Transformations are a key concept in mapping. A transformation is a new, unique combination of elements thatmap Δjkl to Δj”k”l.
Typically, transformations occur at the heart of a story, where changes take place and others are introduced. For example, there is a cookery show airing now called My Life on TV that follows people as they change house, cook and entertain with their dishes.
On the show, someone new to cooking is introduced who makes really weird food that you have to try!
Transformations can happen gradually or abruptly. When they occur suddenly, it is called an abrupt transformation and it can cause havoc for those around it.
This article will talk about some common transformations that map to corresponding changes in the characters and stories of your book.
The associative law of composition for transformations
At a given point in time, there is a certain proportion of things that are δj”l” and things that are Δjkl. This proportion is called the associative law of composition for transformations.
The associative law of composition for transformations describes how many things can be associated with a given thing, or thing can be associated with other things. For example, joining two pieces of paper creates a new document that can be printed, copied, and transported.
This law does not tell us what these associations should be! It only tells us that there must be an association between them. There must also be a way to convert one form into another.
The identity transformation
A transformation’s identity can be traced back to its beginning, either in a past transformation or in a future transformation.
This phenomenon is referred to as a continuity of identity. Transformation is the process of changing one identity to another.
By undergoing this process, one reaffirms their sense of self and acknowledges their changed reality. This may feel strange at first, but after a while you will realize that you are who you really are.
There are many cases where there is no clear-cut definition for the term transformation. Some say it describes changes in social norms, psychological dynamics, cultural expressions, and religious practices. Regardless, it must be understood as an important concept that everyone should understand to better their own health and well-being.
The inverse transformation
When do we need to transform? When do we not need to transform? These questions can be debated and discussed, but at the end of the day, we all know when to transform and when not to.
In our daily lives, we constantly encounter transformations. At work, at school, in our romantic life, in our spiritual life. We rarely think about what transformation means until something isn’t- or shouldn’t- be transformed into something else.
When did you learn how to transform? Where did you learn this skill? How did you practice this art? These are some of the questions that should be asked when someone doesn’t understand what transformation is and how it maps to Δjkl.
This article will discuss the different rule sets that map Δjkl to Δj”k”l”.
Understanding the rules of algebra helps with understanding the rules of composition
Algebra is a powerful tool for composition. There are many ways to create content, and it is not a simple rule-based system like in music or art.
The rules of algebra can be likened to the basic components of composition: melody, harmony, and texture. These components can be juxtaposed or combined in many ways, making composition an infinite array of transformations.
Understanding the basic rules of algebra will help you understand why some compositions seem confusing at first, and why some compositions seem complex at first. It will also help you become aware of rules that apply to you as a person, which could give you confidence in front of an audience.
When listening to music, always listen for the melodies and try to find other elements that make up the “music”.
Composition is not the same as multiplication
When we multiply two variables, we have to consider the number of elements in both variables. For instance, the weight of a gallon of milk is not a variable that can be multiplied twice by the size of a bottle.
When we map variables to other variables, we do not have to consider the number of elements in those new variables. For example, when we add up the elements in a transformation, we do not have to add up the numbers in the transformation itself.
We can instead add up numbers from another source, such as our environment or our own mental representation of the transformation. When we do this, transformations with many elements become common.
This is why transformations that relate large changes in something else can map to many small ones in our mind.
When composing two transformations, you must follow the order of operations
When performing a transformation, you must have the order of operations listed. This includes listing which components of a transformation are list-able and which components are not!
In the case of two transformations that map to the same value, there is no requirement to list both values in the order they are received. The first value picked will be applied, and the second discarded.
For example, let’s say we wanted our transformation to move an object up and down. We could pick one value from each direction, or we could combine them into one. In this case, neither value is list-able!
When composing two transformations that map to the same value, it is important to have enough information listed on each to properly perform the transformation.
There are never any inverses for the identity transformation
This rule describes transformations that map Δjkl to Δj”k”l”. For example, changing a person’s gender doesn’t match any other transformation that maps to Δjkl to Δj”k”l”.
Transformations that map close to a point on the transformational sequence are calledFINE-INTRODUCED REVERSALS (FIRES). FIRES typically don’t have a cause, in contrast to INTRODUCED REVERSALS, which tend to have a cause.
Some transitions, such as death and birth, are so special that they deserve their own category. Such transitions are referred to as SPECIAL TRANSFORMATIONS (STONES). Although not covered in this book, there are specific guidelines for transitioning into new life forms.
Please remember that TRANSFORMATION is not the same thing as IMAGE-MAKING or IDENTITY-BUILDING.
How to determine if two transformations are compatible
How do we tell if a transformation is compatible with another? The answer is in the name of the rule: compatibility.
When we look at a transformation that changes one thing and one thing only, we say that it is compatible if it can be integrated into another transformation that changes only one thing.
For example, when we change a list to a table, our new transformation is compatible with our old one as long as we keep the list.
When we add a row to the table, our new transformation must change the cell background and border colors so that it matches the new dimension.
