Haloed Bane

Magic in its Physicomathematical Aspects


Mermaid and Dragon

It isn't overly difficult for a well-trained third-grade Incula to morph into a mermaid or a dragon as here depicted as far as appearances go. Actually mimicking the qualities of these fantasies -breathing underwater or breathing fire, as the case may be- is far more difficult, and impossible to many. Even the great Sinduin, when she wanted to boast of her skills to that German pilot (cf. SS 16) produced for her grand finale but a mock dragon, whose tail for example was wholly made of a cartilage-like substance which would not done much good if she chose to use it to lash her pursuer. To morph into something like a true dragon, dissection and deep study of an actual draconic specimen would have been a prerequisite.

At heart, the abilities deployed by the sapient spacies of Belklaun, all falling under the umbrella term of saisan, can without exaggeration and despite their ubiquitousness be described in English as magical, because they entail a rupture with intelligible nature. The only difference between a magical process and a natural process is that the magical process includes at some point an event which breaks the laws of physics (or that cannot be at all explained scientifically by the understanding). One easy though unexpected corollary is that magic can be reduced to a science, as the only mystery is why X happens, not how to do X or bring it about so that X happens. The hard consequence is that no matter how much a species may master a set of magical processes, it can never be sure that some other species elsewhere doesn't know of another magical process which breaks physical laws another way, because although the knowable universal laws are a closed set, exceptions to said laws may in theory take an infinity of forms.

In what follows we'll deal with the simplest of cases, the universal magic known as jaisai (the only one the majority of Inculae are able to access) in its first two forms: the malleability of pleasure and pain enjoyed by second graders, and the malleability of form enjoyed by the third graders. Only half of Inculae reach the second grade, and even less the third, so it's a good starting point.

There are four fundamental elements required for the casting of a malleability spell (jaisaim vinonglaiglar or farkom jaisaima). These are:

  1. The Word/Phrase (zior, jaisaizior) = Deploying one of the malleabilities requires a verbal trigger. It can be a word, a phrase, or even gibberish, which option is usually preferred in the interests of secrecy, but the caster (jaisaimir) must be comfortable with the utterance and make it her own, as it were. Changing a phrase for a particular ability is a gradual process that can take weeks to fulfill. This first element is also the least important, but it can be decisive in a couple of instances: a) a person that cannot speak cannot cast a spell, period; b) During a particular martial encounter, a second party can learn (upon hearing it) what someone’s spell is and then adjust accordingly. In general, a spellcaster won't be able to change the phrase in mid-fray so the consequences are potentially enormous. Every spellcaster in Belklaun learns just how softly their phrases can be pronounced and still prove effective (mere articulation of the lips won't do, unfortunately).
  2. The Aura (bavlau) = All sapients have an aura, bound when dormant to their own bodies. When a jaisai spell is initiated, the aura extends out in a particular shape which is universal to all creatures (you may know it as Agnesi's Witch, clipped). The aura is crucial because it is through it that the fuel needed for a spell (see below) is drawn in. More specifically, the base radius of a person’s aura hinges on that person’s weight, so that one Incudean picul (62 kg give or take) produces an aura with base radius of 8.0243 spans (an Incudean span is close to 19 cm); the aura's height will be the larger part of a golden ratio with the base, for a total of 12.9836 spans, and will begin just under te portion of the brain that generates it. These dimensions only apply to first graders. With each passing grade the aura will stretch vertically, though how much depends on the species and even on the individual in question.
  3. Sinduin's aura

    The aura around a typical Incula (measurements in spans)

  4. The Fuel (honja, jaisaihonja) = All abilities, the universal malleabilities included, require fuel to be activated. Species than can deploy more than one power type (universal plus hematoneural, or gamma ray, for example) will often (but not always) have different resource needs for different power types. In some species, even different universal spells (the malleabilities) will require different resources. At first, Inculae feed on the element of fire for their jaisai spells. Starting with the third grade, however, Inculae are capable of using electrum (though at 2-3 times the stamina cost, see below). At the fourth grade and above, Inculae can use fire and electrum indiscriminately. This expanded capability allows for magical battles in space, where electrum is relatively plentiful.
  5. Stamina (berrindas, berrindas jaisaiter) = The extraction and consumption of magic fuel is instantaneous, but it does take a toll on the caster. When speaking of magic stamina, four factors are key: 1) how many spells a person is capable of casting one after another (that is, what is the total stamina available to that individual). Here each species has a particular stamina maximum level, but as one ascends grades that level increases, and gifted folk can through training extend their stamina at any level; 2) how quickly a person is able to recover their stamina (as soon as one casts a spell and thus loses some stamina, their body/spirit begins to recover, though slowly). Stamina recovery is not really affected by grade levels, though a few very gifted sapients can train for a faster recovery level; 3) how much stamina a particular spell consumes (this is pretty much fixed within a species, though interspecies there is a much variation). In general, this factor is not affected by a person’s experience or training; and 4) what the purity of the fuel being consumed for the spell is. If a person needs fire to cast a spell, but is relying on a mineral compound only one of whose elements is fire, stamina consumption for that spell will increase (extraction from fire-dominant compounds might require a third more stamina to employ, fire-dominated compounds might require two-thirds more).

