Introduction to the theory of magic
The first article in the series "Theory of Magic" is an overview. Its goal is to formulate the main issues of the discipline under consideration primarily at a qualitative level, as well as to clarify which subdisciplines are usually identified and how the aspects that are in the center of their attention are related to each other.
Our efforts will be focused on the description of the magic engine. By analogy with the physical engine, we want to create, and first prepare the basis for creating a computer program that should produce computer simulation of the magical laws of the world, but if physical modeling deals with the real world, then in our case the world is imaginary.
This should not be an insurmountable obstacle. After all, for hundreds of years, theologians have built their structures on no less fragile soil; and, as they limited themselves to following holy scripture, tradition, authority, political conjuncture, to a certain extent logic, etc., so the theory of magic should be based on the assumptions of common sense in this field, formed by literature, logic, properties of the real world, where they are required be taken into account, and computing capabilities.
We will deal with spells, leaving aside other magical practices such as prediction, astrology, etc., but note that a spell can be expressed not verbally, but geometrically or, for example, in the form of an alchemical recipe. However, we assume the possibility of translating spells of any kind into a language that we will further call true language. Each spell has the purpose of changing the state of an object or its transformation, and we will assume that such a transformation always requires the expenditure of a resource, traditionally called mana. Another assumption is that the spell has an addressee, whoever is likely to perform the spell; why and how accurately we will discuss further.
So, a spell is a syntactically correct text in a true language (up to translation), containing the subject and object in the corresponding cases and a description of the required action. For the execution of the spell must be given the appropriate amount of mana. The result is also determined by the level of the magician and his state and may not be exactly the same or not at all as expected. The calculation of this result is our task.
The state of an object (S) is a collection of object properties and their values. If the property set is empty, then the corresponding state is called non-existence (N). Creation is the transformation of non-existence into any non-identical state, and the reverse transformation is destruction.
The transition from the state S [i] to S [j] will be written as S [i] → S [j].
The amount spent on the conversion of mana (m) should depend on the initial S [0] and final S [1] states, spells (q), mage (w), object (o) and subject (f). Suppose that w, o, and f are fixed. Then it seems reasonable to assume:
That is, the basis of the mana calculus is metric space, probably the state space, and therefore for any two states the distance r (S [i], S [j]) can be determined, to overcome which part of the mana is spent. The other part is associated with the spell, and the function m takes the form
m (S [0] → S [1], q) = k * (r (S [0], S [1]) + lex (q)),
where k is a coefficient depending on the mage, object and subject, and lex is a lexical function of the text of the spell. It is not difficult to see
We will leave two important questions for the future:
Add a few words about the coefficient k = k (w, o, f). The mana required for S [0] → S [1] obviously depends on the level of the magician, on its affinity for the object and its proximity to the subject. More formally, suppose
k (w, o, f) = intens (w) * res (w, o) * rem (w, f),
where intens (w) is the reciprocal efficiency of the magician (> 1), res (w, o) is the object's resistance to this magician (> = 1), and rem (w, f) is the function of the distance of the magician from the subject in the service space, on at one end of the range of values ​​of which is the avatar of the subject, at the other - its antagonist.
Let's clarify that we actually intens = intens (w, m), but we hope to choose a dependence on m that would give significant deviations from intens (w, const) only in the high-energy region. Another subtlety concerns the resistance of the object, because the object moves from the initial state to the final state, in which the resistance could differ. Then the value of m (S [0] → S [1]) should be represented as the result of integration along the transformation trajectory.
It is impossible to perform an action with one hundred percent efficiency and absolute accuracy. And this is not about the skill and accuracy of the magician, but about the fundamental constraints.
Efficiency
The efficiency of a magic operation is always less than one, that is, part of the selected mana turns into heat. This part is the greater, the lower the level of the magician and, remaining for a fixed magician approximately constant in a large area of ​​everyday magic, with the use of significant amounts of mana, it can increase. This causes heating and luminescence accompanying transformations; This, combined with the arrogance of beginners, is a frequent cause of the burning of young professionals at work.
Mana Volume Errors
The amount of mana allocated for conversion is a random variable with a normal distribution. Of course, the expectation is equal to the volume that the magician is trying to use, and the variance depends on the level. But no matter how experienced a magician is, there is a non-zero probability of how arbitrarily large (within the energy possibilities of a given individual) deviations from the desired mana value. From here we proceed to the next type of error.
Target error
Indeed, how will the magic operation end, if mana is not enough to achieve the target state? Or if its amount is too large?
We said before that the transformation is given in terms of the initial and final states. Now let us clarify: these states determine the desired direction of transformation; desirable, but not real, because here we are dealing with a normally distributed random variable, the variance of which depends on the concentration of the magician. And taking into account all the errors, the given transition S [0] → S [1] turns out to be the transition S [0] → T, where T is an intermediate pseudostate resolvable after a short time to the target state ST.
