HIGHER DIMENSIONS
Lately, I have become obsessed with extra dimensions.
I felt like putting their understandings in perspective, in the following way.
Instead of dealing with the intricacies of combining earthly shapes to form higher dimensional, rather imaginary objects, my method involves spinning and rotating subsequent shapes starting from a point to the higher dimensions. This method helps us utilize symmetry, and convergence of all shapes into circles in one dimension, disks in two dimensions, and three-dimensional spheres that emulate the behaviors of our universe and possibly its emergence into being.
I felt like putting their understandings in perspective, in the following way.
Instead of dealing with the intricacies of combining earthly shapes to form higher dimensional, rather imaginary objects, my method involves spinning and rotating subsequent shapes starting from a point to the higher dimensions. This method helps us utilize symmetry, and convergence of all shapes into circles in one dimension, disks in two dimensions, and three-dimensional spheres that emulate the behaviors of our universe and possibly its emergence into being.
At the beginning, there was a point. Infinite number of points lined up to make a straight line or a bending line, where in case the two ends meet, they make a closed curve. The circle is a perfect example of a symmetrically closed curve. It is formed by connecting a complete circle of points equidistant from a center point. Swiping all points of a line (radius) around a center point makes a disk - a circular plane. This is a two-dimensional shape in space. If we rotate a circular plane on itself (spin) one complete round, it will make a sphere. A sphere is a three-dimensional object. We are limited to a three-dimensional space. So far, we can describe a three-dimensional space in a two-dimensional plane, for example on paper, a monitor, or a blackboard. A fourth dimension in my opinion is a sphere rolling and creating a curvature in space. That is like a three-dimensional scale leaving an imprint on an imaginary canvas.
All other geometric shapes can be inscribed, or circumscribed around a circle, a two-dimensional disk, or a three-dimensional sphere.
All of them converge to their corresponding symmetrical shapes as the number of sides infinitely increases (polygons and polytopes alike) to infinite points. The exceptions are triangles and quadrilaterals, pyramids, and polyhedrons, as they present subsets of polygons. Like polygons, all can be decomposed into triangles and quadrilaterals of the same area and vice versa, which means all of the regular earthly shapes are the decomposed versions of the higher dimension. https://youtu.be/ysV6iF3Rmjo
We can present a three-dimensional object on a two-dimensional plane using xyz axes perpendicular to each other. An imaginary fourth dimension can also be drawn but it looks like two separate systems touching each other. To present a fourth dimension on a true three-dimensional space instead of a plane would show the hidden sides we cannot see. But the possibility of doing it is very dim. As dimensions increase, we lose the sense of imagination about what they should look like, let alone try to present them on a two-dimensional plane. Or we need to learn how to draw higher dimensional figures over a three-dimensional sphere. Otherwise, I guess we need to leave it to those who can see us but we don't.
