The Idea behind this completely made up Arithmancy is this:
Matrix Multiplication, and invertible/noninvertible Matrix.
For those who don't know what it is here is a youtube if you are interested:
<a href='http://www.youtube.com/watch?v=aKhhYguY0DQ' target='_blank' rel='nofollow'>http://www.youtube.com/watch?v=aKhhYguY0DQ</a>
Now what makes this interesting is that it can be used for the canon (Predict the future, and numerology) as well as the fanon (Spell Creation, Runes, excreta)
Lets say you want to predict the future of Hermione Granger's Lovelife 10 years into the future.
You would do that by multiplying a matrix representing Hermione, a matrix representing romance, and a matrix representing a time.
The matrix representing Hermione might be something like.... Birth Date, Magical Number, Name, astrological sign, stuff like that.
Romance might be represented by a certain pattern of numbers, like the 2nd sin of 7, lust, 21 for two souls becoming one, yada yada. (IE The Numerology portion of it)
Time could be based off some Magical time contest, flowing randomly. Maybe there is a spell that coverts "January 1st 1969" into some Matrix to be used.... (Always noninvertible)
Then the result could be read a certain way, which is the prediction of the future.
For the Fanon....
The matrix representing Hermione may or may not be the same that represents her "magical signature". Magical signatures are by nature noninvertible.
Spell Signatures of Transfigurations, and Charms, that do not use any form of emotions are by definition an Invertible Matrix.
In this way two spells may be modified by Multiplying them together. Multiplying lumos with lets say a spell that is just green sparks would result in a green light.
Simple effects can then be combined and built together through multiplication of these Matrix to build more complicated Spell Signatures.
This will be true since multiplying two invertible matrix together results in another invertible matrix..
The Counter Spell is thus easily found by taking the inverse of any of these Matrices. Thus by definition all spells that do not have an element of emotion to them are reversible.
In contrast spells that use emotions to cast, Crucio, Imperio, the Killing Curse, The Patronus, are Not invertible. Thus indestructible. IE they can not be cancelled out by anything Without Emotion. (Fighting the Imperio is done by a combination of Emotion and the noninvertible matrix of the magical signature)
Now examining the Matrix of the Killing Curse by Lily Potter revealed that the Killing Curse interacts only with noninvertible magical signatures. Not only that, but only special noninvertible magical signatures that are close enough to be a living magical signature.
So she was able to make a love/sacrifice spell that when she was killed, her magical signature would create a "shroud" around Harry.
Que killing curse being shot into this shroud, it send the curse back to voldemort, Harry gets his scar, and the shroud is modified by Voldemorts Magical Signature. In a way it turns it to the closest thing that could exist to an inverse of the signature.
Thus in First Year when the shroud contacted Voldemort, it burned him.
Then in Fourth Year he was reborn with a bit of the shroud, changing his signature enough that it wouldn't burn him. In fact the shroud, which grew insync of Harry's magical signature, is also a fair representation of Harry's Signature.
Equal and Opposite.... But not exactly.
The process of creating a Horcrux is the process of gluing a part of your magical signature to something else. It could be said magical signature = soul in a sense.
And yes, this would make the Crucio, Imperio, Avada, and Patronus Ensouled in a sense.
The Resurrection Stone acts sort of like the Farplane does in FFX. It channels the Magical Signature of the person that died.
I think that is pretty much it for now.
Wards and other things possibly....
Matrix Multiplication, and invertible/noninvertible Matrix.
For those who don't know what it is here is a youtube if you are interested:
<a href='http://www.youtube.com/watch?v=aKhhYguY0DQ' target='_blank' rel='nofollow'>http://www.youtube.com/watch?v=aKhhYguY0DQ</a>
Now what makes this interesting is that it can be used for the canon (Predict the future, and numerology) as well as the fanon (Spell Creation, Runes, excreta)
Lets say you want to predict the future of Hermione Granger's Lovelife 10 years into the future.
You would do that by multiplying a matrix representing Hermione, a matrix representing romance, and a matrix representing a time.
The matrix representing Hermione might be something like.... Birth Date, Magical Number, Name, astrological sign, stuff like that.
Romance might be represented by a certain pattern of numbers, like the 2nd sin of 7, lust, 21 for two souls becoming one, yada yada. (IE The Numerology portion of it)
Time could be based off some Magical time contest, flowing randomly. Maybe there is a spell that coverts "January 1st 1969" into some Matrix to be used.... (Always noninvertible)
Then the result could be read a certain way, which is the prediction of the future.
For the Fanon....
The matrix representing Hermione may or may not be the same that represents her "magical signature". Magical signatures are by nature noninvertible.
Spell Signatures of Transfigurations, and Charms, that do not use any form of emotions are by definition an Invertible Matrix.
In this way two spells may be modified by Multiplying them together. Multiplying lumos with lets say a spell that is just green sparks would result in a green light.
Simple effects can then be combined and built together through multiplication of these Matrix to build more complicated Spell Signatures.
This will be true since multiplying two invertible matrix together results in another invertible matrix..
The Counter Spell is thus easily found by taking the inverse of any of these Matrices. Thus by definition all spells that do not have an element of emotion to them are reversible.
In contrast spells that use emotions to cast, Crucio, Imperio, the Killing Curse, The Patronus, are Not invertible. Thus indestructible. IE they can not be cancelled out by anything Without Emotion. (Fighting the Imperio is done by a combination of Emotion and the noninvertible matrix of the magical signature)
Now examining the Matrix of the Killing Curse by Lily Potter revealed that the Killing Curse interacts only with noninvertible magical signatures. Not only that, but only special noninvertible magical signatures that are close enough to be a living magical signature.
So she was able to make a love/sacrifice spell that when she was killed, her magical signature would create a "shroud" around Harry.
Que killing curse being shot into this shroud, it send the curse back to voldemort, Harry gets his scar, and the shroud is modified by Voldemorts Magical Signature. In a way it turns it to the closest thing that could exist to an inverse of the signature.
Thus in First Year when the shroud contacted Voldemort, it burned him.
Then in Fourth Year he was reborn with a bit of the shroud, changing his signature enough that it wouldn't burn him. In fact the shroud, which grew insync of Harry's magical signature, is also a fair representation of Harry's Signature.
Equal and Opposite.... But not exactly.
The process of creating a Horcrux is the process of gluing a part of your magical signature to something else. It could be said magical signature = soul in a sense.
And yes, this would make the Crucio, Imperio, Avada, and Patronus Ensouled in a sense.
The Resurrection Stone acts sort of like the Farplane does in FFX. It channels the Magical Signature of the person that died.
I think that is pretty much it for now.
Wards and other things possibly....
No one comments on my most serious post ever.