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What is music? What purpose does it serve? Can it be objectively understood? I play guitar and write my own songs. I've thought about music quite a bit over the years, and my starting point has been the idea that music is essentially an auditory re-creation of reality. Much like language, it probably began onomatopoetically, through simple singing that mimicked sounds in nature, like the melodies of bird calls or the rhythms of footsteps. Clapping and basic instruments were probably invented to accompany singing, and thus a whole art form was established, perhaps as a means of remembering important cultural events and information. Various musical tools, like early wind or stringed instruments, may have been originally designed to represent particular sound-producing objects or animals in nature, and unique rhythms and melodies were intended to mimic specific sequences of sounds in nature. Perhaps this is still how music works: it is merely another way to symbolize, in auditory form, aspects of nature. On the more sophisticated levels of music, a long and complex melody could be thought of as an imaginary speech that is spoken in a language we don't yet understand. Despite our ignorance of the foreign language and the conceptual meaning of the speech, we can still recognize certain objective qualities. We can ask, for example, whether the melody or speech mimics anything in reality that we do conceptualize, such as a fast or slow pace, an ordered or random combination of elements, a harmonious or dissonant fluctuation in sound, smooth or abrupt changes in tone or volume. The recognition and evaluation of such qualities in a piece of music, or a speech we don't fully understand, will naturally cause us to think or feel a certain way, based on the simple things we do understand about it. Mimicry, of course, is a key factor in human development, and I suspect that it's crucial to understanding the nature of music. In considering a piece of music, my first question now is: what aspects of nature are the elements in the song trying to mimic? And now I leave you with the immortal Steve Vai, using his guitar to mimic the baby-talk of his child.
I have put a lot of effort into this blog over the last few years: Objectivism for Intellectuals | Exploring the depths of Ayn Rand's revolutionary philosophy. I always strive toward intellectual rigor and creating an understanding of principles' contexts in the reader. Sometimes this means that the writing doesn't flow as smoothly as it might if I were to write in a more casual style. But I hope that intelligent and thoughtful people will appreciate the rigor and perhaps gain some insight from it.
Why π is an irrational number This is a question I've had for over 5 months and recently I think I've found the perfect solution for it. This is the first draft of my thesis. Be in mind that I'm only a 17-year-old engineering student and that English is my second language. Also, it is possible (and probable) that many other people have written about this, but I've come up with what I've written by myself. According to the Euclidean geometry, a circle is a two-dimensional figure formed by the points equidistant from a center. This set of points is called a circumference and the distance between them and the center is called radio. The ratio between the circumference and the radius of any circle, according to Euclid, is 2π, π being a number close to 3.14. Throughout history, people tried to figure out the exact value of π, until Lambert proved using tangent theory that π was irrational number, meaning that it can not be defined as a fraction of a whole and, more importantly, does not correspond to anything that exists (hence the term irrational). But how is this true? How can a figure that we supposedly see every day have an irrational measurement, i.e., a nonexistent one? The answer to this intriguing question is that Euclidean circles do not exist. It is impossible to find more than four points that have the same physical distance from a central point. You can see it when trying to find points equidistant from another point on a Cartesian plane in R2 (x, y). This is true regardless of the size of the plane. (Note: only natural numbers can be used in this plan because there are only natural numbers in the universe. There aren't two atoms and a half, and even without knowing what is the basic unit of the universe, we know it has a specific x, y, z dimension.) For example, the point (10,10) only has four points which are 5 away from it: (5,10), (15,10), (10,5) and (10,15). There are, however, points which have a distance close to 5, as the point 14,11) which has a distance of square root of 17. It is easy to see on paper the difference between 5 and 17 ^ 0.5 cm, but not between 5 x 10 ^ -10 and 0.5 x 17 ^ 10 ^ -10, something closer to reality when you look at a circle drawn with a modern computer. Or between 5 x 10^-googolplex and 17^0.5 x 10^-googolplex, closer to the circle used when super-computer software tries to estimate estimate π. For this reason, we are faced with (approximate) "circles" in our day to day lives, but in reality there are no perfect circles as Euclid described them.
“Don’t tell me it’s impossible; tell me you can’t do it. Tell me it’s never been done… the only things we really know are Maxwell’s equations, the three laws of Newton, the two postulates of relativity, and the periodic table. That’s all we know that’s true. All the rest are man’s laws.” – Dean Kamen, inventor of the Segway and recipient of the National Medal of Technology and Lemelson-MIT Prize. This quote really struck me. It really got me wondering if this is true? I presume he is talking of Physics and Chemistry. Is everything else, except these things he mentions, we know theories we ourselves have developed with our own experience and thought?