Mathematician  Spiritual Powers  Tier 3
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Mathematicians are a scholarly character class. They have poor combat skills and low hit point accumulation. However, they have five Tiers of spells as well as a large number of spells within each Tier. By solving complex formulas, a Mathematician can create geometric structures from nothing, grant animating to inanimate objects, create protective barriers, and summon weapons of exquisite sharpness. Most formulas can be cast from a distance and thus allowing the Mathematician a better chance of surviving combat.
Fractal Compression
This formula is a more advanced version of the Tier2 formula "Compression". function enables a person or object to be temporarily shrunk down to 10% normal size. The shrinking of an object does not affect any of its properties. A shrunken person could still have normal BAtCh, Hit Points, AC, and the like. However, the individual's weapon damage and movement speed would be quartered (because twodimensional objects shrink in proportion with the square.) The weight of a shrunken person of object decreases with the cube. In other words, a character that is shrunk to 10% size would weigh 1% as much (likewise, a character who somehow increases size by 10x would weigh a thousand times as much! Don't believe it? Take a d6 and make it ten times larger by stacking dice in a 10die x 10die x10die matrix. You'll find (if you somehow have enough dice) that you've you've used 1,000 D6 dice to accomplish this increase of dimension. If this function is used against an unwilling target, the individual is entitled to a save versus system shock for negation. This function can affect 30 pounds per level of the Mathematician. If the target is too massive, the formula simply fails.
This power cannot be used to create an "instant slay" condition. For example, a Mathematician cannot use Fractal Compression to shrink a foe's necklace by 90% and thereby severing his/her head. The shrinkage will always stop after doing a maximum of 2d6 points of damage. Supernatural items get a +1 save versus harmonics per degree of enchantment to negate the effects of this formula. The Mathematician can choose to shrink an object to a lesser extent. For example, if a Mathematician only needs to shrink an object by 70%, that can be accomplished with this formula.
Changes from the printed (book) version: The formula now has a fixed maximum shrinkage of 90% instead of randomlyrolled dice. It also lasts turns per level instead of rounds per level.
Fractal Orb
Like many Mathematician spells, the formula becomes more potent as the caster ascends in level.
Levels 1 to 4: The damage is 2d6 and the saving throw is 2.
Levels 5 to 9: The damage is 2d6+1 and the saving throw is 4.
Levels 10 to 14: The damage is 2d6+2 and the saving throw is 6.
Levels 15 to 19: The damage is 2d6+3 and the saving throw is 8.
Levels 20 and higher: The damage is 2d6+4 and the saving throw is 10.
Changes from the printed (book) version: this spell is now a "mass driver" attack instead of a "homing missile" attack.
Fractal Thorn Vines
Levels 1 to 4: The Mathematician can case four 10'x10' squares of Fractal Vines. The damage is 1d6/round. The vines have AC(5).
Levels 5 to 9: The Mathematician can case six 10'x10' squares of Fractal Vines. The damage is 1d6+1/round. The vines have AC(4).
Levels 11 to 14: The Mathematician can case eight 10'x10' squares of Fractal Vines. The damage is 1d6+2/round. The vines have AC(3).
Levels 15 to 19: The Mathematician can case ten 10'x10' squares of Fractal Vines. The damage is 1d6+3/round. The vines have AC(2).
Levels 20 and higher: The Mathematician can case four 10'x10' squares of Fractal Vines. The damage is 1d6+4/round. The vines have AC(1).
Changes from the printed (book) version: The targets do not take damage if the remain fully passive.
Geometric Tube
Imaginary Translation
This powerful formula allows the Mathematician to temporarily banish one person or living creature to the Imaginary Realm. This other plane of existence is the realm of thoughts, ideas, and dreams. Abstract concepts take on visible shape in the Imaginary Realm. Few things are as they appear. When a living being is sent to the Imaginary Realm, there is a strong tendency for the person to create a new reality out of whole cloth. After all, thoughts have power in the Imaginary Realm, and thoughts shape the environment of that realm.
If the trapped character does nothing, he/she will automatically return to the ordinary realm when the power of the formula expires. However, by force of will, the banished foe can return sooner if he/she makes a successful attempt to rationalize one's self out of the Imaginary Realm. Regardless of bonuses, the duration of this formula is never shortened to less than 1 round per level. As always, ordinary Constructs and Undead are immune to this formula due to them having no imagination.