Very briefly about the transition T → ST. We introduce the function of attraction T to S [i] as
gr (T, S [i]) = n (S [i]) / r (T, S [i]) ^ 2,
where r (T, S [i]) is the distance between T and S [i],
n (S [i]) == 1 for natural states, that is, states that are stable and in the absence of a magical background, and for unnatural states it depends on the density of the background and does not exceed one. Then the transition probability T → S [i]
p (T → S [i]) = gr (T, S [i]) / Sum (gr (T, S)).
')
It has already been said that the language of spells is a true language, and now it is time to ask what makes a language true? Why are some combinations of signs true names and others not? It is known that for any magic effect on an object, it is necessary to indicate in the spell its name, the name of this particular object, and not its kind or class. But how can a magician find out the name of a stone picked up on the road? And does it exist?
There is evidence that every object at least once in the past had a true name; consideration of this evidence, however, is beyond the scope of our review. In practice, in the overwhelming majority of cases, the magician names the object using the shell creation procedure, thereby connecting mana, language and location. First, the border is described around the object as a barrier of the future shell, and the name is interwoven into this border, containing its part the generic name of the object. Then, a mana is emitted inside the border, the amount of which determines the volume of the name space (the initial mana density is fixed). The shape of the bounding surface or shell depends on the boundary line and the volume of the area, and its permeability is mainly associated with the force of the magician.
From this point on, the object and the area of ​​the name are connected, even being separated in space, and, as the name is a sign of the object, so the object becomes a sign of the namespace. Until, of course, as a result of the leakage of mana, the density will not be less critical, and the shell will not disappear along with the name. And each use of the name in the spell increases the amount of mana in the namespace by the value of the lexical function, as a result of which the density increases to the maximum, and then the volume of the area increases.
It may happen that several objects are named the same. Then, if the name is used in the spell, only one object will be turned. The choice is made as follows: nominal areas try to respond in decreasing order of volume, the probability of using is equal to the ratio of mana density in the nominal area to the maximum density.
It can also happen that a single object has several names. Until an object is invoked, all its names are superposed. Under the influence of the spell, one of the names is updated. The choice of this name is made as follows: first, the name used in the spell tries to respond, the probability of a favorable outcome is equal to the ratio of mana density in the nominal area to the maximum. If this name fails (and, at the same time, the transformation operation), then the remaining names are moved in decreasing order of volume, and the next name tries to be updated. Having received the current name, the object for some time, depending on the amount of mana in the namespace, responds only to it. Then relaxation occurs, and the names are returned to the superposition state.
For a long time, the following paradox from the realm of the original true names is given under the name “Linguistic Catastrophe”.
The question arises: why does not the chaos and catastrophe cover us? Why are we there?
In short, the usual answer is this: a world in which the original names of key objects with low resistance to magic are known, collapses very quickly. A world in which the original names are short, plunges magic into chaos and collapses. The fact that we are still alive is evidence in favor of long initial names or that it would be safer and more beautiful to name infinite length.
The subject is the subject nominal domain, which arose from the object nominal domain as a result of practical faith and continues to exist thanks to this faith.
Practical faith refers to the use of a name in the subject case as a subject of spells, prayers, and ritual texts accompanying sacrifices, and, as a result, the allocation of mana into a subject named area.
If the subject area does not exist at the time of the act of faith, then it appears in a volume equal to the current volume of the object area. Then the dynamics of this area is similar to the dynamics of the object area:
The likelihood of a subject's response is equal to the ratio of mana density in the subject area to its maximum value. A subject can perform a spell that requires mana in an amount much smaller than the amount of mana in the subject area. The corresponding ratio and the method of its experimental obtaining is considered in the theory of the subject.
List of main topics and directions:
Formulation of the problem
Our efforts will be focused on the description of the magic engine. By analogy with the physical engine, we want to create, and first prepare the basis for creating a computer program that should produce computer simulation of the magical laws of the world, but if physical modeling deals with the real world, then in our case the world is imaginary.
This should not be an insurmountable obstacle. After all, for hundreds of years, theologians have built their structures on no less fragile soil; and, as they limited themselves to following holy scripture, tradition, authority, political conjuncture, to a certain extent logic, etc., so the theory of magic should be based on the assumptions of common sense in this field, formed by literature, logic, properties of the real world, where they are required be taken into account, and computing capabilities.
We will deal with spells, leaving aside other magical practices such as prediction, astrology, etc., but note that a spell can be expressed not verbally, but geometrically or, for example, in the form of an alchemical recipe. However, we assume the possibility of translating spells of any kind into a language that we will further call true language. Each spell has the purpose of changing the state of an object or its transformation, and we will assume that such a transformation always requires the expenditure of a resource, traditionally called mana. Another assumption is that the spell has an addressee, whoever is likely to perform the spell; why and how accurately we will discuss further.
