Math & Mechanus (Retrieved from Old Site)

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Math & Mechanus (Retrieved from Old Site)

Math and Mechanus I: Introduction

In the Vedas, Ka realizes that the equivalences (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


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

"You could not see my face."

These beings, if they can be called such, are simply ghostly pieces of faces that float and blink as per the blink 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.

Observers 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 illusion 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 are long chains of numbers floating like rebuses over certain cogs of Mechanus. They drift lazily like seaweed, spiraling out into infinity. However, these 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 life".


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 certain 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.


Silver chipmunk-like rodents with mathematical symbols etched in black fur, lemmas can only loosely be considered vermin. Fastiduously clean, lemmas are found 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 prufe will capture the attention of the pack as it rises through their tunnels into Mechanus's infinity of cogs. Prufe flocks always know when this is about to happen, suggesting a pattern unknown to others. The prufe flocks fly in harmonious arcs over the lair to receive this new progeny into their midst.


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 supposed simplicity. "A circle who smiles upon yourself" as one Prime poet named Dante describes them.

Modrons, who are terrible liars, occasionally 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 must 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 Dice Freaks guide to Hell!).

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Math and Mechanus III: A sea,

Math and Mechanus III: A sea, a hand bag, a prophet

Zahlen, the Sea of light/darkness/void.

Even on the Plane of Law, a god can die. However, the thought of crumbling edifices is anethma to the mediators who regulate the plane. However, the lingering power of a god leaves evidence of its passing all the same for even the mediators have limits to their power.

Zahlen is the former site of one such god, a massive gear that serves as the shore and boundary for a wonderous body of apparent liquid. One can never see the whole cog, the view is blocked by other cogs interlocked around it, and so one arrives on the Light Shore or the Dark Shore, or the Horizon.

The Light Half--a sea of positive energy made of droplets, or better put packets, of energy. These infitesimal spheres do not actually melt into one another like water would, though they do adhere to each other. This gives the positive sea a foamy quality. No one has touched the bottom of the sea, in fact those who try usually end up in the Positive Material Plane. Occaisonally one will find hungry ravids or xag-ya floating around. Even rarer are the Deathless, ash white elves who survive on positive energy who sometimes ply their boats across the sea, asking of nations and even planes no one has heard of.

The Dark Half--Similar droplets make up the sea that greets one on the dark shore, but the entropic force of the Negative Material plane faces the visitor. To even attempt to ply these deceptively gentle waves is madness, as shadows and specters await in the dark depths to drag victims into the Negative. Xeg-yi float lazily, observing travelers. Against the expected symetry of the plane is a tower made of blue-ice, the home of the last "surviving" servant of the forgotten deity that once resided here. A vampire driven mad by the death of his god, the apparently former noble sits in the tower obsessing over the sums to infinite series and combinatorics, branches of mathematics it believes will ressurect its former master. The vampire is in fact NG, and an amicable enough fellow for those who don't mind listening to expositions of higher mathematics. There is also the fact that visitors are confused with sentient simians never seen on the planes, mammoths, and giant avians. These were possibly servants of the dead god, apparently an army of which had a great desire for specific pastries. So much so, that the vampire's servants--apprentices of the Mathematician faction--are always baking them for guests.

The Horizon--This is the border where the Positive and Negative parts of the Zahlen Sea meet. As it is known that such a meeting would be explosively violent, it is hypothesized that that there is something between the two, an impossibly thin sheet of elemental vacuum. Those crossing from one side to the other experience a feeling of blindness, weightlessness, and breathlessness, but it passes in the next moment.

Bag of Collaries

An object from the fairytales of Mechanus, this object is either a relic (possibly of Primus, Shang-ti, or Varuna) or a minor artifact. Reaching into the bag, a user will find a minor magic item of some sort. For example it might allow the user to cast a divination spell or allows one to masquerade as a formian. Often the item either protects against, or aids in the attack of, chaos. Of course, these are just some of the potential properities, and many a merchant would eagerly pull out a host of valuables. What prevents this is that the bag loses its "charge" once an item has been pulled out of it. One must hold the bag out and let it brush the bodies of a prufe flock in their eternal migration.

Several members of the Merkant sect have recently embarked on a joint venture to find the bag. Why they are convinced it actually exists is unclear, though once in their possession criss-cossing a flying vehicle through prufe flock would not be so difficult and could be quite profitable.

