The origins of various sciences are dependent on existence of other fields of science. A single experiment can lead to the creation of a whole new field, which is true in the case of very important discoveries. Although there are perceived and documented pressures on some groups of individuals, those situations frequently lead to important discoveries being made by unexpected individuals, like Galileo, who worked on the fringes of science.
In the introduction to the trial letters, Thomas F. Mayer writes that the trial is similar to a myth and that “ This is not at all that surprising, since the trial has almost never been studied as a legal event” (1). A reader might ask why the trial is not being studied as a legal event. Also, Mayer points out: “ Almost equally important, studying the trial more closely takes some of the heat out of the often violent debate over the rights and wrongs of what happened” (1). Federico Cesi, an ambitious grandnephew of a cardinal, banned members of religious orders from his club called Academy of the Lynxes. He had become a patron of Galileo’s and continued to insist the prevention of members of the Jesuit order from entering the Academy (2). Galileo disaffected the Jesuits, which helped lead to his downfall (2). The Jesuits began as a collection of approximately 20,000 teachers and missionaries who ran various academic institutions. These universities often were home to the the world’s greatest scientific instructors (3). Cesi died before he was able to complete publishing Galileo’s Dialogue (45). Although he was instructed not to use interpretations of the Bible in his explanation of Copernicus’ ideas about astronomy, “ [Galileo] acted as he always did, ruthlessly pursuing an agenda of liberty for philosophy and fame for himself” (3). Cardinal Conti was a lawyer instructed by the Jesuits, his ambition of running the papal state threatened the position of his nephew, and he remained outside of Rome for a long time. Galileo asked the advice of Cardinal Conti because one of his servants was a scientist whom he had known previously (41).
In the Greek tradition, mathematics was portrayed as having originated within the studies of early Egyptian philosophers. Although mathematics was more of an extrapolation from the other natural sciences which were based in a reality with which one could individually react, it developed its own internal cosmos. In “ Making Modern Science: A Historical Survey,” by Peter J. Bowler and Iwan Rhys Morus, “Philosophers talked of experiment and of mathematics as providing new tools and even a new language that could be used to understand nature” (Bowler and Morus, 25). Mathematics was a method of reformatting knowledge about the physical world so that it could be manipulated into providing extensive information into the unknown. Despite the conviction the Greek philosophers had about the origins of the field of mathematical inquiry, discrepancies arose. In “The Dialogue of Civilizations in the Birth of Modern Science,” by Arun Bala, “He [Historian Colin Ronan] counters the prevalent Greek view that their mathematics began in Egypt” (Bala, 17). Greek philosophers and mathematicians held this belief, excited by having the exotic terrain as the remote source of their area of study.
The symmetric group is the group defined over “any set whose elements are all the bijections from the set to itself, and who’s group operation is the composition of functions”, while the symmetry group is “the group of all transformations under which the object is invariant, endowed with the group operation of composition” (Wikipedia) “Isometry” comes from the Greek word for “equal measure”: Isometros. An n-dimensional space in the real numbers has an isometry from one function in R to another. The set of isometries that map a function onto itself on the set of real numbers is called a symmetry group. The symmetry group of an object is dependent on both the object itself and the space in which it is viewed. There are four types of symmetries in two-dimensions: rotation, reflection, translation, and glide reflection. Rotation consists of spinning either left or right. The axis of reflection, or mirror, is the line which acts as a two-way mirror between the original structure and it’s reflection. A translation moves all the points an equal distance in the same direction while a glide-reflection consists of both a translation and a reflection.
Farmers have been developing favorable traits by selectively breeding crops since the beginning of agriculture. The age old practice of creating more tolerant and pest resistant plants with higher yield has turned into a complicated, and sometimes secretive and modern process of genetic engineering. With modern technology, alterations can be made directly to the DNA of various plants. With only a few companies leading the market in genetically modified crops, and sometimes entire strains becoming eradicated by a single illness, controversy envelops present-day regulations concerning genetically modified foods. Issues being discussed include the safety and treatment of farmers, gene-patenting, food affordability, the environment, and the quality assurance of the crops being produced. How do genetically modified foods affect humans and other wildlife? Do consumers have the right to know when genetically modified crops are present in food products?