On Spectra: Part II
The one-dimensionality of our thought is not solely evident in the immediate and concrete world that we walk through, but it also projects itself dutifully onto to the abstract aspects of our lives. This may well be related to a fundamental limitation in our thinking, perhaps the limitation that maybe we can only think in a linear manner in this stage of our evolution, that all of our thought processes must progress down a narrow path, but that is for later discussion. More importantly, one-dimensionality exposes itself most blatantly in society’s thinking when we use the concept of spectra to analyze complex issues.
Take, for example, the political arena. Although I am not at all well-versed in politics, and surely have no right to speak authoritatively regarding any of the bigger controversies, the one thing that I can point out is the almost constant reference to the political spectrum. This spectrum consists a single line, just a segment marked down in one stroke by a pen upon a sheet of paper. Upon this line, we find ourselves describing all of politics. We find ourselves attempting to describe every person, every party, every group of individuals that give themselves a title, via the use of this spectrum. By standard convention, we speak of the left end being more “liberal” and of the right end being more “conservative.” But again, this is just convention, something only necessary when comparing one’s own opinions to the opinions of others.
But still, where we suffer is not in where we place each person or party, or how far one is to the “right” or “left.” We lack in that we plot an entire universe of differentiated thought onto a single pen-stroke. This whole idea actually reverts back to one of the simplest mathematical ideas in set theory, that of mapping. Mapping is defined as the comparison of the elements of two different sets of data, and is used almost constantly in daily life. In linear algebra, it shows its importance when mapping one set of higher dimensional vectors onto a second set of lower dimensional vectors. For example, we might map an arrow pointing up and to the northwest onto a flat plane below it. The best representation of the arrow that we could draw on the plane would just be an arrow pointing northwest. By mapping that three-dimensional arrow onto a two-dimensional plane, we lose crucial information about it, and our drawing becomes only an approximation of the real arrow. From the two-dimensional perspective of the plane, not only would we not know if the arrow had been pointing up or down, but we would have no concept of up and down at all. No matter how hard we tried, we would have no way of accurately describing what up and down even meant. To take it one step further, imagine mapping this arrow not onto a plane, but onto a single north-pointing line. In this case, we would remove both the up and westward components, losing even more information about the true nature of the line. However, were we actually confined to this one-dimensional perspective, our drawing of the northward component would still be the best approximation we could make, even though it may well be a very poor one.
The ideas related to mapping that I’ve just described are all well when speaking in mathematical terms, but they sadly actually “map” themselves onto abstract real-life situations quite frequently. Again returning to the example of the political spectrum, what we are essentially doing here is projecting a subject of infinite complexity and relatively high dimensionality onto a single, one-dimensional, unbending line. This is an act we choose to do, not one that we are forced to do. Unfortunately, in our linear laziness, we prevent an enormous amount of information from reaching through to our consciousness and understanding. Even with the addition of another single dimension to “the political spectrum” (thus, of course, destroying the spectrum) we would gain an enormous amount of comprehension of such a detailed and complex problem. Imagine comparing three candidates or parties or ideas not on a simple line, but on a graph with two defined axes. Even this simple expansion of our descriptive ability would tremendously augment our awareness of the nature of politics.
Of course, politics is but an example of a matter that we imprison to the spectrum. There exist countless other areas that we as humans feel inclined to illustrate through the use of a single line, such as philosophical beliefs, religious practices, and emotions, for example. Why we do such a peculiar thing I do not know. Perhaps this thought process was the one that survived after millions of years of evolution. But the evolution of the human race has become obsolete. No longer do our traits and behaviors significantly determine whether we survive and pass on our genes. Thus, we do have the ability to revert from our instinct of linear-thinking and to begin seeing the world, the universe, the ocean of possibilities and ideas, in a multi-dimensional manner. True, some things may be of infinite complexity, of infinite dimensionality, if you like, and they be unreachable in their absolute form. However, if we continue to add dimensions to our thinking, even though we may never be able to perceive the true and unmasked nature of certain things, we can always come closer in our understanding, and that is what is most important.
