by Sofia Carbonell
1. Man is an individual with two aspects, just like one rope with two ends. If you look at the ends, it is two; if you look at the rope, it is one. One end of the rope is limited , the other is unlimited. One end is man, the other is God. Man forgets that end and knows only the end of which he is conscious; and it is the consciousness of limitation which males him more limited. Otherwise, he would have far greater means of approaching the unlimited which is withib himself which is only th other end of the same rope, the ropw which he calls or whcih he considers to be himself. Charan Singh Ji
Mathematics are universal, to truly understand them in one language is to truly understand them in all languages. It is an intricate part of who we are and of practically everything that surrounds us. Many of us are often content with doing well in English, Spanish, and History, yet should not be acceptable. Before I did this project I must confess I did not actually believe I was setting bounderies for myself just because I refused to accept that maybe I could someday be good in math, not only that, I thought it was acceptable to do well in some classes and terrible in others. I believe that Charan Singh Ji is trying to communicate that we must not limit ourselves and good math skills will help us get through college and life itself. Math actually stimulates thought, and many times problem solving is an unconscious process which could allow us to reach beyond what we believe are our limits. Using the rope analogy, Singh Ji describes the conscious mind and the unconscious mind. When a artist is creating a masterpiece, or a mathematician is proving the impossible, they are each forgetting themselves, and the world around them which sets the boundaries; they are transcending the limits of the conscious mind and using their unconscious to reach infinity. When I am concentrated and I am solving a problem I can actually do it, I don’t really think about the time or anything around me, I am focused on the problem, and although I’m no mathematician, I have the capacity to put my mind into what I’m doing at times, something I should do more often. The other day I realized that once I got started with my homework I finished it quicker than I thought I could, not only that, I got most of the answers right. I did not use my unconscious at the level math geniuses do, but I was actually capable of understanding what I was doing. For years I have repeatedly told everybody I am not a good math student, that is the limit I have been placing on myself. I have lost my confidence when I’m answering a quiz or a test, but I never realized I had the ability to do better in math through my unconcsious, and it is a new tactic I will put into use next time, I’ll just have to wait and see the results.
2. For since the fabric of the universe is most perfect and the work of a most wise Creator, nothing at all takes place in the universe in which some rule of maximum or minimum does not appear. Leonard Euler
Although I don’t believe in absolutes in life, I do believe, however, that to keep a balance between what we do wrong, and what we do right, between good and evil, truth and lies, there most be a way to map it out, whether it be in our minds or in paper, the rule of maximum and minimum applies to almost everything. Because our human and conscious minds are limited, and the universe, knowledge, and our unconscious mind are infinite, maximums and minimums help us keep a clear spectrum of what is within our reach. To go beyond what we believe are our limits, to discover something new, or understand something we thought we would never be able to answer, is possible when we focus on one quest, question or exploration at a time. Math’s maximums and minimums are tools that help us maintain concentration on what is possible, and at the same time, help us obtain that which seems impossible. Life is full of ups and downs, maximums and minimums mimick this movement. When the economy suffers a recession, our families suffer strains, and we closely observe the graphs which show the trend to come, to learn from past mistakes, to make investments or sell stocks. Our world is kept in balance because for every maximum there is a minimum, and when this order is altered, something will take place, which will restore the order. In our lives as individuals, for every tear there laughter, for every joy there is pain, and for every achievement there is failure. In our society, for every good man, there is an evil man, and for most of us the capacity to be either one. The rule of maximums and minimums exists as a tool to map out our lives, and everything that takes part in it. It exists because there is a balance to maintain, and that balance is found around the middle of two extremes. Mathematicians and philosophers have often been the same person, in this case Leonhard Euler expresses his admiration towards the perfection of the Creator’s universe which may sometimes seem flawed. I believe that Euler utilizes this “maximum and minimum” analogy, to demonstrate that it is imperfection which makes life and the universe perfect.
3. Mathematics takes us still further from what is human, into the region of absolute necessity, to which not only the actual world, but every possible world, must conform. Bertrand Russel
Bertrand Russell’s statement is a valid position, considering that mathematics is often said to be the language of the universe. Yet, in such a concise declaration there are too many absolutes and assumptions I don’t believe any human being is ready claim. First we must focus on our existence, before we demand mathematics to be part of every world in a universe in which the farthest we’ve been to is the Moon. One of the ways we have communicated with the past is through mathematics, our ancestors, the Aztecs and the Mayans where experts in that area. To them, mathematics was a necessity, but not an absolute necessity, considering that many of them survived and lived a healthy life without knowing much about numbers and signs. Today, mathematics plays a big and small role in everyone’s life, it is a necessity in our modern world. But, to attribute such a characteristic to the entire universe just because it defines our system, is simply arrogant. In many ways, the assumption is valid, afterall, many of the discoveries that have been made in outer space have something to do with mathematics, physics and general science. Yet, we have no idea of what is our there, and we probably never will in our life times. There are probably diverse systems that we can’t even begin to comprehend, so when someone makes a claim such as the one Bertrand Russell made, thinking that being incredibly intelligent in our world gives him the right to demand other worlds to adopt that which he believes is the most important aspect of our lives is, again, arrogant. I believe that it is dangerous to make assumptions like the one Russell makes. Although mathematics aids us on a daily basis, whether in a restaurant collecting money to pay the bill, or at a store figuring out the discount on a shirt, or simply adding how many students are in one’s class, the fact remains that we know nothing about the universe other than what takes place in our galaxy, which we don’t even understand fully yet. It is a matter of approaching the world that surrounds us humbly. For years philosophers and ordinary human beings have been trying to figure out our existence, where we come from, what’s our purpose in life, and where do we stand in this inmense and posssibly infinite universe. First we must focus on our lives and the things that affect us, and how we affect other worlds, before we “conform” those worlds to our way of thinking.
