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Questions that deal with research, strategies, math and theories

  1. Nov 29, 2011 #1
    I read that theories are a framework of explanations of experimental data and that they predict experimental results. I have also read that sometimes data comes before there is a theoretical explanation and vice versa; theoretical explanations predict data that has not been yet proven by experiment. Also, if experimental data proves a theory wrong, the theory has to be reworked.
    I am also confused by the fact that Galileo proved Aristotle and his school of philosophy wrong (about how the Earth is not the center of the universe and how larger masses were thought to fall at faster accelerations than smaller masses) by developing a systematic method of observation, experimentation, and analysis. The Greeks in the philosophical school of Aristotle simply tried to explain observed things by solely logical arguments. Galileo started his method to disprove Aristotle.
    I read “There is no single ‘scientific method.’ All scientists combine systematic experimentation with careful measurements and analysis of results. From these analyses, conclusions are drawn. These conclusions are then subjected to additional tests to find out if they are valid.” I see a jump from observation as the first step for both Aristotle and Galileo to experimentation by modern researchers. Also, from the beginning of these questions I wrote about what they said in this book about how theories are frameworks of explanations of experimental results and that predict new experimental data. I see that with Galileo there is also experimentation before analysis. This leads to conclusions that are then tested to see if those conclusions are valid. Are these conclusions forerunners of explanations that when put together in a framework are a theory? Are these conclusions the explanations that make a framework called a theory (and what is meant by a framework?), or are these conclusions the actual theories (these conclusions explain the analysis of data and can be tested to see if these conclusions are valid or not)?
    Also, professors, “Much of their work consists of doing research—that is, exploring ideas, creating hypotheses, performing experiments and publishing findings.” In what way do they do research differently than the rest of the researchers? It sounds different that the other research I’ve read.
    I’m reading about research and also about strategies I’m not sure if this is strategy solely employed in physics, but I feel it may be used in all kinds of ways, but for such an abstract study as mathematics and physics, I feel it work especially well.
    I need examples or at least a clue to the following quote from the book.
    “A strategy is an organized approach to a problem that breaks down the task of obtaining and organizing information into stages. Strategies can be the ‘bridge’ in solving problems. Several strategies are in the following list:
    Strategies:
    List all possible solutions
    Look for a pattern
    Construct a table, graph, or figure
    Make a model
    Guess and check
    Work backwards
    Make a drawing
    Solve a simpler or similar related problem.”
    I know that mathematics is the language of physics, but I don’t have a clue how all of the parts (and what are all of the parts? Corollaries, postulates, theorems, if-then statements, premises, independent and dependent variable from experiments that make equations that can be graphed, etc.) work together to be used for the advancements in physics and its applied math as well as pure mathematics? Whoever replies, keep it simple, I’m only a little ways into Calculus and my understanding of Algebra is far from complete. I need to know what each part is and how they work together and what each part does from a bird’s eye view.
     
  2. jcsd
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