The Prophet of Fractals

Aleister Weierstrass is a portly pale fellow with curls of white hair ringing the smooth baldness of his scalp. A member of that Guvner sect the Mathematicians, he vanished some years ago but has apparently turned up in those cogs distant from known portals with his new religion.

In Mechanus, math and religion are often the same thing. Which is why most give some degree of worship to the Axioms, if only to call upon them in moments of distress. Yet the purposes of these beings remain unclear. If they created the multiverse and are originators of Law, why did they create chaos? Why have they allowed the formians to overrun the cogs? This insectile plague is scattering families who try to remain disciplined in the face of change, yet often as not descend into dreaded chaos. Such recent events have called faith in the Axioms into question, which is threatening the very underpinning of spirituality across the gears.

Aleister Weierstrass has only added to the confusion with his claim that unpredictablity isn't necessarily chaotic. In fact, there are unpredictable patterns which exist in the multiverse, and all chaos inevitably conforms to these patterns. Many laugh at the paradox of his statement, others see this a dangerous heresy. You see, the prophet believes that if all chaos yields to pattern, then all are free to do as they will. "Do what ye wilt shall be the whole of Law!" his followers cry, as mad as Bacchae in the eyes of their brethren...meaning these Mechanusians take different routes to work, or vary their weekly meal schedules. Even this has transformed societies on the cogs, though the distance from the familiar portal network makes the danger seem distant.

But if Weierstrass is right, then perhaps the Axioms don't plan to stop the Formian incursion, as many had hoped. In fact, perhaps they don't plan to do anything for anyone, and merely watch the emerging patterns--what Weierstrass calls "fractals". Others have only become stronger in their faith, believing the Axioms are so great that even wild randomness can be encompassed by holy Law, and that all unpredictability is accounted for in the algorithms that guide creation to the state of ultimate Harmony.

Yet observe the inhabitants closely. Did that one put one extra spoonful of sugar in her tea? Did the law hound's puppies come a day too late? The Fractal Heresy may soon transform the town/the cog/the plane, and true bloods will keep their distance...or reap the profits. Not the least of which is the promise of silks of new colors created by Renbuu, Slaad Lord of Colors, for the capture of this so called prophet.

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Math and Mechanus IV:

Math and Mechanus IV: Funxions

Funxions are immortal axiomatic humanoids in simple white robes with the heads of animals that direct silver barges and fly them from from one area of Mechanus to another. Each Funxion has their own drop points, but all of them will only travel between two places. Funxions with the heads of ants with purple eyes and lavender chitin take travelers between points on a single cog. Funxions with the heads of pirannah are covered with silvery fish scales and take travelers from one point on Mechanus to another. Funxions with the heads of terns have white feathers covering their bodies & take travelers to & from other planes. Funxions differ in their fees, the size of their barges, and the time they will wait before moving. Even if their barges are empty they will fly them to the opposite destination point as per their set schedule. However, a Funxion never changes its fees or departure schedule. Funxions will only fight in self defense, to protect passengers and their crafts, or to prevent anyone from attempting to hitch a ride without paying. Once every bench on the barge is taken, no one else is allowed to board. Ant-headed funxions can spit acid, pirannah-headed funxions can attempt to bite off limbs (they ignore non-magical armor), and tern-headed funxions can speak a word of law once per day and their oars have the same powers as a mace of disruption. All funxions can cast castigate, which works even on deaf creatures, as 12th level clerics once per round. All funxions are also 12th level favored souls, and will heal and protect their passengers until the drop off point. Attacking funxions on Mechanus is regarded as a violation of unspoken Law, and so tern-headed funxions actually are most short-lived of their kind since they journey to other planes.

Regardless of plane, while on its way to a destination point the funxion's barge and all upon it are immune to any harmful effects of the plane's environment. The barge, when not on Mechanus, should also be considered hidden from sight by a non-detection spell as cast by a 20th level Illusionist that even counters any observers inherent immunity to such a spell. Such is the might of the Axioms.

Funxions are generally friendly though shy so long as they are able to perform their duties. They face opponents calmly, and in addition to the above abilities physically fight as 10th level clerics armed with their oars, which are considered staves whose magical natures vary depending on the danger of the funxion's travels. Funxions are happy to talk about the locations they travel between, though like other mathematical creatures refuse to speak on their supposed creators, the Axioms. Once at a drop off point, however, all passengers must get off even if there is a battle or they are in a lake of fire. Once off, they can then get back on--if they can pay the fee. Upon death, a funxion explodes in a perfect orb of white light that attempts to hurl their killer onto a random plane, even a previously unknown one, so long as it is not Mechanus or Limbo.

