The definitions of 0 and 1 as symmetries and its unification with physics and formal logic through a transformation.
Let's first clear something out : I AM AN ARTIST, . I never practice or understood any high level mathematics well enough to work with it. So for most of you my words are nonsense. However the path they follow is making-sense in term of transformation .
In other words all I do is talking the numerical terms and define them by some experience we can all agree on. Then I keep that definition across some other disciplines such as physics and logic.
Lets start by defining numbers as symmetries and use integers as the numbers we like to express:
Thus a symmetric number is a number that can be constructed out of even parts (two or more)
An asymmetric integer is a symmetric number + 1
1 is the fundamental a symmetric unit
2 is the fundamental symmetric unit
0 is none exited thus is not a number and represent nothing.
In order to define the numbers we had to use operations
any number that is not 1 requires an operations to be constructed, thus an operation is part of the number definition not a separate definition.
Since numbers are constructed we can attribute the "construction" quality to the operations.
Only 1 is a none constructed number, and as such is unique and is own category
All other integers are either prime or non prime .
Now lets look at symmetries and at the meaning of 1 and 0 from the point of view of binary based system in which the term "binary" means a system of numerical notation that has 2 rather than 10 as a base. In such system we have two numbers 0 and 1
When we do this something very interesting emerge : The value of each number have no fundamental meaning. the only meaning is that: One term represent all that the other term dose not.
This is very profound on a few levels:
First it means that the most fundamental idea of numbers, that of unit, is not valid. 0 can mean nothing (no unit) and 1 means everything that exist (a unit of infinite size). This then means that in order to make use of it as a unit we must introduce the idea of a pattern. When we do this we realize that the most fundamental formation of a linear structure is that in which time generate the geometric expression of what we then consider as spacial dimension. It explains time as the generator of any spacial expression. Not an added forth dimension but rather the basic condition for space to emerge.
Now the second reality that emerge from the binary based system is that in a binary system, The terms, standing alone are each symmetric representation of a state as being everything that the other term is not. Thus here asymmetry can only represent a a state rather then a term.
So what is an asymmetric state of a binary system?
That state is expressed in logic as "true" or "false" . However the meaning of 0 and the meaning of 1 as a symmetry is not consistent once expressed as a truth table.
Thus or the case I am trying to make here which is forming one coherent and consistent definition for 0 and 1 , I will need to assign 0 to a logic term which say that if both sides are the same then we get a true term in the truth table .
Thus Xnor which means that a true result is a product of only one of the two terms holds reflect the proper symmetric representation of 1 an of 0 . This result as shown by by truth table keeps the consistency of 1 as representing an asymmetric state even if is as a true state.
0 0 0
1 0 1
0 1 1
1 1 0
At this point let me remind you what is it that I try to do here. It all can appear as total nonsense unless one realize that the core operation which I perform is a "transformation" . I take a term that have no meaning and assign meaning to it . then I move it between different disciplines while using consistency as a guideline . Once I perform one consistent transformation using one or two terms , I can then apply all other terms that may emerge in one discipline to all other disciplines
Now also this work in the other direction since in fact we have used a binary state and apply to a non binary representation of objects.
The thing that I try to show here is how we can perform full transformation without any contradiction.
Once we do that we can use the same terms to all disciplines and by doing that, creating a unification of concept under a single representation we consent to an the function of transformation as the most fundamental one.