The Solar System and a Great Deal of Harmony and Beauty - Essay Example

Marissa Elliott The golden ratio, or golden mean, of 618 is a proportion known since antiquity to be the most aesthetically pleasing and has been used repeatedly in art and architecture. Both the golden ratio and the allied golden angle of 137.5° have been found within the proportions and angles of the human body and plants. In the human heart we found many applications of the golden ratio and angle. (Henein et al.) They point to the fact that fashion and beauty change incredibly frequently, that what is desirable one generation seems undesirable in the next, and how fast furnishing or clothing go out of date and while these people are not necessarily wrong. However, this position ignores the fact that there are some elements of beauty that are universal and immutable, that stay and progress through the ages and that do not change with the impulses of the population. These kinds of beauty are usually found everywhere throughout nature, but are also simultaneously elements of pure mathematics that is, they are naturally occurring but can be described by simple formulas which exist in the world of mathematics (Mackenzie, 32). I suggest a proof for immutable beauty, based on research conducted for this paper. Therefore, things that are beautiful in this way have fundamental laws of nature supporting their beauty, both in the natural and theoretical realm. Some examples of this type of beauty include conch shells, which follow a spiral described by creating Fibonacci squares, or tree branches that grow in predictable fractal patterns, or the classic example of the golden ratio (Dunlap, 8). One of the most important examples of this type of beauty is the solar system. The solar system is beautiful in part because relatively simple mathematical laws describe it and because it follows these models in repeating and highly harmonious ways (MacKenzie 38). Finally, there is a significant degree of general acceptance of the solar system’s beauty. Attempts to create mathematical formations to unify the structure of the solar system go back to Copernicus’s discovery that the structure of the solar system actually involved the planets orbiting around the sun rather than everything in the universe orbiting around the earth. One of the earliest and most important of these is the so-called Bode-Titius law, named after the two people who discovered the laws independently of each other nearly simultaneously (Hoskins). This law was an attempt to express order in the distance between each of the planets and the sun. Each planet was equal to the distance of 4+n, where the series for n is 0, 3, 6, 12 etc., and any given planet is assigned its number on the sequence (for instance mercury would be 4+0=4, and mars would be 4+12=16) (Hoskins). This formula describes the distances between the planets, for many of them, but only if one counts Ceres (now considered a dwarf planet in the asteroid belt) a planet, which was considered when these laws were created back in the late eighteenth and early nineteenth centuries (Hoskins). The fundamental idea is that this was an early attempt to express the basic regularity and beauty of the Solar System, using a similar idea and structure as the well-known golden ratio, even if it did not work that well (Hoskins). Even though it does not fit this particular solar system perfectly, the idea of planetary resonance means that it will have a high likelihood of describing any random solar system with planetary masses to some degree of accuracy. This is surprising and delightful as it is mathematically derived rather than based on observations (Hoskins). In the early seventeenth century, Kepler also created a series of laws to describe the progress of planetary motion around the sun, using three simple laws from which much more advanced and accurate ideas, that are derived. Though, like in the case of the Bode-Titius law, these mathematical formulas did not perfectly predict the orbits of the planets around the sun in exact detail, it did provide another element of the same fundamental idea that is that there is an underlying regularity and beauty to the solar system that are understood through mathematical means (Mackenzie 33). Since these scientists did their work we have discovered that there is actually a large section of solar system formation that relies essentially on random chance, the size and shape of bodies in the solar system, and that orbits and shapes of planets are actually governed by relatively complex physics of relativity and not the simple physics of the eras before it, the fact remains that these early scientists saw some inherent beauty in the solar system and tried to describe it, and that inherent immutable beauty still remains. The solar system can be interpreted as being essentially harmonious. Though we now know that planets are in fact slight ellipses instead of perfect spheres, it does not mean that the inherent beauty of the harmony of the solar system is any less pronounced One of the fundamental elements of that harmony is the repetition of elliptical forms the structure of the solar system consists of a massive ellipse at its centre, the sun (Herbest). Surrounding that sun are a wide variety of different ellipses, the planets, that mirror the first ellipse very strongly in shape if not in size or scale, as the sun is much larger than any of the planets (Herbest). These planets all also mirror each other in another important function, rotation. All of the planets except for Uranus and Venus rotate in the same direction as the sun, all spinning clockwise, all on the same plane and traveling in the same direction (Herbest). The paths that the planets travel on mirrors not only the planets themselves in their shape, but also the sun and every other orbital path. The solar system has a very regular form of natural beauty, with ellipses upon ellipses, all of the same basic shape and movement, all rotating in the same direction as they dance around the sun. Even though these movements cannot be described in detail by anything but complex mathematics, their basic movement is enough to demonstrate the immutable beauty of the solar system (Mackenzie). The final element of immutable beauty in our solar system is the fact that this harmony is not just with the major features of the solar system, that is, the sun and the planets that orbit it, but also extend upwards and downwards in scale from the solar system. Looking at each individual planet, one realizes that most planets are in fact planetary systems unto themselves, with a larger body in the middle and several smaller bodies rotating around it, often on the same plane and using the same orbital trajectory. These systems range in scale from earth, which only has one moon, to Jupiter, which has countless, many of which are just as large as Earth’s moon. So the solar system consists not just of one harmonious body, but of a large series of harmonious bodies that all follow the same rules and behave in the same way, twirling through the stars. While taking a step towards the solar system and looking at it in great detail can show an incredible amount of beauty, one can also see harmony by taking a step back from the solar system and looking at our galaxy. When you do that you realize that the galaxy itself is fundamentally structurally similar to the solar system, but this has many solar systems orbiting around a central point instead of just one. So the galaxy is a central point with stars that rotate around it, and rotating around all the stars are planets, and around all the planets are moons, all enacting a beautiful harmonious cosmic dance. It is perhaps impossible to convince everyone of any particular item’s beauty, but if there are such things as immutable beauty than the solar system has it. It follows basic mathematical laws that lead to a great deal of harmony and beauty, with the whole resembling the part and the part resembling the whole. This harmony in structure extending upwards and downwards in detail can be described as nothing other than immutable, ever lasting beauty. Works Cited Hoskin, Michael. "BODES LAW AND THE DISCOVERY OF CERES." INAF - Osservatorio Astronomico Di Palermo. Churchill College, Cambridge, 2006. Richard A Dunlap, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 1997. Henein, M. Y., Zhao, Y., Nicoll, R., Sun, L., Khir, A. W., Franklin, K., & Lindqvist, P. The human heart: Application of the golden ratio and angle. international Journal of Cardiology, 150(3), 239-242. 2011. Herbest, Daniel. Structure of the Solar System. Retrieved from: http://sciencepark.etacude.com/astronomy/solar_system.php Mackenzie, Dana. Beautiful Minds guru makes truth = beauty. Science 294(1), 28-39. 2002. Read More