Constructing an aura

Let's construct a one-picul-based aura mathematically to get a better sense of this important phenomenon. We can round the key figures of base radius and height to 8 and 13 spans respectively. The aura will be defined by the surface of revolution of the formula y(x2 + 82) = 83 from 0 to 13. We assume that our Incula is of an average 9-span height (we also disregard the tiny distance between the top of the head and the middle of the aetherlobe). It is readily apparent that the aura naturally consists of two zones: the superpedal and the subpedal (zumainkrisden and zukuikrisden), as 13-span tall Inculae have never existed!

superpedal aura

Superpedal zone of an aura (measurements in spans)

subpedal aura

Subpedal zone of an aura (measurements in spans)

The zones are important because the elemental composition of each is in most cases radically different (the air one breathes and the ground walks on, in short). There is a natural tendency, which requires conscious opposition by the caster in order to be stemmed, for spells to consume fuel in an outer, then inner; higher, then lower progression, and when Inculae are purely relying on their environment to cast, this means the ground all around them will be consumed in that sequence (various minerals are partly composed of fire). Of course, if the Incula can start a blaze, then consumption straight from the air will probably make a lot more sense. (It will become clear why physical suspension of an individual is a good preventive tactic in many cases, as it may deprive her access to fuel for magic.) The aura of a one-picul-weight individual will have a volume of around 1,178 cubic spans. 55% of that volume will be in the subpedal zone, 45% in the superpedal. As the individual ascends the trinities, the ratio will incline ever more in favor of the subpedal zone, due to the stretching tendency of the aura (the more advanced along the trinities a sapient is in Belklaun, the heavier he or she becomes, thus the aura grows with weight increase). Another important concept, culturally as well as practically, is that of the heroic pedestal (fehionalil ilkareth). The pedestal is said to be where the aetherlobe sits, magically speaking.

What is the mechanism behind the triggering of universal jaisai powers?

To get to the heart of the question, we have to examine further the phenomenon of the aura. We'll begin with the more common understanding and then delve deeper. When according to the common understanding we speak of aura, we usually refer to potential aura (the cyan field in the image above). The potential aura is the effective range of fuel extraction for a spell generated by an individual upon casting, which is described mathematically by the revolved Witch of Agnesi curve as described above. In contrast to this, the actual aura is that portion of the potential aura which finds and consumes the magic fuel. By consumption (tanugrama) we mean that the material in question instantaneously transforms into aether upon uttering of the spell. Thus, the only way the actual aura will conform precisely to the potential aura is if the environment in question is 100% composed of the element that the individual can use in a spell , and only if the spellcaster consumes it in one swoop. You can easily imagine how unlikely these conditions are to be met, though one hears of Inculae trapped in a blazing fire who will call upon the second-grade malleability and thus kill two birds with one stone: the spell soothes the pain suffered in the fire even as it transforms the latter into aether, thus eliminating the threat altogether. As an aside, stories are told of ignorant aliens trying to burn Incudean "witches", with catastrophic results. It should be noted that nothing within the jaisai spellcaster’s body is available as fuel to the spellcaster (at least not without the use of banned sorceries). However, a caster may consume elements within another individual's body provided that person is within their aura. This, please note, is a grave crime in Incudean law, and punishable by death.

