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Math and Mechanus I, II: Introduction, Inhabitants and Items

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Math and Mechanus I: Introduction

In the Vedas, Ka realizes that the equivlances (logical associations or possible musical notations) are the key to cheating Death. The gods cannot fight Garuda because he is made of meters, whereas the gods who fear dying are merely clothed in them. The idea here is that meters/math/Logos is eternal and underlying the universe.But Teilhard de Chardin, famous Jesuit (a Catholic order) who is perhaps the major figure in theocentric evolution, made the observation that humans were making mathematics. This goes in line with others in that field, who posit that information is the key to transcending entropy.Now, the Mathematicians are usually seen as a harmless bunch tinkering on Mechanus, but what if they are creating math, thereby adding to the overall Law in the multiverse. Perhaps they are creating moignos with each equation, and an army of moignos will overrun the Great Wheel and descend upon Limbo. But Ygorl has a trick up his sleeve--the irrational numbers, which outnumber the rationals and surround them "like the night surrounds the stars."

Math and Mechanus II: Inhabitants and Items

Eies -- "Show yourself. I want to know what you look like."

"You could not see my face." -- Invisbles

These beings, if they can be called such, are simply ghostly pieces of faces that float and blink as per the spell. Although not uncommon on Mechanus, they also appear on the Outlands in places nearest to Automata, Arcadia, and Acheron, and rarely on Celestia and Baator. Observes note the gorgeous golden skin and silver brow surround a socket with silver lashes. The whites of the eye are lightning bright, while the orb is burgundy, sea green, or frost blue. The pupils are in the shape of numbers. These eyes cannot be attacked save by illusionary spells that are "real" for determining attacks. (The immunity to illusion rule for Mechanus inhabitants does not apply.) It is said these are the spies of the Axioms, if not pieces of their faces.Ceirees--Ceirees are long chains of numbers floating like rebuses over certain cogs of Mechanus. The drift lazily like seaweed, spiraling out into infinity. However, sequences are of finite length, and this can clearly be seen from far away. Only approaching their base on foot does one get the sense that they continue on forever. This has made certain Gunvers, particularly the Mathematician sect, argue that the spire itself is some mutated species of this "plant".Prufes--Prufes are believed to possibly be ascended Moignos, perhaps similar to the advancement of other planar exemplars. Prufes are collections of numbers and symbols that reveal certain mathematical truths. Glowing with soft blue-silver light, they flutter or swim in schools migrating across infinity. Immortal, they feed on nothing but the essence of Law. Prufes can be killed, but the Truth that gives them being will replace them almost instantly. Axial dragons also dislike any harm coming to these beings, and almost every natural inhabitant of Mechanus believes it is taboo to hurt them. Thus Mathematicians are especially careful when they seek to capture these elusive beings with butterlfy nets to see what secrets they reveal, or attempt to follow them to the hidden Axioms whose existence, they believe, allows the Multiverse to exist.Lemmas--Silver chipmunk-like rodents with mathematical symbols etched in black fur, lemmas can only loosely be considered vermin. Fastiduously clean, lemmas are come in packs as prufes come in flocks, but unlike rats they do not feast on waste. Lemmas have the magical ability to burrow into the metal cogs of Mechanus, which they use to create incredibly organized but complex mazes for their lairs. Lemmas are connected to Prufes, but the relation is unclear. At times a Prufe will descend down to visit lemmas, who come out of their burrows and make a perfect circle around its landing area. In a flash of light, the prufe will leave a silver egg from which a lemma will be born. However, when it is born, a lemma will sometimes cough up a prufe in its infancy, and the silver light of the creature will capture the attention of the pack as it rises through tunnels into Mechanus's infinity. Prufe flocks always know when this is about to happen, suggest a pattern unknown to others. The flocks fly in harmonious arcs over the lair to receive this new progeny into their midst.Axioms--Beyond gods, beyond Primus, beyond even the mediators that regulate the law of Mechanus, there lies the legend of the Axioms. Secure in the deepest parts of the Plane, they are the foundation of existence. Their power and their nature is unfathomable. No one understands their mystery, though the Mathematicians and other Mechanusians beseech them endlessly in their prayers. "Why are the rationals so few? Why did you grant so much power to the trickster Pi, who dances outside pattern yet supports the curving swoops of Everything? What is the function that maps our mortal shells to Transcendance?"Spoken of in reverent tones, they are at the least principles if not living beings. They are sometimes noted to be precious secrets, and most of those on the Plane of Law treat them as cosmic entities in their own right. Yet who are the servants of the Axioms? Every so often, favored souls arise who claim to serve a Truth so powerful it cannot be fully glimpsed, yet its power lies its simplicity. "A circle who smiles upon yourself" as one Prime witness describes them. Modrons, who are terrible liars, occaisonally malfunction and babble about these beings, though descriptions always differ--perhaps the Truth has more than one facet? Axiomatic creatures possessing sentience grow tense when questioned, and refuse to speak of them. Certain Mathematicians who disappear without any trace are sometimes later found on distant planes, serving those they call the Unnamed.Rod of Induxion--A weapon carried by the most powerful supposed servants of the Axioms is the Rod of Induxion, Induxion apparently a powerful proxy or even the name of an Axiom. A group of artifacts, each rod appears to be a smooth object exactly 1.5 feet in length, carved of bluish iron with no markings. The rod has a ray attack of a certain effect (enfeeble, nausea, etc). It can be used against one person every hour. But if successful, the spell will affect everyone in a one-mile radius excluding one individual unless saved against. The user of the rod does not know who this is before hand, but it will be a sentient being. The rod's wielder must touch this one person with the rod within the next hour, and the effect will become permanent on that victim and all those previously marked, whether they saved or not. If successful, only a wish can remove the effect, and then only one person at a time. If unsuccessful, the rod vanishes and the user explodes in a burst of snowflakes. Those scholars who believe the rods exist usually agree the slaad lord Chourst can destroy the artifacts. They also name the rods Sleep, Weakness, Sickness, Frozen, Parai, and Disintegration. note: If everyone in the vicinity is transformed into a parai save one person and those who saved, the person the user touch in the next hour is ignored by all those who were transformed.Intruding Sets--Once every few centuries, prufes and lemmas are sometimes found in massive swarms in a feral state. Off-plane, lemmas can bite and claw even through metal and prufe flocks become living storms as arcs of eletricity jump between their delicate bodies. Strangely enough, they will only attack inhabitants of Baator and Celestia. None of the lemmas or prufes will leave alive, though one notices amidst these attacks that there are eies flashing in and out existence across the skies, searching for something. One must wonder if there is any truth to obscure references to a being once whole, now three, broken to form three planes of Law (yes, obvious nod with all respect to DF!).