So, a spell is a syntactically correct text in a true language (up to translation), containing the subject and object in the corresponding cases and a description of the required action. For the execution of the spell must be given the appropriate amount of mana. The result is also determined by the level of the magician and his state and may not be exactly the same or not at all as expected. The calculation of this result is our task.
Mana
Mana is scooped in places of power
trapped in magical streams,
taken away from the victim and borrowed from an ally.
Only a fool tries to translate energy into mana, for
no magician can ever break
conservation laws.
From an engineering magic tutorial
The state of an object (S) is a collection of object properties and their values. If the property set is empty, then the corresponding state is called non-existence (N). Creation is the transformation of non-existence into any non-identical state, and the reverse transformation is destruction.
The transition from the state S [i] to S [j] will be written as S [i] → S [j].
The amount spent on the conversion of mana (m) should depend on the initial S [0] and final S [1] states, spells (q), mage (w), object (o) and subject (f). Suppose that w, o, and f are fixed. Then it seems reasonable to assume:
- m (S [0] → S [1], q) = 0 <=> S [0] = S [1].
- For any q, there exists! Q such that m (S [0] → S [1], q) = m (S [1] → S [0],! Q).
The spell! Q is called the inverse of q. - For any q [0] and q [1], there is q [2] such that
m (S [0] → S [1], q [0]) + m (S [1] → S [2], q [1])> = m (S [0] → S [2], q [2]).
That is, the basis of the mana calculus is metric space, probably the state space, and therefore for any two states the distance r (S [i], S [j]) can be determined, to overcome which part of the mana is spent. The other part is associated with the spell, and the function m takes the form
m (S [0] → S [1], q) = k * (r (S [0], S [1]) + lex (q)),
where k is a coefficient depending on the mage, object and subject, and lex is a lexical function of the text of the spell. It is not difficult to see
- There is a zero spell q0 such that lex (q0) = 0.
- lex (q) = lex (! q).
We will leave two important questions for the future:
- How to really choose a metric function on a set of states?
- Why does a spell as text require mana, and based on this, how is the lexical function calculated?
Add a few words about the coefficient k = k (w, o, f). The mana required for S [0] → S [1] obviously depends on the level of the magician, on its affinity for the object and its proximity to the subject. More formally, suppose
k (w, o, f) = intens (w) * res (w, o) * rem (w, f),
where intens (w) is the reciprocal efficiency of the magician (> 1), res (w, o) is the object's resistance to this magician (> = 1), and rem (w, f) is the function of the distance of the magician from the subject in the service space, on at one end of the range of values ​​of which is the avatar of the subject, at the other - its antagonist.
Let's clarify that we actually intens = intens (w, m), but we hope to choose a dependence on m that would give significant deviations from intens (w, const) only in the high-energy region. Another subtlety concerns the resistance of the object, because the object moves from the initial state to the final state, in which the resistance could differ. Then the value of m (S [0] → S [1]) should be represented as the result of integration along the transformation trajectory.
Errors
Not a shot is a sin, but a miss.
Principles of the War of Master Xavier
It is impossible to perform an action with one hundred percent efficiency and absolute accuracy. And this is not about the skill and accuracy of the magician, but about the fundamental constraints.
Efficiency
The efficiency of a magic operation is always less than one, that is, part of the selected mana turns into heat. This part is the greater, the lower the level of the magician and, remaining for a fixed magician approximately constant in a large area of ​​everyday magic, with the use of significant amounts of mana, it can increase. This causes heating and luminescence accompanying transformations; This, combined with the arrogance of beginners, is a frequent cause of the burning of young professionals at work.
Mana Volume Errors
The amount of mana allocated for conversion is a random variable with a normal distribution. Of course, the expectation is equal to the volume that the magician is trying to use, and the variance depends on the level. But no matter how experienced a magician is, there is a non-zero probability of how arbitrarily large (within the energy possibilities of a given individual) deviations from the desired mana value. From here we proceed to the next type of error.
Target error
Indeed, how will the magic operation end, if mana is not enough to achieve the target state? Or if its amount is too large?
We said before that the transformation is given in terms of the initial and final states. Now let us clarify: these states determine the desired direction of transformation; desirable, but not real, because here we are dealing with a normally distributed random variable, the variance of which depends on the concentration of the magician. And taking into account all the errors, the given transition S [0] → S [1] turns out to be the transition S [0] → T, where T is an intermediate pseudostate resolvable after a short time to the target state ST.
Very briefly about the transition T → ST. We introduce the function of attraction T to S [i] as
gr (T, S [i]) = n (S [i]) / r (T, S [i]) ^ 2,
where r (T, S [i]) is the distance between T and S [i],
n (S [i]) == 1 for natural states, that is, states that are stable and in the absence of a magical background, and for unnatural states it depends on the density of the background and does not exceed one. Then the transition probability T → S [i]
p (T → S [i]) = gr (T, S [i]) / Sum (gr (T, S)).
