Think back to grade school when you had the dreaded (or beloved) art class that you couldn't get out of. As part of the curriculum, the powers that may be decree that we must all be flexible in our mindset and broaden our horizons of creativity. Thus, the youth of America is forced to take mundane and often tiresome creative arts courses such as "visual arts". In this class, we learn the fundamentals of visual aesthetics, to intuit the meaning of a painting that an artist may have only thought to be a pretty picture, the science of colors, and spatial perception/illusions if you are lucky. However, I've got a little bit of a beef with those who have done me wrong -- I don't believe in the color wheel.

As a child we are lead to believe that there are absolute opposites. Night and day or black and white, for example. These are absolute opposites. However, as we broaden our mindscape and our intuition becomes increasingly developed, we start to realize there are generally no such clear-cut certainties in life. The idea of a graduated progression of two polar opposites dawns on us as we start to observe the world a bit closer. We see that the judicial system isn't always so simple -- yearlong trials with a panel of our peers to decide the fate of the accused. Considerations, factors, circumstances all tie into the complicated process of deciding the truth-value of complicated issues. Black and white are no longer clearly defined, and in its place is now the spectrum of opposites with a blather of gray in between.

Eventually, young adults are introduced to the idea of the spectrum. Colors mix, colors add, and colors subtract. Ideas converge and conflicts arise as we further explore the fundamentals of absolute truth. Century-long battles have been waged over divergences in the same fundamental beliefs. Absolute truth has become a matter of, "My God is more powerful than yours." And thus the realization of similarities amidst differences. The equation of life becomes a little trickier. Even through high school, the same lame "fine arts" courses are pushed on the unsuspecting. Pressing the ideas of identifiable boundaries and fine lines – we've all been a little lied to. Think back, way back, to that visual arts class you had your sophomore year of high school you remember the color wheel, and it's immense value to humanity as a whole.(stupid color wheel) "Opposites go on opposite sides of the wheel, complements go next to each other." I wonder if these art teachers ever have to take complex upper level calculus courses or differential equations classes to broaden their understanding of the abstract universe?

Sometimes things just aren't as simple as they seem. Things were never as simple as black and white, although in our primitive state of mind we believed them to be. Perhaps the fine arts teachers were on to something. The right idea, but the wrong dream. The "Sphere of Opposites", as I call it, is a bit of a home brewed idea of the color-wheel, but can be applied to all areas of logic and science and taken to the third dimension. In our model, we simply have a sphere that contains areas of focus. Such areas contain ideas or thoughts, or in the case of art, colors. Compliments rest next to each other with a graduated transition into each other, and opposites lie on the opposite side of the sphere, with a graduated array of possibilities connecting the two opposites. The center of the sphere is the focal point of all opposites, and is the opposite of everything. So the basic picture that should be painted in your brain is a patchwork of colors on a globe dangling in space. Be careful, however, as the center of the sphere may or may not exist. Consider the following: Think back to calculus III and the existence of limits of three-dimensional surfaces. In order for a limit to exist, all sections, or linear equations that constitute the 3d surface, must approach the same value (i.e. not divergent). Think of it in terms of a bunch of tiny bugs or particles crawling along the surface of a infinite plane in space -- if all the bugs walk towards one point on the plane, in order for that point to exist, all the little critters must meet at an single point. If they do not, there must be some asymptotic effect stretching the plane to infinity in one direction or the other. Much in the same way in our spherical model of truth, all conditional statements (or colors) must approach the same opposite value -- the center of the sphere. In the case of a "Color Sphere", you may not have a hollow sphere, because the center may not exist. If, instead of considering black and white as achromatic pigments that are part of the neutral gray series, you consider black and white as being members of the visible color spectrum, the model of the color sphere gets a little hairy – it has no center. Reason being that, if you were to somehow manage to fit black and white into the complex web of compliments on the surface of the sphere, there are no opposites of any color that are opposites of black and white. So, instead, we might reserve a separate color sphere for these pigments.

The same would follow for all other logical inductions, or scientific ideas. Adding a third dimension to the descriptive capabilities of a graphical representation can be highly beneficial. Having the property of depth can add a whole new level of comprehension. However, with the complicated nature of three-dimensional representations, other considerations such as diverging limits might occur.