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UMaine SMS 691 - Creating and critiquing scientific hypotheses

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Creating and critiquing scientific hypothesesWhere ideas, theses and hypotheses come from, and how to identify good onesSternberg’s triarchic model•Synthetic or creative intelligence, an ability to deal with new problems and situations by recombining knowledge in novel ways •Analytic intelligence, an ability to solve clearly defined problems (what is normally tested) — assumed but not covered in SMS 691 •Practical intelligence, an ability to sell your ideas and get the resources needed to implement them — covered later in SMS 691Nature experimentsIt is natural selection that gives direction to changes, orients chance, and slowly, progressively produces more complex structures, new organs, and new species. Novelties come from previously unseen association of old material. To create is to recombine. — François JacobStill the best resource•You can find much of the science-transferable advice online •Search under {Pólya heuristics}!4Guides for creativity•Somewhat ironically (because math is often portrayed as lacking in ambiguity and imprecision), the best examples come from math. •George Pólya developed a set of heuristics for developing and solving math problems that apply as well to science. •William Byers’ simple advice: Seek ambiguity, contradiction and paradox (author of How Mathematicians Think [2007, Princeton Univ. Press]).!5George Pólya quotes•To be a good mathematician, or a good gambler, or good at anything, you must be a good guesser. •To conjecture and not to test is the mark of a savage. •If you can't solve a problem, then there is an easier problem you can solve: find it. •My method to overcome a difficulty is to go round it. •The future mathematician ... should solve problems, choose the problems which are in his line, meditate upon their solution, and invent new problems. By this means, and by all other means, he should endeavor to make his first important discovery: he should discover his likes and dislikes, his taste, his own line. •The open secret of real success is to throw your whole personality into your problem. •The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them.— emphasizes prediction— emphasizes testingPólya’s steps!First, you have to understand the problem. After understanding, then make a plan. Carry out the plan. Look back on your work. How could it be better?What did you learn from this experience?Pólya’s heuristics•Draw a diagram. •Write an explicit equation. •Simplify the problem. •Generalize the problem. •Change it in some other way. •Look for analogs in earth sciences, limnology and engineering.•Decompose and recombine. •Add a component and see if it helps. •Guess at a solution and see if you can work backward. •List possible solutions and see if you can eliminate any. •Solve part of the problem or an offshoot of the problem.The ones I use most frequentlyA monk climbs a mountain, slowly all day, and reaches the summit at sunset. He climbs down the next day, reaching the bottom at 1500 hours. Was he ever at the same place at the same time of day on the two successive days?•When you draw a graph, the answer is trivial. •Writing an equation is feasible, but much more difficult.Not all approaches work well with all problems.060018001200Scaled altitude01Time of day (hours)ClimbDescent2007•Ambiguity involves a single situation or idea that is perceived in two self-consistent but mutually incompatible ways. •Central role of the “idea” or “what is really going on” •Ideas are organizing principles, but what is being organized are other ideas. •False ideas can be valuable. •Tension between ideas and logic •Some true math is unprovable.It is much easier to derive hypotheses from ideas than to build ideas from a collection of hypotheseshttp://legacy.lclark.edu/faculty/jsmiller/objects/idea_bulb.jpgH1H2H3H1 + H2 + H3 ≠ http://arunrafi.files.wordpress.com/2009/12/idea.jpegOne approach•Choose a problem •What seems to be limiting the rate of progress? •Lack of theory? •Targeted lab experiments? •Key lab or field observations? •Key field experiments?Field vs. Lab Experiments•Most people are more familiar with lab experiments, wherein the general philosophy is to hold all but one or a few factors constant. They are excellent for identifying mechanisms. •Field experiments have a wildly different philosophy. Nothing is held constant. You vary one or a few factors to see if they matter in the face of all the other things that Mother Nature throws. The answer will not be the same in different places or at different times.N.B.: Physical, geological and chemical oceanographers often call organized field observations “experiments,” whereas for biologists “experiments” imply manipulations.IBMs, ABMs or automata•A relatively new kind of modeling/prediction •Convince yourself that you know the rules by which an individual operates (including what it does when interacting with like and different individuals and with environmental variables). •Let it rip in the computer. •See what spatial, population and community features emerge.Examples from my experience•A thesis needs a big idea. •Examples taken from Ph.D. theses in my lab; I write broad proposals and find a coherent piece that suits the student and the problem; I so the high-risk startup and the cleanup. •I did my Ph.D. and postdoc on the spatial structure of soft-bottom benthic species diversity in the deep sea (practice problem). •While teaching benthos at UW for the first time, I asked myself what was the most important problem someone with my skills could attack and how.Idea•Deposit feeding is hugely important, but the literature was a nearly random collection of unconnected observations. For example, people measured assimilation efficiencies without measuring feeding rates. Prediction was nonexistent. •Optimal foraging theory was recently born. •Deposit feeders are unusual; they wallow in food; quantity is not the issue. •What particles should a deposit feeder select? •How fast should a deposit feeder eat?•Question: What size particles and how fast should deposit feeders eat? •We decided that theory for deposit feeding was lacking. •We simply took the theory that John Lehman developed for suspension feeders


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