Legends speak of a group of marraenoloths who, tainted by the greed of their race, sought to find the Axioms and use an artifact in their possession to usurp their power. Somehow, these planar travelers managed to find the hidden kingdom of the Axioms who emerged from their immaculate dwellings of perfect geometries. Upon seeing the indescribable beauty of those who are Foundation of All Things, the marraenoloths surrendered without a battle and begged only to serve. These risen fiends became the funxions, and the artifact they brought with them--the horn of a primordial unicorn,one of Mielikki's first children,crafted into a spear--was transformed into the Rods of Induxion.

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Math and Mechanus V: The

Math and Mechanus V: The Amulets of Sets

These magical items, which range in power from minor trinkets to powerful artifacts, are usable only by members of the Geometer prestige class from Complete Arcane. In your own game you may wish to make them available to Guvners, or other classes as appropriate.

Set A/B: Known as the Amulet of Exclusion/Inclusion, when activated the user must specify what creatures are included and which are excluded from a specific species. For example, one might say, "Humans are included, save for those serving Bane." Then in a 20ft zone around the user, all humans save for those serving Bane gain a +1 sacred bonus to attack, damage, and saving rolls.

Set A-in-B: Known as the Amulet of Membership, each use of this item allows one species to masquerade as another. So if all the members in the party are elves, one can say "Elves are Black Dragons." In the next instant, any elves in a 10 foot radius zone centered on the caster are then transformed into black dragons of varied age categories. In some ways, using the amulet carries the dangers of misphrasing a wish spell.The difference between original and transformed hit dice for all in the area is what determines the drain on charges (it's the sum of hit dice changes). There are a 100 charges whenever the amulet is discovered. Any transformation that would bring the amulet to less than 0 charges does not occur, and upon reaching such a minimum the amulet vanishes.

Set A or B: Known as the Amulet of Allies and Enemies. The user defines two sets, perhaps "Good" and "Evil". For the next hour, all those in a 20 ft zone centered on the caster gain a +5 AC bonus if they are good, and -5 to AC if they are evil. Any sentient being of neutral alignment entering the zone negates the effect. Similarly, for whatever two logical categories the user specifies, any being that cannot be classified by either category negates the effect.

Null Set: Once per week the user can attempt to make a successful touch attack that transforms a creature into elemental vacuum, placing them in the "empty set" without contradiction. The creature is destroyed and cannot be resurrected with anything short of a wish or cosmic intervention. A fortitude save negates, but is made with a -2 penalty. Known as the Amulet of Void, the wearer is also on friendly terms with inhabitants of either the Void (if playing Oriental Adventures) or the Elemental Plane of Vacuum. (Or both if both are used.) Unless provoked, inhabitants of these planes will not attack the bearer of the amulet. This amulet will also negate the effects of all the other amulets of sets in a 30ft radius instantly, but contact with any other set amulet destroys it.

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Math and Mechanus VI: Sets as

Math and Mechanus VI: Sets as Monsters

Living Sets are akin to living spells, but rather than being manifestations of magic they are manifestations of Law. As such, most living sets are either LE, LN, or LG and only in rare cases are they chaotic. Each living set has some assortment of magical abilities which it uses in its chosen mission. They cannot be seen save by spells such as true-seeing, which reveal an amobea like creature formed from light. Geometric crystals sparkle within its body, flickering with their own energies. Sets vary in color and size as well. The origin of living sets is unclear, some believe they arise from the plane of Mechanus, others suspect the hand of the mysterious Axioms. The beings may come from Mechanus, but they are found across the planes though they are incredibly rare to the point many believe members to be unique.

Wherever they come from, living sets are protectors. Each set seeks out a group that it considers its members to bond with, whether this a forest or a tribe of nomads. The set then grants some magical blessing or bonus to those within its boundary, or makes them difficult to locate so long as they remain in its body. Those seeking to enter at best experience miasma (even if set and members are willing), at worst they are attacked with death magic. The closer an "intruder" is to a "member", the less it feels any undirected effects.