Now, the description above is a bit of a simplification when compared to how modern science views the process. According to the best minds in Incudea, we should speak of two instants (identical points in spacetime, but different in another no less real sense) within the spellcasting as such. In the first instant, the aura lashes out from the body and operates on all fuel element within its grasp, turning it into aether. This is immediately felt by any outsiders (but not by the caster) as a soft force, due to the fact that the suddenly materialized gravitons (the aether) push out from their position around the caster. In the second instant, all of the new aether attempts to revert to it original status (as if to amend this crass violation of physical laws). It is here that the caster, by forcing some of the new aether to remain as such, intentionally consumes “fuel”, spends stamina, and directs, by the creation of a localized, intentional acceleration of time, the conditions for the fulfillment of her spell. Let me unpack the last statement: Time is nothing more than a sideffect of gravity in its "lifecycle", which latter is defined as the general and ceaseless flow and transformation of elementary particles from the water phase through true ice to the aether phase and back again into water. According to nature, only true ice can degenerate into aether (this is a topic for another page, alas). Therefore any sudden conversion of another element into aether produces a time skip in the zone of the transformation, which can be used by the spellcaster to exert her will. Fundamentally then, all abilities consist of time travel to produce effects that could in theory be caused given enough time (malleability of pain as accelerating the natural healing process, transformation of bodies as an accelerated purposeful evolution, etc). As to the consumed fuel, now aether, most of it will quickly escape into space, though a small amount may go on to become water vapor that can be seen and felt.

I might as well note here that some in Incudea go even further and claim unity for the potential and actual auras. According to them, in the first instant all non-aether is transformed into aether, so that potentially all sapients could use anything as magic fuel, but that each species has its affinities that practically (though not theoretically) decide the issue. No experiments that I know of support this theory, however, and most consider it downright outlandish.

At any rate, the aural transformations are the stuff of magic par excellence, and that magic proceeds from the aetherlobe (nuzi in Horgothic, located and dominating what in human anatomy is known as the brain's limbic system). Stamina in magical matters refers to the exhaustion of this particular organ. The phenomenon of quasi-quinary transformation effected by the aetherlobe is something which has never been replicated by science. Such a feat would at the very least rival the transoptical flayers!

Fuel acquisition

In ancient times, Inculae used the word fersen to refer to a magical item, for example an object that would make you fly or a beverage that would give you super-strength. After we learned that such things simply did not exist, we corrected our use of the term and now mean by it a container for magic fuel (which fuel, by the way, is itself never supernatural in any way). A fersen can come in many shapes and sizes, always trading convenience for quantity or viceversa: pouches and belts are popular. On the battlefield, magic tanks (formionis mafari), halfway between what you call war tanks and water tanks, carry fire-rich compounds inside wheels. They are remote-controlled and sometimes border on abominatech. Another primitive method, still seen often enough in battle, is simply to get a fire going, in which case the fersen carries flammable substances that can generate fuel on the run (flammable substances need not contain any fire in it of themselves!).

Duration and "species" of spells

All deployment of abilities is instantaneous, except for the (trivial) length of the trigger word or phrase. However, the effect of spells may have a duration. Duration is ruled by two factors: 1) Free will = the caster can always call off the effect of a spell at will, unless she has been mentally impaired or is in a state of deep mental confusion such as amnesia; 2) The lifetime of a spell (more precisely, of the duration of its effects). There is a specific lifetime for each spell cast. A spellcaster cannot extend that, except by the roundabout way of casting the spell a second time. That said, with some practice a spellcaster can deliberately cast a durational spell with a shorter lifetime than is usual, thus consuming less stamina than usual (notice that if a spellcaster casts a durational spell at full effect, the stamina loss occurs at the casting, so that even if the spell effects are called off early it will not mean any stamina recovery).

Often a spell will have different resource/stamina needs depending on a number of variations. In particular, the malleabilities are each a sort of genus with many, often infinite, species. The malleability of pleasure and pain is easily divided into a pleasure genus and a pain genus. The pain genus, far and away the most often deployed among Inculae, in reality consists of a single species, as fuel/stamina considerations hinge on a single variable: the severity of the pain (not, mind you, of the damage!) that is to be assuaged. On the other hand, malleability of transformation as deployed will have different requirements depending on what one is transforming to. In shallow transformations (famakins narshinter), the more different in external appearance and size from the caster, the more “expensive” the spell will be. As opposed to these mirages, the deep transformations will depend also on how much the spellcaster is to replicate the internal workings of the target "form", or maybe more useful, how different the workings of the transformation will be from her own natural organism. The same is true for the higher grade abilities. For the malleability of space, the larger the distance and size of object/s being manipulated the more… “expensive” the spell will be. Note that for the range of action of the spellcaster is NOT the aura, which only determines the range of resource extraction. The range of action will only be determined by the stamina of the person, and may very well extend far beyond the aura.

