Algebra As Thought Experiment

3042 Words7 Pages
bulb-icon

Recommended: The history of algebra

Algebra As Thought Experiment

ABSTRACT: This paper addresses the problem of understanding what mathematics contributes to the exceptional success of modern mathematical physics. I urge that we give up the Kantian construal of the division between mathematics (synthetic a priori) and physics (experimental), and that we ask instead how algebra helps synthetic a posteriori mathematics improve our ability to study the world. The theses suggested are: 1) Mathematical theories are about the empirical world, and are true or false just like other theories of empirical science. 2) The air of artificiality in mathematics lies exclusively in the use of algebraic method. 3) This method is constructive much like all fiction is, but this construction is for the purpose of experimental investigation of the physical world to the extent that anything in the world has objects like those in the fictional world of a particular algebra. 4) This is why algebraic techniques are successful even when the assumptions of the system are false: they may still be applicable to some things considered from some perspective. 5) The success of mathematical physics is also due to Descartes' discovery of a remarkable truth: we live in space and time which can be described as a whole. 6) Therefore, what distinguishes modern science from earlier and later philosophy is not a general method of science, but the fact that it happened to find a truth, and a particular way of studying reality which bore fruit.

In the sixteenth century, physics was a part of the general subject known as philosophy. When Galileo wrote the Dialogues Concerning the Two Chief World Systems, he was commenting on some aspects of Aristotle's Philosophy. He was more favorable to the use of mathematics in various problems of physics than was current in his day. He may be described as trying to revive an Archimedean conception of motion in terms of geometry, which may be called "kinematics."

Galileo also introduced the experimental method into physics. The experimental method had been very successfully utilized in Alchemy, which was a low or a clandestine science at the time. Its success in physics brought the issue of experimentation into the spot light. Since there are few claims original to Galileo that we may still wish to defend, we may want to describe his success as the introduction of these techniques which he invented or adapted for subsequent physicists to employ. Experimental techniques have improved considerably since Galileo's day.

Show More
Related

  • Galileo Galilei: Who Is Galileo The Great?

    886 Words  | 2 Pages

    At this point, Galileo’s career took a dramatic turn. In spring of 1609 he heard that Netherlands this instrument was invented that showed things that are far as though they were nearby. After, few tries he quickly found out the secret of the invention is a three-powered spyglass from lenses for sale in spectacle makers shops. To improve this, he taught himself the art of lens grinding, and produced powerful

    Read More

  • Galileo Galilei

    662 Words  | 2 Pages

    “I have never met a man so ignorant that I couldn't learn something from him” (qtd. in “Nothing But the Facts About Galileo Galilei”). This was the adage that Galileo lived by. He consistently made it his purpose to understand and decipher the world for himself, and there was not a single person in the world that he was incapable of learning something from. During his youth, Galileo’s father had wanted him to study medicine in order to make a profitable living; at this urging, Galileo attended a medical university, but almost failed and ended up leaving without a degree. During his time at the university, however, he did make his first (and one of his most important) discoveries. He found that the period of each swing of a pendulum was exactly the same. This would come to be known as the law of the pendulum and would provide the basis for the regulation of clocks. A few more of his benefits to society came purely from the fact that he needed money in order to pay his debts. Some examples of what he threw together during these times of need include a rudimentary thermometer and both a military and civilian compas...

    Read More

  • Stand Up For Your Beliefs

    966 Words  | 2 Pages

    ...ath. Through Haimon’s character, Sophocles reveals the importance of staying true to one’s beliefs no matter the circumstance.

    Read More

  • The Impact of Westward Expansion on The Cherokee Nation

    1470 Words  | 3 Pages

    2. “Cherokee Culture and History.” Native Americans: Cherokee History and Culture. N.p., n.d. Web. 02 Mar. 2014. .

    Read More

  • Galileo

    529 Words  | 2 Pages

    In 1564 Galileo Galilei was born. Pursuing his love for science, he grew up to become the father of experimental physics. Among his accomplishments were the isochronism pendulum and the hydrostatic balance. He also is credited with improving and profiting off the telescope. All these discoveries gave Galileo a great reputation allowing him to land a job at the University of Pisa. While there he started to develop interest in the Copernican theory of heliocentricity. This was dangerous work. The heliocentric theory directly conflicted with church teachings that everything, sun included, revolved around the earth.

    Read More

  • Analysis Of Michael Guillen's Five Equations That Changed The World

    1061 Words  | 3 Pages

    Michael Guillen, the author of Five Equations that Changed the World, choose five famous mathematician to describe. Each of these mathematicians came up with a significant formula that deals with Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. The book is divided into five sections, one for each of the mathematicians. Each section then has five parts, the prologue, the Veni, the Vidi, the Vici, and the epilogue. The Veni talks about the scientists as a person and their personal life. The Vidi talks about the history of the subject that the scientist talks about. The Vici talks about how the mathematician came up with their most famous formula.

    Read More

  • The DIary of Anne Frank

    1077 Words  | 3 Pages

    ...eams; he moved on from his rainstorm and worked hard to get to the position he wanted to be in. His success was carried through his mindset and what he believed he could achieve.

