it happens, each Platonic solid has a dual, which share the same symmetry group. Hence the octahedron is paired with the hexahedron (cube), the dodecahedron with the isocahedron, while the tetrahedron is paired with itself. One obtains a dual solid by interchanging vertices and faces of the original solid.

To create a familiar, one must first carve its own soul into the shape of the dual type desired. Then, the familiar is obtained by connecting the adjacent faces of one's own soul with Orgone, which produces the geometrical core of the familiar.

The last step consists in letting the familiar exit the mage's body, which requires to animate it: that's why the mage has to embed the geometrical core into a creature with its own will. The specific way this is done is left at the courtesy of the mage, which explains why every mage has their own familiar.

familiar_binding

Figure 3: Fully formed familiar (artist rendering)

The price to pay is that the Orgone flow out of the mage's soul are now bound to the nodes of the geometrical core of the familiar, therefore the mage can not produce Orgone circuit via a transmutation circle as before. This means that only one type of circuit can be achieved, and hence one type of spell.

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  • $\begingroup$ I apologize for the clumsy 3D views: they are based on hand-drawings. I will generate better ones if I find the motivation some day. $\endgroup$ – Alexis Dec 24 '18 at 16:46
  • $\begingroup$ And if you need complementary magic types, have a look at Kepler solids. $\endgroup$ – Alexis Dec 24 '18 at 17:25

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