Finsuin's Tricks

Some further insight into the workings of universal magic can be obtained from the apocryphal stories of Finsuin the Spellcaster. Finsuin usually finds herself battling great monsters with nothing but her wits to aid her. Alas, she never does her homework and always ends up coming short and having to be saved by others. For example, in one story she has a duel with a cave drake. The fray lasts so long she exhausts practically all of the ground beneath her and comes perilously close to falling through a hole of her own concoction. She suddenly comes up with an unusual plan: as the drake watches incredulously, she does a handstand, hugs the stalactite above her and begins to draw from its components to fuel a new slew of spells. Well, this doesn't work at all, and thank goodness because if it did and she wasn't careful the whole thing could collapse on her. The reason it doesn't work is because Finsuin hasn't understood how her aura works. She knows that it extends from her head downward into the ground, so she figures if her body is upside down then the aura will flip along with it. In fact, Finsuin's aura is now hanging down from her head as if she were doing a handstand with a long skirt, and this because the auras always extend from the aetherlobe in the least aethereal direction. What this means is that for anyone on the surface of a planet, the aura will always extend in the direction of the center of that planet (the gravitational nadir), as there is less aether there than elsewhere. Newton's apple, but operating on wholly different principles from those regnant in your own world.

Another time, Finsuin finds herself battling a giant through magical means. After literally exhausting the elements around her, and being too lazy to run to another spot so her aura can reinitiate consumption, she hits upon a great idea. Using the malleability of form, she grows to enormous size, figuring that since her aura depends on her weight, by becoming larger she'll be able to absorb more elements instantly! The experiment is a failure, because magic cannot be prolonged by magical means. This is a principle known to most learned beings in Incudea. A being changing her size through malleability of form will retain their original aura throughout the duration of the spell. Finsuin's trick just won't work.

Further along in her adventures, Finsuin finally ascends to the fourth grade and begins wielding the malleability of space. Once again she picks a fight she is not equipped for, against an elf of all beings. She notices the elf has a as yet unused fersen, and decides to snatch it from her to use the fuel herself and deny it to her enemy. She thinks briefly of using the malleability to make the object come to her, but then thinks better of it because of the non-prolongation principle pointed out earlier. Well, Finsuin is wrong yet again. Yes, in an indirect fashion, this is a case of using magic to seize fuel from someone so one can cast more magic, but that is irrelevant to the actual action. Seizing the item is not prolonging anything, and so the principle doesn't apply. That said, it's probably a good thing Finsuin thought better of stealing an elf's fersen...

Another Example: the Sherbeta of Hellcloud

Sherbeta in St. Peter's

Auras can be enormous given individuals large enough, and their effects can literally be earth shattering. Such is the case of the Sherbeta, whose last specimen died around 600 years ago. A full-grown Sherbeta typically had 19 segments, each of which was about one and a third the length of an adult Incula. However, an erect Sherbeta tended to lift itself only about 8 segments' distance from the ground. With a weight of over 7,000 picul, however, even the aura of a Sherbeta who managed to stand on its hindmost legs would have been overwhelmingly subpedal, as the 300 spans height of the creature itself would pale in comparison to an aural height of close to 100,000 spans! The Sherbeta only reached the second grade, but they were quite adept at wielding the corresponding malleability in peace and in war. They had no predators to speak of on their own planet, and practically the only real threat to them came from the hedonists among them, who would provoke massive landslides through their consumption of herlane (plentiful compound in the Hellcloud world) indulging in pleasure spells without a care in the world. Then we came, and they had a much bigger -figuratively speaking, of course- threat to deal with.

Sherbeta aura

Aura of a typical Sherbeta. Note that at the diagram's scale, the Sherbeta is too small to be seen (measurements in stadia, where 1 stadion is 2,405.5 spans)

To make things clearer to you humans, let me use your standard measurements. Say the Sherbeta is around 60 meters long, but it stands erect at about 25 meters (from head to ground). If it weighs around 450 kilograms, then the aural height will be around 18 kilometers (17.75 of which will be underground), the heroic pedestal will extend for 6 kilometers and the bottom radius of the area will exceed 22 kilometers. When Incudea went to war against the Hellcloud, our soldiers were very aware of the these dimensions, and they were ordered to stay above the pedestals at all cost. But atmospheric conditions being what they were in the Hellcloud (the moniker was not at all fanciful), this was hard to do, and many paid the cost. The great Ransain finally figured out how to win, as she always did...

Since the obelisk in Saint Peter's Square in Rome is roughly the same size as a Sherbeta, it might be helpful to imagine the obelisk as a Sherbeta. If so, as you can see from the map below, the area affected by the aura around th giant itself would be considerably larger than the Vatican City, and at its maximum diameter at 17.75 kilometers under the earth, all of Rome within the Grande Raccordo Anulare motorway would be in peril, and even beyond. And let's not forget, these creatures could and would move.

Rome within an aura