Algebra As Thought Experiment :: Education Mathematics Learning Essays

Algebra As Thought ExperimentABSTRACT This paper addresses the paradox of understanding what math contributes to the exceptional success of modern mathematical physics. I urge that we give up the Kantian construal of the division between math (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 virtu all in ally the empirical world, and are true or false just analogous 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 sensible world to the extent that anything in the world has objects like those in the sham world of a particular algebra. 4) This is why algebraic techniques are fortunate even when the as sumptions of the system are false they may still be applicable to some things considered from some perspective. 5) The success of mathematical physics is likewise due to Descartes discoin truth 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 16th 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 Aristotles 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 experiment al 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 electrical outlet 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 fetch improved considerably since Galileos day.