The Identity Property
There is a property in math, called the identity property. You take the input, stick it into a function, distortions and contortions and portions fly around, spit it out and its the same thing that came into the function in the first place. f(a) = a. 21 years into my life and I feel like this function. The fun part is finding new iterations that represent the same thing.
The fun part is finding new iterations that represent the same thing.
See a³/a² = a, but so does 2a/2 or a^(log base a of a). There are so many ways of writing an identity function. Some ways even involve other characters like [(a² + 2ab + b²)/(a+b)] — b. Each one has its own value in its own context and each allows us to see the world in a different way. While yes that admittedly got very mathy very fast, I believe it was important to give each of those examples because you see the variety of ways in which we can have the exact same thing.
Now of course, this is only one way of putting a through a function. a can be put in a situation that is “not” an identity situation. Taking the last example (a² + 2ab + b²)/(a+b). This is the crux of the example I’m going to take but instead of -b, we will set it EQUAL TO b:
(a² + 2ab + b²)/(a+b) = b
Now you no longer have an identity situation. While yes you can simplify the left hand of the equation like so:
(a+b)(a+b)/(a+b) = (a+b)
Put it in context of the full equation:
(a+b) = b
Subtract out:
a = 0
So you started with a new assumption, f(a) = b. Then you set out to find the condition of a, given the above function, which makes that true. Imagining that you are a in this scenario, that a is a variable representation of your person, you see that you can only become this new quantity b, by making nothing of yourself — by setting yourself equal to 0. Now granted, I chose a completely arbitrary function in which it so happened that a comes out to 0 in order for f(a) = b to be true. But the result a = 0 was only used for dramatic and metaphorical effect to make a larger point hit home. If you are a in this scenario, you realize that a is just a variable. It is an empty void, which can take on any value it so pleases. A different function, 1/2b (a + 1), has the solution for f(a) = b as a = 1. Different function, same general equation, f(a) = b, but entirely different value of a.
Now I want you to really stretch your mind and imagine that YOU ARE A. That this variable in this equation isn’t just an arbitrary symbol representing some thing, it is YOU. It represents YOU. Now, what is truly remarkable is that while it is not difficult to put yourself in these abstract shoes and say, “Yes, I am a”, you can do so and simultaneously still see the bigger equation. So then, you are a, but at the same time you have the ability to step outside yourself, set the equation, create the function as you will, and take on the necessary value needed to complete the function. You have the ability to set the goal and the method while still being a the whole time. You have the ability to set the equation and the function to get the result you want, to be the a you want to be.
And let me ask you this — through this whole process, what is a? What is a — I ask you to really think about this. It is not until we set the equation, form the function, and set the parameters that a takes on a value. And this begs the question, if you are a, but you can see and set the equation and parameters to some destination you want to reach, how do you know what that destination is? Since a is nothing until it is defined, how can it define itself? The answer of course is that a is everything just at the same time it is nothing. In a single variable, we have the entirety of the cosmos.
In a single variable, we have the entirety of the cosmos.
But the moment it tries to define itself, the moment it sets its boundaries and destination, it loses this quality of the infinite. You get a solution, like a = 1, or a = 0 and that is what it must be. You see then, that you CANNOT set a definition for a because a in of itself is indefinable and the moment it is defined, it is no longer a.
So then, we must not attempt to define ourselves. We must not attempt to set the parameters of our functions and reach an end point we determine we must reach. Because in so doing, we have lost all the infinity of what we were to start with, we have lost the fact that f(a) = a. You see then that the only way TO define ourselves, is to say we are nothing other than what we are, and what we are is nothing! And therein lies the truth we’re all searching for, only it comes when we stop searching!
Now, this is not to say that a should never take on a value. Specific iterations of a are invaluable, but in so defining yourself as a specific value, do not forget that beneath that definition is this capacity for the infinite. It is through this property that I say that we are uniquely one and the same — we are all f(a) = a.