 

Jem
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I really liked this article.

I really liked this article. It took me a while to respond since I wanted to digest it properly. I ended up with rather a lot of comments!

Could you elaborate on the first paragraph of Section I? I don't recognize any of the Veda references and can't tell what you've picked up from real-world myth and what you've made up. How does this paragraph juxtapose with the next, in which you suggest the two statements are in opposition? Is this about the question of whether mathematics is made or discovered, with the Mathematicians claiming to answer it by making mathematics?

What do the irrational numbers have to do with defending against an army of moignos? It's true that they're a greater order of infinity than the rationals... how does this apply?

I like the eies and their vulnerability to illusions. Normally illusions can't be cast on Mechanus at all, but perhaps an eie perceives even a failed illusion spell as if it were properly cast there...

The ceirees make a cute plant for the plane. Graphical trees (graphs with no cycles) probably could as well! Perhaps most of them appear to be finite, but some very old colonies of ceirees are so long and entangled that no one is sure whether they're actually infinite or not?

The lifecycle of prufes and lemmas is fun, with the two species assisting each other in reproduction and all. Prufes seem like a sort of law elemental and thus don't need to eat, perhaps, but lemmas seem organic -- *do* lemmas eat, and if so, what? I would be interested to see a fuller writeup; a lemma could make a cute familiar for my Guvner wizard, who doesn't have one yet! :^)

Axioms are a concept already officially named. They are described in supplements pertaining to the Fraternity of Order and the Mathematicians; they are indeed principles, though on Mechanus perhaps they really can take human form. I would not give modrons or axiomatic creatures any particular knowledge of such beings. A PC can play an axiomatic creature, after all.

I'm not sure what's going on with the rod of induction. It doesn't seem to have any thematic connection with the proof technique of logical induction to me. Alternative proposition: if the wielder of the rod successfully casts a spell with a saving throw his target fails, then in the next round he may use the rod to recast the same spell with the same statistics on a new target, without expending one of his own spells or spell slots. This can continue until he runs out of targets, chooses to stop, or a target makes a saving throw or spell resistance roll.

