Originality

Original:
1 used or produced at the creation or earliest stage of something : costumes made from the original designs | the plasterwork is probably original.
• [ attrib. ] present or existing at the beginning of a series or process; first : the original owner of the house.
2 created directly and personally by a particular artist; not a copy or imitation : original Rembrandts | playing original material.
3 not dependent on other people’s ideas; inventive and unusual : a subtle and original thinker. See note at creative .

Originality in a mathematical sense is hard to define. It’s not inequality, it’s not incongruence. It is being unique.

Unique:
being the only one of its kind; unlike anything else : the situation was unique in modern politics | original and unique designs.
• particularly remarkable, special, or unusual : a unique opportunity to see the spectacular Bolshoi Ballet.
[ predic. ] ( unique to) belonging or connected to (one particular person, group, or place) : a style of architecture that is unique to Portugal.

In a sense though, uniqueness is being unequal or incongruent, which seems to make my previous statement oxymoronic. However, uniqueness isn’t just being unequal or incongruent, it’s being so in a context dependent manner. Example, if we were judging the uniqueness of colors in birds, a red colored Black Bird may be unique under the context of Black Birds, but it wouldn’t be unique under the context of all birds.

I’m sure we have all heard a statement such as “Nothing is truly original”. I will attempt to disprove this.

The general reason some people arrive at the conclusion that nothing is truly original is not due to a logical fallacy, but an incorrect definition of original. Example:

Proof 1: Carbon is an element, and there are multiple elements, thus Carbon is unoriginal. Carbon is an element, and no other element is like it, thus Carbon is original.

Both of these statements are true, carbon is an element, and no other element is like carbon. However, the conclusion of such statements is contradictory, thus, one of these statements is using the principle of originality incorrectly, or, one of these statements is incorrect. Since both statements are correct, one of them must be using the idea of originality incorrectly.

In the first statement, we define carbon as being unoriginal because it is an element, and not the only element. In the second statement we define it as original because nothing else in it’s category is like it. So, which is correct? I would argue that the first definition is incorrect. There is even a simple proof to prove that it’s incorrect. Before I cover this proof, I would like to explain object oriented logic/objects/statements a little bit for those who are unfamiliar with it. If you are familiar with such principles though, feel free to skip over this part.

Object oriented logic is essentially categorical logic in which we can make a statement such as:

All mortals die eventually. People are mortal, therefor they will die eventually.

Object oriented objects state there are ‘nodes’. Each node contains various variables and operations which can be done to this node. Each node can have child nodes, where the child has all of the attributes (variables and functions/methods [operations which can be done to said node]) of the parent, although it can also have it’s own variables and functions/methods. This is called ‘inheritance’. You can then use object oriented objects as variables. An example:

Lets define an object “plant” with no parent. This object has the variables “size” and “growthRate”, as well as the function “grow”. Grow causes the operation size = size + growthRate. Lets define another object “tree” which is a child of “plant”. This object has the variable “fruitType”. We could then create some sort of variable such as

tree appleTree

appleTree.size = 500
appleTree.growthRate = 3
appleTree.fruitType = apple

Also, from the categorical logic sense of object oriented objects, we know that since tree’s parent is plant, a variable that is a tree is also a plant. Therefor, appleTree is a plant.

Getting back on topic, lets see that proof I was talking about.

Proof 2: there is an object B. B is the parent of object C, C is the parent of object D. Object B has the variable “1”, object C has the variable “2” and by inheritance “1”. Object D has the variable “3” and by inheritance the variables “1” and “2”. There is a fourth object Z which has no parent. It has the variables “1” and “2” and “3”. For this proof we will presume that all variables are actually constants that equal 1337. Now, we have an object Z and we have an object D which have the same variables (1, 2, and 3), of the same type (constant), that are equal to the same value (1337), however, by the definition that originality is based upon the parents of the objects, these two objects are fully original. Clearly they aren’t original though, thus we have proven that the first definition is bogus.

So, lets now assume that the second use of originality is correct, however, lets further define it to make it more clear. First, to find out if something is original there must be a context. This context will act like a searching parameter. The context will represent a parent context, in which we search for matching values/variables/patterns in all child objects. If none match, then the object is original. If a context isn’t defined or implied, then the originality of the unknown context is defined as being the originality of the most significant context for that object.

With this understanding we will use this paper to prove that there are in-fact things that are original.

The most significant context for this paper would be papers (of course I mean paper as in thesis’s or essays, not as in thin sheets of pulp). There is no paper with the exact same characters, format, and patterns as this paper, covering the same theories, proofs, and proving the proofs in the same way as this one. Thus this is an original paper, and thus some things are truly original.