Bonuses and penalties are as follows:
Modifier  Check  Result 
Foe is a Mathematician  Willpower  Spell duration halved if successful 
Foe is a Shaman or Barbarian  Willpower  Spell duration doubled if the check fails 
Foe has the Mathematics proficiency  Knowledge  Spell lasts 9 rounds per level if successful 
Foe has high Knowledge (16+)  Knowledge  Spell lasts 9 rounds per level if successful 
Foe is a Wishsinger  BMS  Spell lasts 11 rounds per level if failed 
Foe has high BMS (16+)  BMS  Spell lasts 9 rounds per level if successful 
Foe has low BMS (<10)  BMS  Spell lasts 11 rounds per level if failed 
Foe has low Knowledge (<7)  Knowledge  Spell lasts 11 rounds per level if failed 
Foe has the Occult Knowledge proficiency  Knowledge  Spell lasts 11 rounds per level if successful (in other words, the character gets distracted) 
All of the modifiers stack. therefore, a Shaman with BMS 16, Occult Knowledge, and Knowledge 16 that gets banished by a 12th level Mathematician could theoretically have the following modifiers: double duration (class), 1 round per level (BMS), 1 rounds per level (Knowledge), and +1 rounds per level (Occult Knowledge, for a total of 264 rounds (i.e. 24 11round periods in sequence).
The Mathematician does have the option of using this formula on himself/herself. For example, the Mathematician might be trapped in a burning building and use this power in order to be whisked away to the Imaginary Realm and then return several turns later when the fire is exhausted. All of the standard modifiers apply when casting this spell upon one's self. However, the Mathematician can also choose to ride out the full duration.
Changes from the printed (book) version: the timing modifiers have been slightly altered. The Mathematician can now cast this spell on himself/herself.
Limits
 Levels 1 to 4: The Mathematician can stop an object of dagger size (or up to 5 pounds)
 Levels 5 to 9: The Mathematician can stop an object of watermelon size (or up to 25 pounds).
 Levels 10 to 14: The Mathematician can stop an object the size of an engine block (it would also hold the town bully at arm's length) or up to 250 pounds.
 Levels 15 to 19: The Mathematician can stop an object the size of a piano (or up to 1,500 pounds).
 Levels 20 and higher: The Mathematician can stop an object the size of a delivery van (or up to 4,500 pounds).
Changes from the printed (book) version: The original spell was missing the range component. That has been corrected.
Monofilament Whip
 Ordinary nonliving matter: 1d6
 Living matter (and people): 2d6
 Energybased shields not created by pure geometry: 3d6
 Constructs and geometric contrivances: 4d6
Changes from the printed (book) version: "Ranged touch attack" is explained; the damage is scaled more logically.
Phase Object
This formula allows a Mathematician to translate a physical object from ordinary space into an outofphase reality. Examples of outofphase realities are: the Plane of Light, the Conflagration, the Dark Matter Universe, the Imaginary Realm, the Plane of Shadow, Elemental Planes, and the Ethereal Realm. Of course, many more realities exist than just these. Gaianar is fortunate (or unfortunate, depending on one's perspective) to be exist at the crossroads of numerous planes of existence.
While, on the surface, this formula looks like one that would be rarely called upon, a clever Mathematician could find several lifesaving uses for this formula. For example, a Mathematician could phase a ticking timebomb into either the Conflagration or the Plane of Fire. As both realms are dominated by fire, it is unlikely that a detonating bomb would cause any harm to the residents therein. A broken nuclear fuel rod could be translated into the Dark Matter Realm and would be very unlikely to do harm to creatures who make their home in that plane of existence. Likewise, an enemy's sword could be sent to the Plane of Earth, thus disarming one's foe.
In the latter example, the foe holding a targeted item would be entitled to a Save versus Magical Weapon to avoid his/her item being translated away. Living creatures cannot be translated to other planes. However, it is helpful to remember that Undead and ordinary Constructs are not considered to be "living".
Like other "utility" spells of this nature, the area of effect is as follows: 1 pound per level of solid matter; one quart per level of liquid matter; one 10'x10'x10' volume per level of gaseous matter. Note also, that translated objects don't actually move much. For example, a sword translated to the Plane of Earth would materialize in the closest possible relevant coordinates in that Plane when compared to the coordinate location in Gaianar.
Changes from the original (book) version: This is a new spell that has been rewritten from scratch. It replaces "Create Minor Dark Matter", which has been discarded.
Radiation Beam
Changes from the printed (book) version: this formula has been expanded in scope to include utilitarian functions.
Radiation Storm
Changes from the printed (book) version: This is a new spell that has been written from scratch. It replaces "Dark Matter Storm" which has been replaced.
Reinforce
Changes from the printed (book) version: This formula now lasts for turns per level instead of just one turn.
Sight of Logic and Reason
Changes from the printed (book) version: The casting time is one round instead of one turn; the duration is turns per level instead of rounds per level; it is no longer a substitute for See Into Spirit Plane.
Subvert Construct
Changes from the printed (book) version: Living Constructs will automatically know if a subversion attempt was made. There is now a 1round reboot at the end of the spell.
Things to Consider
