Thinking about Thinking

Science is simply common sense at its best-that is rigidly accurate in observation and merciless to fallacy in logic T. Huxley
Scientific thinking is not different from any other kind of thinking, though it is often more rigorously applied. It is IDENTICAL to the procedures you use to pick a route when you have many errands to run, solve a crossword puzzle, or determine why a light no longer comes on.This page presents some rules of thumb or observations of my own that you may find helpful or insightful. Of course, what’s good for the goose may not be good for the gander—take what works for you, and preserve the uniqueness of your own mental processes. The last thing the world needs is another one of me.

Laying the foundation:

Dress for success-Title of Dale Carnegie book
Begin with the attitude that you can & will triumph; proceed with determination. Nothing is as lethal to your mental processes as deciding you are not capable of solving a given problem. Approaching with the attitude of “I wonder if I can do this” is equally abhorrent—you may well retreat in confusion at the first roadblock. Besides, what if you’re wrong—assuming you couldn’t succeed when you could’ve robs you of a novel insight or achievement. Assuming you can succeed when in actuality you cannot wastes some of your time—for most of us this hardly constitutes a capital crime.

Be Prepared!-Boy Scout Motto
UNDERSTAND THE MATTER AT HAND! The tools of thinking can only function if they have something to work on. There’s a reason most brilliant mathematical discoveries come from mathematicians and most theories about the nature of physical law comes from physicists. In terms of exam preparation, this doesn’t mean being able to recite a paragraph about a topic-if you cannot predict outcomes of perturbations, you don’t understand—and that will be the goal of this course and its exams. Facts are just tools to be manipulated--and if you're unfamiliar with your tools, you're not going to get anything built--particularly within the artificial, stressful conditions of an exam.

Genius is one percent inspiration and ninety-nine percent perspiration. —Edison
I don’t know a lot of geniuses. But I’ve never met ANYbody who says “Oh yes, brilliant ideas just fall into my head fully formed. Especially in areas in which I have no expertise.” If you want to get THERE from HERE, you have to walk—taking discrete steps in an orderly fashion. Break down the problem-take small bites. As an everyday example, a crossword puzzle looks blatantly impossible at first glance. How many people sit down and just fill it in from top to bottom? Most of us look at the clues, identify those that we can nail, and then incorporate the clues from these small successes to solve bigger and more difficult issues.

Generating Hypotheses:

The best way to have a good idea is to have lots of ideas —L. Pauling
Having good ideas is not like being struck by lightning (see above). For most of us mere mortals, ideas derive from extensive study and contemplation with the occasional flash of insight—which itself generally has roots in past experience, other thought processes, ideas and conversations of other people... There’s no harm in having ideas off the top of your head—the trick, however, lies in scrutinizing them to see if they have that kernel of insight or not. The idea is the starting point of a long, rigorous procedure—not an endpoint. There's a big difference between a guess and a hypothesis.

For an algorithmic approach to generating ideas, follow this link.

Testing Hypotheses:

One of these things is not like the other &-Sesame Street
Once you have an idea or hypothesis, how do you determine if it is valid and interesting? The best way is to contrast it with alternative hypotheses and decide on the merits. The goal of course is to identify a key point where two models make starkly differing predictions and then see which is correct. My general procedure is as follows:

  • List ALL differences between the hypotheses or models that you can think of. Then list 2 more.
  • Ask if there is any way to you AMPLIFY the differences? (this is geneally applicable to model testing—since our experimental tools are almost always indirect and often crude, we want to have a big target to aim them at)
  • How con you observe/detect the differences? Given that different models make different predictions (i.e. describe different outcomes or the existence of different states) how can we ‘take a look’ and see which is the most accurate description of the world?

A beautiful model or theory may not be right; but an ugly one must be wrong. --Jacques Monod
The point of training (and memorizing factoids) is twofold: First, to provide ‘grist for the mill’—it’s all very well and good to want to solve important problems but for better or worse, the facts as we know them and (sometimes) the thoughts and opinions of others are the sina qua non (‘that, without which, not’) of forward progress. Second, only by getting in the rink and mudwrestling with the facts and tools will you develop the kind of familiarity required to bring the amazing pattern-matching and category-recognizing features of your brain to bear (a.k.a. your ‘intuition’—a crucial part of scientific problem solving if it is properly trained and informed).

This quote also provides a caution in terms of building unwieldy models--if your model is "Aliens exist among us, but can't be seen because they move faster than light, can't be heard because their special devices move all their sounds to high frequency, can't be smelled because they hypnotize us to ignore their raunchy odor, and can't be detected because they have no mass and thus exert no gravitational influence." it suffers from too many caveats. Far simpler the model "Aliens do not exist amongst us, though some people are really weird." This is an example of Occam's Razor, which can be stated "The simplest hypothesis is most likely to be correct." (though the original rendition, by William of Occam, is on the order of No more things should be presumed to exist than are absolutely necessary.)

Above all:remain orderly & methodical in your thinking!
It is an old and ironic habit of human beings to run faster when we have lost our way.-Rollo May
What more needs be said? One useful tip—I personally have found that pretending to be calm can actually help. Other than that, simply maintain perspective: will the world really come to an end if you fail miserably?

Beware the bugaboo of sloppy thinking! Here's a neat site explaining and giving examples of a ton of different sloppy/fallacious arguments.

Practice, practice, practice
There’s a reason most of us aren’t performing in the next Olympics. Given that your brain is a heck of a lot more powerful and complex than your body, do ya really think it comes out of the box ready to rock and roll? Train incessantly—ideally by 1) watching and coaching yourself as you solve problems of all sorts, and 2) finding ways to train that you enjoy. Some that work for me can be found in the BrainGameRoom (hint: you are advised to have MasterMind and BlackBox working for you by exam IV).