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~~Could you elaborate on the

~~Could you elaborate on the first paragraph of Section I? I don't recognize any of the Veda references and can't tell what you've picked up from real-world myth and what you've made up. How does this paragraph juxtapose with the next, in which you suggest the two statements are in opposition? Is this about the question of whether mathematics is made or discovered, with the Mathematicians claiming to answer it by making mathematics?~~

Honestly the Introduction is me just rambling on to get the juices flowing. The Veda references concern Prajapati, though I based that line on the writings of Calasso and his book Ka. So it's second hand information, for which I apologize - I was just typing away without thinking.. I'll try to hunt down the references. My thought here was that mathematics is part of the eternal, coming from a place like that of the Platonic ideals.

~~What do the irrational numbers have to do with defending against an army of moignos? It's true that they're a greater order of infinity than the rationals... how does this apply?~~

This is actually a simplistic notion on my part, in that I'm equating irrational numbers with Chaos. I know Dedikind's cuts place them neatly into the real number line, but I still can't help but feel even this is an admission of their unruliness.

~~I like the eies and their vulnerability to illusions. Normally illusions can't be cast on Mechanus at all, but perhaps an eie perceives even a failed illusion spell as if it were properly cast there...~~

This is again a little bit of silliness on my part, as there isn't anything truly 'imaginary' about complex numbers. But both complex numbers and illusions exist on a mental plane in my mind, though I realize that's a cop out on my part.

~~The ceirees make a cute plant for the plane. Graphical trees (graphs with no cycles) probably could as well! Perhaps most of them appear to be finite, but some very old colonies of ceirees are so long and entangled that no one is sure whether they're actually infinite or not?~~

Oh, I really like the idea of graph trees as plants! I can also see less experienced travelers getting lost in oceanic digraph and cyclic mazes. I'd love to have currency based on graphs where the inhabitants intuitively calculate the cost of a weighted graph.

~~The lifecycle of prufes and lemmas is fun, with the two species assisting each other in reproduction and all. Prufes seem like a sort of law elemental and thus don't need to eat, perhaps, but lemmas seem organic -- *do* lemmas eat, and if so, what? I would be interested to see a fuller writeup; a lemma could make a cute familiar for my Guvner wizard, who doesn't have one yet! :^)~~

I definitely want to explore lemmas and prufes, I see the former as the ratatosks of mechanus but I don't want their role to be redundant. Need to think about it.

~~Axioms are a concept already officially named. They are described in supplements pertaining to the Fraternity of Order and the Mathematicians; they are indeed principles, though on Mechanus perhaps they really can take human form. I would not give modrons or axiomatic creatures any particular knowledge of such beings. A PC can play an axiomatic creature, after all.~~

Who/What the Axioms are, if they can even be legitimately personified, is unclear. I like the idea that the most ordered place in the Multiverse has its own superstitions and where the gods walk its nice to have hyper-gods who must be taken on faith.

~~I'm not sure what's going on with the rod of induction. It doesn't seem to have any thematic connection with the proof technique of logical induction to me. Alternative proposition: if the wielder of the rod successfully casts a spell with a saving throw his target fails, then in the next round he may use the rod to recast the same spell with the same statistics on a new target, without expending one of his own spells or spell slots. This can continue until he runs out of targets, chooses to stop, or a target makes a saving throw or spell resistance roll.~~

Basically the rod works by assuming the "truth" of the spell. So you have the base case, the assumption, and the necessity of "proving" the n+1'th case. Is that still unclear? Again I have to admit this is somewhat tongue in cheek.

I like your idea, which seems to be based on the idea of the "Least Criminal" number (the minimal integer in the finite set for which P(n) is true?).

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What about fractals? As

What about fractals? As both a being, a concept, and possibly a "plant", they have a lot of potential. For one thing, they would be able to influence things according to their liking- they arrange for a sword strike against them to be pushed by a gust of wind, causing the strike to lop off a diseased "branch", and thus healing the fractal instead of harming it. (think "butterfly effect")

Also, the unseen edges of a fractal would be infinitly sharp. ouch!

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Thinking of fractals

Thinking of fractals relating to unpredictable patterns, I actually have ideas about a Fractal Heresy taken root in Mechanus. The idea that all events resolve into patterns would mean the souls of the plane could do whatever they want without fear of descending into chaos.

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