<![CDATA[My Site - Blog]]>Fri, 13 Mar 2020 14:00:25 -0700Weebly<![CDATA[Is Math a Science Essay]]>Fri, 27 Dec 2019 00:02:35 GMThttps://thesiswritingservice668.weebly.com/blog/is-math-a-science-essayUpon arriving at this topic, I had previously been asked a simple opinionated question, is math is a science, an art, or a philosophy. I thought to myself, well of course all three. Mathematics is for the most part (at least what people see) is a science; adding, subtracting, multiplying, dividing, differentiating, integrating, etc. These are all very well defined operations which, for the most part, have very algorithmic solution methods. The art comes in the proofs. Typically, when formulating a proof youâ€™re not given anywhere to start and so, just like in art, practice makes perfect. Also, when writing theorems this process is completely in reverse and the amount of creativity required is staggering. Just try drawing a conclusion from a set of fragmented, typically unrelated information (this doesnâ€™t even have to be math related). The philosophy comes from concepts of infinity and most of set theory. A lot of early mathematics (after the Dark Age) were, for the most part, philosophers. They were fascinated by how something so simple as mathematics could model something so abstract and complicated as nature, and yet could itself become as abstract as to not be visualize-able by humans (infinite, dimensions greater than 3, etc.) So it is all three, although rarely is it simultaneously all three. One of these usually dominates while working with math at any one time. But there have been points in history where all three of coincided and it is some of the most mind-boggling and beautiful work youâ€™ll ever see. But it had got me thinking after taking this course that is math really a science, an art, or a philosophy, though for more thought out reasons. Having an art background and studying art history front and back, I came to the idea that mathematics and art go hand in hand. (And now knowing this, I have a stronger connection as to why math would be considered an art compared to a chemical engineer who would be more likely to lean towards a more scientifical view of mathematics). Math and art have quite a long, historical relationship. The ancient Egyptians and the ancient Greeks knew about the golden ration, regarded and an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid, the Parthenon, and the Colosseum. There are many examples of artists who have been inspired by mathematics and have studied mathematics as a means of complementing their works. The Greek sculptor Polykleitos prescribed a series of mathematical proportions for carving the ideal male nude. Renaissance painters turned to mathematics and many, including Piero della Francesca, became accomplished mathematicians themselves. Even look at Galileo Galilei, he wrote that the universe is written in the language of mathematics, and that its characters are triangles, circles, and other geometric figures. On the other hand, mathematicians have sought to interpret and analyze art through the lens of geometry and rationality. All of this made me realize that this all had to do with algorithms. Algorithms had to fit into the mathematical relation with art which then got me to the concept of algorithmic art. Algorithmic art, also known as algorithm art, is visual art explicitly generated by an algorithm. It is a subset of generative art, and is practically always executed by a computer. If executed by a computer, it is also classed as computer-generated art; typically, this is usually categorized as digital art. Fractal art and equation art are both subsets of algorithmic art. For a work of art to be considered algorithmic art, its creation must include a process based on an algorithm devised by the artist. Here, an algorithm is simply a detailed recipe for the design and possibly execution of an artwork, which may include computer code, functions, expressions, or other input which ultimately determines the form the art will take. This input may be mathematical, computational, or generative in nature. Inasmuch as algorithms tend to be deterministic, meaning that their repeated execution would always result in the production of identical artworks, some external factor is usually introduced. This can either be a random number generator of some sort, or an external body of data (which, I found, can range from recorded heartbeats to frames of a movie.) Some artists also work with organically based gestural input which is then modified by an algorithm. By this definition, algorithmic art is not to be confused with graphical methods such as generating a fractal out of a fractal program; it is necessarily concerned with the human factor (oneâ€™s own algorithm, and not one that is pre-set in a package). The artist must be concerned with the most appropriate expression for their idea, just as a painter would be most concerned with the best application of colors. By this definition, defaulting to something like a fractal generator (and using it for all or most of your creations) would in essence be letting the computer dictate the form of the final work, and not truly be a creative art. The artistâ€™s self-made algorithms are an integral part of the authorship, as well as being a medium through which their ideas are conveyed. Though, after delving into the fact that math is and can be very well classified as an art, I do strongly agree that math is a science because I think that math can be considered a science if you look at it from the right perspective. Letâ€™s say you have a hypothesis (imagine you are Fermat or Pythagoras). How would you prove that you were right? You would do an experiment (the proof) and arrive at a conclusion. This is the scientific method, and it does fit how mathematics is done. Sometimes it takes a while to do enough experiments to prove your theory. For one, I still cannot think of mathematics as entirely a science; the two are fundamentally different in a very important aspect: in science we have to look at reality and then give explanations, usually enlisting the aid of mathematics as a coherent language in which to frame our explanations, but mathematics is done in many other situations beyond science. Pure mathematicians are sometimes proud to claim how useless their discoveries are. In science we experiment. We go into the â€œreal world,â€ observe phenomena, go back to the drawing table, and try to explain these phenomena. Then we go back out to the world, see if we can predict a new phenomenon before it happens (when we can do that we usually say that we have discovered â€œa fundamental law of natureâ€), and either smugly rest for the day, or crawl back to the drawing table, slightly disappointed if our hypothesis did not work as we intended. This, in general, is what we call the â€œscientific method.â€ Mathematics is different. Though I do agree that mathematics is becoming an experimental discipline, particularly with the recent introduction of powerful calculating machines, it does not rely on these experiments in order to claim â€œEureka! I have discovered a new truth!â€ Mathematics requires proof, and itâ€™s very picky about what it considers proof to be. For a scientist, ten experiments with consistent results might constitute proof, â€œwithin experimental error.â€ For a mathematician, a googolplex of successful experiments is not enough proof. Instead, we rely on logic, and this thing we call â€œcommon sense,â€ fundamental logical rules we believe no one will dispute, very basic rules. Mathematics is very often inspired by nature, but it is a purely intellectual pursuit. It is just a bunch of ideas in our heads, like philosophy. Unlike most of philosophy, there is some â€œglueâ€ to it all, some fundamental unity, something we call logic, reason, order. Pure abstract reasoning. Thatâ€™s why I sometimes like to say that mathematics is applied philosophy. Philosophy under the influence of very specific rules. Then thereâ€™s the aesthetics of it. The capacity of mathematics to be an art. This is one of my favorite interpretations. The sheer simplistic beauty, the awe one can feel when one reads an entire proof and understands every aspect of it, when a surprising truth is found by unsurprising means; this is a very personal experience, I think. You really have to feel it in the flesh to understand it. That flash of understanding when a complex problem has been solved. That simple marvel of seeing many unrelated ideas congregates under a single roof of logic and order. This is what spurs the most romantic of mathematicians to keep on trying to prove that ancient conjecture. Personally, as it turns out, I do not think that anyone will really know what math really is. There may be a myriad of ways of how math can be classified, whether it is an art, a science or a philosophy. There will always be opinions for and against each concept. But as for me, my heart solely believes that math can be absolutely any of the three concepts above. I feel that maybe there are many ignorant people who do not care enough to be open minded to the fact that mathematics may in fact be all three. Who knows, I may have an opinion that can be completely inaccurate, but it wouldnâ€™t be an opinion if it could be proved wrong. ]]>