The more powerful sets can simply exclude non-members with an effect similar to a wall of force. Any who wish to enter can attempt to exorcise the set, or attack it. Sets cannot be harmed by physical means, and are immune to all spells save those possessing the lawful or chaotic descriptor. They take double damage from chaotic spells, and half damage from lawful ones unless lawful beings are immune. Fooling the set with enchantments is possible only if one is fooled themselves, i.e. to convince the set you are a goblin you must enchant yourself to believe it. Shapechange can lessen the effect of undirected effects.

Once it has decided who its members are, sets are incredibly limited in their ability to change their members. Members can be added in accordance with the existing members. Any being that is expected to remain a member for its lifespan may become a member--thus members by birth and marriage are usually acceptable. This also works for removing membership for any reason that exclude a being from the group. LG beings may exclude murderers, while harsher LN groups may say divorce excludes a member. Exclusion means suffering the undirected effects of being a non-member, and crueler sets will use their spell-like abilities to drive this person off.

However sets do have the following abilities:

Not: A set that is betrayed by its members can invert its protective power so that now harmful effects are targeted on those it once trusted. Upon killing all its former members, a set now has limited power against anything similar to its original membership. A Not-Set that once protected gnomes can now use some of its power against other gnomes, though these other victims gain bonuses to saving throws. Betrayed by those it considered family, these sets often end up bitter and malignant. Not-Sets are far more likely to be chaotic. The change to Not-Set is permanent.

And: Two sets can allow their members to interact without penalty using the "And" power. And effects can be temporary, but it is up to the set to decide when to negate the effects. "And" is often used by sets found near each other, protecting groups at peace.

Union: Union joins two sets into one composite being, an action that is never taken lightly. Sets must have good reason to desire such a transformation. Sets that undertake a Union combine their powers, their HD, etc. If two groups of members build a city together, or migrating animals protected by one set enter the forest of another, the two may combine their powers. Using the Union power naturally increases the effect of their powers in accordance with their increase in HD.

Null: Beyond becoming a Not-Set, Sets can become Null-Sets if all their members are dead. As a set that has unwillingly lost its members is consumed by emptiness, they more often than not go mad and become Null-Sets. Null-Sets become living portals to the Plane of Vacuum, and can be seen without aid as dark blotches draining light and heat. Their madness creates a pall of physical and mental gloom around them.

Anyone engulfed by a Null-Set is affected as though by a cone of cold for every round they remain in its borders, and the victim cannot see or breathe unless they possess specific protections for travel in the Vacuum. For every round someone remains in the Null-Set, there is a 10% cumulative chance per round of being transported to the Elemental Plane of Vacuum, though this forceful transference can be negated by a will save. After ten rounds, the person must save every round they remain in the set or be transported. Null-Sets are driven to avenge their members, and their near immunity to most forms of attack make them dangerous foes.

As Void is Everywhere, Null-Sets can also planeshift at will. Upon gaining revenge, Null-Sets wander in a destructive-haze until they are put down by embarassed forces of Order. Only Null-Sets will attack other living sets.

Fixed Sets: Sets whose members are killed by someone else that choose not to become Null Sets are very lonely. However, they can still use their powers if they are protecting the remains of their members. These guardian sets are lonely enough that they may learn how to communicate with other beings and become sages in the field of abstract mathematics, which they have an intuitive grasp of. They can befriend new beings, but cannot accept new members. As such, all those entering their boundaries are still subject to some level of miasma though this doesn't usually have a rule based effect.

Subsets--Subsets are the offspring of living sets, who further specify a group of original members. A set protecting a city may create a subset to protect sailors who were born in the city when they travel. Subsets can be created twice per year, but are freewilled beings. These subsets may decide they have no wish to serve and wander off, or worse come to hate the members and become a Not-Set.

Inversion-- While Not-Sets are born of betrayal, inverted Sets are those who seek to make its members prisoners. Inverted sets bond with their members, but by doing so prevent them from leaving their area. Each member is allowed single Will Save to avoid this, afterward they are imprisoned within the boundaries of the set and cannot leave even in death. A Freedom Spell or Wish can free a single member. Inverted Sets are rare, as a set must come across a group that it wishes to imprision so strongly it is willing to forsake a more pleasant bonding. This is actually incredibly painful for the set and never done lightly. Inverted Sets are most likely all lawful, and those that have been encountered in recorded history have always been LN or LG and have chosen to secure great evils or chaotic beings.