4. Our minds are finite, and yet even in those circumstances of finitude, we are surrounded by possibilities that are infinite, and the purpose of human life is to grasp as much as we can out of that infinitude. Alfred North Whitehead
Our lives are not infinite, yet the possibilities to transcend mortality, and the finitude of our minds is within our grasp. We are meant to search and discover new things, to acquire new knowlege, and to live life, to really live it expands our possibilities to reach that which we believe to be impossible. Alfred North Whitehead’s statement is not only mathematical, it is philosophical. Mathematics are infinite, so is the world that surrounds us, and the fact that we have such a tool as math to understand it is a great help. Mortality forces us to do as much as we can in our life times, it forces us to live with passion, and to seek that which will surpass the limits of our existence. In mathematics, limits are infinite or finite, depending on the function affecting it, in life, the same things happens, it depends on the person’s drive to reach as much as he or she can of the infinite world around him during his life time. Whitehead wishes to define, through this quote, the purpose of human existence, and that is to find our own answers and “live as if will die today, and dream as if will live forever” (James Dean). The finite, and the infinite, are part of the same universe, therefore they are related. Our minds have limits, considering most of the time we think with our conscious mind, and are guided by our subconscious. Yet, these limitations allow us to focus on a few things at a time, giving us the opportunity to explore that which we are interested in and are passionate about, which fuels our expedition to infinitude as we learn as much as we can of that unchartered territory. Mathematics is a tool in our minds to aid us in the journey of discovery, not only that, mathematics is an infinite world far from being reomtely understood. I have come to realize that mathematicians are philosophers as well, they relate numbers, equations and their discoveries to our existence, much like the artist does in his own way. I was never aware of this world, I knew of art and history, but I forgot one of the most important aspects of our world, perhaps even our universe, which is the impact of mathematics in our lives, the role it plays explaining phenomenons, and the unexpected impact it has on philosophy. The universe, and its infinitude is made of art, science, history and mathematics, and my purpose, and duty as a human being, is to take advantage everything around me and beyond me, not only the aspects in life I believe to be the only ones I enjoy.
5. The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. Albert Einstein
This quote is important, not only because it came from one of the most brilliant mathematicians of all times, but because it is true, without mystery there would be no curiousity, hence, there would be no desire to explore and reach beyond the limits and finitude of the naked eye, and the human mind. Einstein creates a direct relationship with art and science which many believe to be opposites, not only that, he integrates the importance of imagination, mystery and the interest it sparks in human beings. Last but not least, this quote demonstrates, the reason the world has progressed, inventions have been made, and exploration has expanded into the stars; and because it is in our nature to journey into the mysterious the world will continuously change.
BIOGRAPHY
- Albert Einstein was born on March 14, 1879 in Ulm, Württemberg, Germany, and he died on the 18th of April of 1955. - He is one of the most famous mathematicians in history - When he was young, he failed physics and the entrance exam to attend high school in Germany. He later left for Zurich, abandoning his citizenship, and continued his studies. He was hired as a part time teacher, and he once wrote he had given up his dream of attending university. - During his lifetime, he was known for his goofy attitude, and his incredible commitment to mathematics and physics. - He made major contributions to the quantum theory, and also in calculus - In 1921 he received the Nobel Prize He developed the patent for atomic energy, and the theory of relativity, which is one of the things he is mostly known for.
6. To explain all nature is too difficult a task for any one man or even for any one age. ‘Tis much better to do a little with certainty, and leave the rest for others that come after you, than to explain all things. Sir Isaac Newton
In our lifetimes, we must focus on a few things, do them right, and do them for as long as it interests us. In mathematics, the same rule applies, when a mathematician is trying to prove a theorem, or simply working on a new discovery, he or she must focus on that particular problem, not try to solve many at once. Newton asseses that it is better to do the few things we do right, than do many and leave things incomplete.
BIOGRAPHY
- Sir Isaac Newton was born on January 4th, 1643 in England and died on the 31st of March of 1727. - His life can be divided into three distinct periods: his youth years in Lincolnshire, his adult life in London and other part of the world, and his most prolific period as a professor in Cambridge. - He suffered form what is called today clinical depression. - He wrote many books, including: Principia which was never published - He made advancements in Optics, and he was a very skilled mathematician making important contributions to calculus, and geometry He was mostly known for the discoveries he made regarding mechanics and gravitation