')
Names
In true language, the sign and denoted
often change places.
Sacred geography
It has already been said that the language of spells is a true language, and now it is time to ask what makes a language true? Why are some combinations of signs true names and others not? It is known that for any magic effect on an object, it is necessary to indicate in the spell its name, the name of this particular object, and not its kind or class. But how can a magician find out the name of a stone picked up on the road? And does it exist?
There is evidence that every object at least once in the past had a true name; consideration of this evidence, however, is beyond the scope of our review. In practice, in the overwhelming majority of cases, the magician names the object using the shell creation procedure, thereby connecting mana, language and location. First, the border is described around the object as a barrier of the future shell, and the name is interwoven into this border, containing its part the generic name of the object. Then, a mana is emitted inside the border, the amount of which determines the volume of the name space (the initial mana density is fixed). The shape of the bounding surface or shell depends on the boundary line and the volume of the area, and its permeability is mainly associated with the force of the magician.
From this point on, the object and the area of ​​the name are connected, even being separated in space, and, as the name is a sign of the object, so the object becomes a sign of the namespace. Until, of course, as a result of the leakage of mana, the density will not be less critical, and the shell will not disappear along with the name. And each use of the name in the spell increases the amount of mana in the namespace by the value of the lexical function, as a result of which the density increases to the maximum, and then the volume of the area increases.
It may happen that several objects are named the same. Then, if the name is used in the spell, only one object will be turned. The choice is made as follows: nominal areas try to respond in decreasing order of volume, the probability of using is equal to the ratio of mana density in the nominal area to the maximum density.
It can also happen that a single object has several names. Until an object is invoked, all its names are superposed. Under the influence of the spell, one of the names is updated. The choice of this name is made as follows: first, the name used in the spell tries to respond, the probability of a favorable outcome is equal to the ratio of mana density in the nominal area to the maximum. If this name fails (and, at the same time, the transformation operation), then the remaining names are moved in decreasing order of volume, and the next name tries to be updated. Having received the current name, the object for some time, depending on the amount of mana in the namespace, responds only to it. Then relaxation occurs, and the names are returned to the superposition state.
Linguistic disaster
They spend their whole lives
making names longer and longer
hoping to pick up once a great Name,
which was at the beginning and will be at the end.
Journey to the edge of the world
For a long time, the following paradox from the realm of the original true names is given under the name “Linguistic Catastrophe”.
- Let the original name of some object is well known, as, for example, the name of our planet. Then any magician can perform arbitrarily destructive action. Let's say move the axis of rotation, change the mass, and so on. We know very few of the original names of objects, all of these objects have extremely high magical resistance. However, the world is full and very responsive objects, the original names of which we, fortunately, do not know.
- A random operation on an object is possible, even when its name is not known if it coincided with the name given by the magician to the working object. The situation looks even more strange when considering virtual background spells, that is, texts that spontaneously arise from a magical background.
The question arises: why does not the chaos and catastrophe cover us? Why are we there?
In short, the usual answer is this: a world in which the original names of key objects with low resistance to magic are known, collapses very quickly. A world in which the original names are short, plunges magic into chaos and collapses. The fact that we are still alive is evidence in favor of long initial names or that it would be safer and more beautiful to name infinite length.
Subjects
Gods are born every moment.
And then they disappear.
Nether Book
The subject is the subject nominal domain, which arose from the object nominal domain as a result of practical faith and continues to exist thanks to this faith.
Practical faith refers to the use of a name in the subject case as a subject of spells, prayers, and ritual texts accompanying sacrifices, and, as a result, the allocation of mana into a subject named area.
If the subject area does not exist at the time of the act of faith, then it appears in a volume equal to the current volume of the object area. Then the dynamics of this area is similar to the dynamics of the object area:
- Mana density decreases with time as a result of leakage through a semi-permeable shell. When the minimum density is reached, the area disappears.
- Any use of the subject case in acts of faith increases the amount of mana in the subject area. First, the mana density increases to the maximum value. Then the volume of the area increases.
The likelihood of a subject's response is equal to the ratio of mana density in the subject area to its maximum value. A subject can perform a spell that requires mana in an amount much smaller than the amount of mana in the subject area. The corresponding ratio and the method of its experimental obtaining is considered in the theory of the subject.
What's next?
List of main topics and directions:
- Theory of state space.
- Manodynamics.
- Theory of magical resistance.
- Mathematical theory of shells.
- The grammar of the true language.
- The syntax of the true language.
- The structure of the texts: spells, prayers, accompanying sacrifices.
- Subject theory.
- Theory of relations with the subject.
- Birth spaces. Metamagia.
Source: https://habr.com/ru/post/188692/
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