    Read More

  • Chaos Theory

    1962 Words  | 4 Pages

    Since its inception, science relied on predictability and order. The true beauty of science was its uncanny ability to find patterns and regularity in seemingly random systems. For centuries the human mind as easily grasped and mastered the concepts of linearity. Physics illustrated the magnificent order to which the natural world obeyed. If there is a God he is indeed mathematical. Until the 19th century Physics explained the processes of the natural world successfully, for the most part. There were still many facets of the universe that were an enigma to physicists. Mathematicians could indeed illustrate patterns in nature but there were many aspects of Mother Nature that remained a mystery to Physicists and Mathematicians alike. Mathematics is an integral part of physics. It provides an order and a guide to thinking; it shows the relationship between many physical phenomenons. The error in mathematics until that point was linearity. “Clouds are not spheres, mountains are not cones, bark is not smooth, nor does lightning travel in a straight line.” - Benoit Mandlebrot. Was it not beyond reason that a process, which is dictated by that regularity, could master a world that shows almost no predictability whatsoever? A new science and a new kind of mathematics were developed that could show the universe’s idiosyncrasies. This new amalgam of mathematics and physics takes the order of linearity and shows how it relates to the unpredictability of the world around us. It is called Chaos Theory.

    Read More

  • Galileo Galilei

    1961 Words  | 4 Pages

    Inventor and astronomer Galileo Galilei is one of the most well-known scientists in the history of the world. Galileo has been credited for many astonishing inventions such as the pendulum and the telescope. Through many years of research and studious acts, he discovered behaviors of the universe that still hold true today. Galileo, “the Father of Modern Science”, changed the world.

    Read More

  • United States Route 66

    1501 Words  | 4 Pages

    Kilfoye, C. (2013). A voice from the past calls for classroom technology. Phi Delta Kappan, 94(7), 53-56.

    Read More

  • Anne Frank: The Diary Of A Young Girl

    1437 Words  | 3 Pages

    Anne Frank: The Diary of a Young Girl narrates the journey of adolescent Anne Frank during World War II. The diary provides insight into the changes Anne went through during the war after going into hiding to avoid persecution. Over the course of her time in hiding, she matured and used her diary to voice her innermost thoughts and desires. Anne’s diary shows how she came to terms with change, and how she herself changed and conventions such as point of view, characterization and voice enhance the themes and key ideas expressed through Anne’s journey.

    Read More

  • Technology in the Classroom

    1792 Words  | 4 Pages

    Technology is becoming more and more dominant in our society.Everyday upgrades are being made and new innovations are being discovered. Technology is all around us whether we want it to be or not: it is the vehicles we drive, it can be found in our homes, and can even be found in the grocery store.Every place we look there is some type of technology.I believe technology has had a major impact on our school systems and is still impacting it today.There are those who do not agree, though, that technology has impacted our schools.Eric Gormly writes, “In fact, many theorists point out the overall impact of technology on education has been quite small, manifesting little discernible change in the classroom.” [1]Yes, there are some schools that are not as advanced as others, but many of them do have a significant amount of technology in them.I find it fascinating that so much technology has been incorporated into our classrooms, but I believe that, even with all of the positive aspects that are associated with technology, there are some negative and even dangerous aspects that should be taken into account.I will be sharing some of the equipment that has been used in the schools, how both the students and the teachers use the equipment, and also the positive and negative effects that technology has had on our schools.

    Read More

  • Galileo Galilei

    750 Words  | 2 Pages

    In 1609 the telescope was invented and Galileo began making his own lenses for better telescopes and then started looking at the sky. In December and January (1609-1610) it is said that he made more discoveries that changed the world that anyone has made before or since. He wrote a book called the “Starry Messenger”, and said that there were mountains on the moon, the Milky Way was made up of many stars, and there were small bodies in orbit around Jupiter. He used his mathematical skills to calculate the motions of these bodies around Jupiter. In 1610 he started looking at Saturn and discovered the rings, and the phases of Saturn (just like our moon’s phases).

    Read More

  • Replacing Textbooks with Tablets

    1009 Words  | 3 Pages

    As more people began to access the Internet through smart phones and tablets rather than laptops and computers, it is not a surprise that they would also want to transform the American education system by bringing tablets into classrooms. In fact, a few schools around the country have already replaced textbooks with tablets and have seen improvements in students’ standardized test scores. Using tablets instead of textbooks is not only convenient and helpful, but it can also reduce the amount of paper wastes in school. However, it is not a good idea to completely transform textbooks with tablets with the current technology, for it can not only be damaging to the environment and costly to set up, but also might not be effective in improving K-12 education in the long run.

    Read More

  • The Diary of Anne Frank Book Review

    1379 Words  | 3 Pages

    Anne Frank: The Diary of a Young Girl was a very distressing yet amazingly written book. Who would have thought that such a little person could have such a huge effect on the world? Anne?s father lived for many years after the war and made sure that Anne?s diary was published. Her diary was published in 1947 and was then made into a film. This diary helps people remember what Jews had to go through and hopefully reminds them of how lucky they are. By remembering, it is hoped that something like this will never happen again. This book was intriguing while incorporating many life lessons. Discrimination, unfair judgment, and racism are only a few of the many lessons that this book has to offer. With that, after reading this book, we have learned to not take the things we have for granted because in a matter of seconds, days, months, or even years, it could all be gone. As Anne said in her diary, ?In spite of everything, I still believe, people are truly good at heart?.

    Read More

More about Algebra As Thought Experiment

Open Document