Matt+King+Entry+1

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The articles selected for this week's readings give the history of the earliest known numerical systems, sciences, and mathematical forms. In my opinion, the most interesting of theses articles was the one titled, "Early Greek Science: Thales to Plato," by Michael Fowler. Much of the information given makes it seem like the mathematical and scientific methods of the Greeks was very advanced for the time period. For example, I was somewhat shocked to learn that, "Pythagoras is ... most famous for the theorem about right angled triangles, that the sum of the squares of the two sides enclosing the right angle is equal to the square of the long side, called the hypotenuse" (Fowler 1). I recognized this as the Pythagorean Theorem, or a^2 + b^2 = c^2, which is still used in mathematical calculations today. I also found it interesting that the Pythagoreans discovered what an irrational number is, "one that is not a ratio of integers." The discovery, "greatly upset the Pythagoreans, since they revered the integers as the mystical foundation of the universe, and now apparently they were not even sufficient foundation for the numbers" (Fowler 2). Their belief that numbers hold some sort of mystical or religious power seems much different than the way we look at numbers today; as nothing more than figures used to represent amounts. Although some scientists, engineers, and mathematicians may greatly respect and appreciate the significance and ease of use of numbers, they certainly do not make any connection between numbers and a higher power.=====

The most important sections of the article, in relation to the course, are the sections about Plato and Hippocrates. The article tells us that Hippocrates was, "the first great doctor", and that he, and his followers ,"...insisted on careful, systematic observation in diagnosing disease, and a careful sorting out of what was relevant and what was merely coincidental" (Fowler 3). This seems to be an ancestor to the scientific method that we use today. We also learn the Plato created the first university, and that his, "concentration on perfect underlying forms did in fact lead to a major contribution to astronomy..", although he disliked systematic observations. (Fowler 4). Finally, perhaps the most important point made in the article refers to Plato's view on matter. He believed that air, water, fire, and earth were the basic elements, and each had its own "perfect form". He suggested, for example, that, "...water could be decomposed into fire and air...This looks like a kind of atomic or molecular theory, but his strong conviction that all properties of matter could eventually be deduced by pure thought, without resort to experiment, proved counterproductive to the further development of scientific understanding for centuries" (Fowler 5). The point made by the author is that we should always look to the scientists and researchers who came before us for theories and ideas on what we know scientifically, but we should not believe that everything that they thought or believed is absolutely true or without flaws. If we were to blindly follow their beliefs without question, our true knowledge about science will either be led in the wrong direction (towards incorrect theories or beliefs), or will not progress at all. In other words, if we hold everything said before us to be true, we will believe we are incorrect if we find a contradiction (such as that found by the Pythagoreans regarding irrational numbers), and be afraid to follow what we have discovered. Science is all about the will to occasionally be wrong in theories and beliefs, but to always try to test every preceding theory, and to learn from one's mistakes.