What Is Infinity?

At the beginning of class, our first group discussion was to introduce ourselves and state why we were interested in taking this course. For many, the interest laid in infinity and what connections it had in both mathematics and art. Next, the most basic question was asked; “what is infinity?” Everyone had an opinion. We could all agree the infinity was something large scale, something massive, that doesn't have an end. When asked for examples of infinity the universe was brought up. This seemed logical at first, yet we were stumped. Our critical thinking skills began to take place as everyone pondered at this question. Seeing our confusion, Professor Hamman asked us what defined something finite. Surely, if we can determine what makes something finite, then we must be able to determine what is infinite! As a class, we began throwing out examples of things finite: Oil, an inch, life, roads. What makes these things finite? We determined that if something has an end, it must be finite. Therefore, something that does not have an end must be infinite. We began to look back at the universe, as we debated whether this is really an example of something infinite or not. Part of the class argued yes, while others disagreed. After much debate, it was decided that if you believed in the big bang theory, then all the matter in the universe is the same as it has always been, just more widespread. This meant that the universe wasn't infinite after all. However, this is only true if you believe in the big bang theory, thus; your perception plays a part in what’s infinite or not. Could something be infinite? What about the number of books that could be written? We examined this notion. We found that if you wrote a book with one letter, or two letters, or three or four, the number could go on indefinitely creating an infinite library. We began to look at things differently. We thought of infinity as something large, but what about something small? Can the space between two items be divided infinity? One half of an inch is a half inch. Half of a half inch is a quarter inch and so forth. This theory shows that space can divide infinitely. Have we discovered what infinity is? Or are we just as lost as we were? 

By the end of class I think we all understood why the concept of infinity could drive a person crazy. Professor Carter introduced us to John Stuart Mill, a musician who believed that music was finite and went into depression. So if the idea of infinity will drive you mad, and finite make you sad, I ask us as a class; what have we gotten ourselves into? Although our class extended past our release time, we still only seemed to scratch the surface. 

Finite Music

Jade Ballard

Finite Music

When we began to discuss the concept of infinity during HP 102, one of the first things that came to my mind was, “Music is infinite.” After further exploration, I began to understand the point of view of that music, when looked at as a series of possible combinations, is actually finite. Although it was very hard for me grasp this concept, there is a mathematical way to measure the possibilities of music based on using a formula. Although music is considered finite from a technical standpoint, I think if you’re too concerned about the possibility that we might run out of music or that there will be a time when the musical combinations will be exhausted, you’re missing out on the beauty of music.

In the Autobiography of John Stuart Mill, he writes about his great love for music but after discovering the idea of music being finite, he becomes depressed. For instance, he writes, “The only one of the imaginative arts in which I had from childhood taken great pleasure, was music; the best effect of which (and in this it surpasses perhaps every other art) consists in exciting enthusiasm; in winding up to a high pitch those feelings of an elevated kind which are already in the character, but to which this excitement gives a glow and a fervour, which, though transitory at its utmost height, is precious for sustaining them at other times” (7). These words express how music makes Mill feel joyful, enthusiastic and excited from hearing music. Furthermore, Mill writes, “And it is very characteristic both of my then state, and of the general tone of my mind at this period of my life, that I was seriously tormented by the thought of the exhaustibility of musical combinations” (8). This idea of “the exhaustibility of musical combinations” refers to Mill’s his discovery that music is finite.

However, Mill perceives this idea of finiteness as a terrible, depressing concept. He elaborates by writing, “The octave consists of only five tones and two semi-tones, which can be put together in only a limited number of ways, of which but a small proportion are beautiful: most of these, it seemed to me, must have been already discovered, and there could not be room for a long succession of Mozarts and Webers, to strike out, as these had done, entirely new and surpassingly rich veins of musical beauty” (8). These words illustrate how Mill feels that because music is finite, there are only a limited number of ways in which music could be expressed. His tone of voice implies that the fact that music is finite is a hopeless thing, because there would no longer be any musical greats such as Mozart or Weber to arise. I would argue that Mill has a limited point of view when it comes to music and he has a distorted perception of what musical beauty is. I believe Mill is solely basing his ideas on musical beauty from a Western standpoint, and keeping a narrow minded perspective when it comes to music. Many years have passed since this piece of work was written and there are still thousands of musicians creating music today. Although the number of musical combinations is considered finite, it doesn’t stop thousands of musicians to continue to create works of art.

I feel that music is a subjective experience, and that being said, everyone has their own unique interpretation of what music means to them. I think this is also true in how you perceive the idea of music being finite. Just because music is finite and has a set number of possibilities does not mean it is not valuable or important as a whole. Even though there is a way to measure the large number of possibilities of ways to create musical combinations, does that mean everyone should give up making music or enjoying music? I have to disagree with Mills and I don’t believe this is true at all. To me, the number of possibilities for musical combinations is so vast it is very difficult for my mind to even comprehend this idea. It seems like it is such a large number to even fathom. Even if you were to calculate the number of possibilities for music, the number would surpass the possibilities to be created during my lifetime. And besides, music means so much more to me than a mathematical formula. I feel that we imbue meaning onto the music we love and can relate to. Listening to music, actively engaging in music and experiencing music is hard to define, but I feel it would be most akin to a spiritual experience. To me, the meaning of music is something that is difficult to pin down, but I know it something that stirs the emotions and is beyond a limited definition of a mathematical formula. If we are too concerned with the idea of “exhausting musical combinations” in the future, we fail to recognize and acknowledge the musical beauty in our present lifetime. Creating meaning is part of what it means to be human and I feel that the joy which resonates from music can be universally experienced by everyone.

Bibliography
Stuart Mill, John. Autobiography. N.p.: n.p., 1873. Print.