The Essence of Mathematical Reality | Teen Ink

The Essence of Mathematical Reality

February 19, 2021

Our reality is the totality of all things containing existence. But, how many kinds of reality are there, out in the vast universe, or even beyond. The truth is, many. If it wasn’t for reality, we wouldn’t be here. But, for now, two of the most know realities are physical and mathematical reality.

Grab a pencil and paper and draw a point. Is it a perfect point? The answer is no. A point is a geometric element that has no dimensions. Does the point you just drew really have zero dimensions? Apparently not. It has a certain amount of width and height. And it’s not perfectly a dot, it will always have a ton of miniature circles and unsymmetrical pixels in the dot, even if the dot has been printed by the cosmos’ finest printer. All of this is in physical reality; an inadequate, unpleasing, and imperfect reality. Any measurement made is just a rough approximation. Physical reality is a disaster, nothing is what it appears to be.

What we really envision in our mind is mathematical reality; an imaginary reality where anything we want can be perfect. No matter how impossible it is in physical reality, it’s still perfect in your mind. A dot is perfect. A line is perfect. A circle is perfect. This opens up a whole new perspective on math. A perspective of which is one of the founding fathers of math.

“It can be as simple and pretty as I want it to be. I get to have all those perfect things I can’t have in real life. I will never hold a circle in my hand, but I can hold one in my mind. And I can measure it. Mathematical reality is a beautiful wonderland of my own creation, and I can explore it and think about it and talk about it with my friends.” — “Measurement” by Paul Lockhart

Physical reality and Mathematical reality are two whole different fields, one being imperfect and the other being perfect. The world wouldn’t be here without them. Their significance marks humans with their essence forever, and us, never being able to lose our grip on them.

Physical reality is a mess. Mathematical reality is the real hero.