E How to Discover Your Own Hypothesis
This book focuses on the hypothesis, yet as I've noted a couple of times, hypotheses are products of our unconscious minds, and we don't know much about how our minds work. There are a few methods, or collections of hints, that may be useful if you're stuck and need a boost in developing a hypothesis, however.
For many people, these techniques help train their intuition.A hypothesis is an explanation. Your problem might be either that you don't have a clear picture of what you need to explain or that, while you know exactly what you want to explain, you're having trouble explaining it. The following sources of inspiration may jostle your mind enough to become unblocked.
14.E.1 Induction
Whatever the process of induction is, there is no denying that the effort of trying to find and generalize from a pattern in your data is beneficial; it may call attention to a gap in your understanding that needs to be filled and perhaps how to fill it. In other words, looking for regularities in your data is a good way to generate a hypothesis.
14.E.2 How to Solve It
A (maybe the) classic text for those who seek to enhance their problem-solving ability is How to Solve It: A New Aspect of Mathematical Method, second edition,17 by George Polya. If you're a math-o-phobe, don't be put off by the reference to math in the title. Polya's suggestions are good for solving nonmath- ematical problems as well. You don't even have to work through the relatively simple geometric problems he does use; just read the words and get the message. There is a lot of excellent advice about how to develop your own “common sense” and a convenient “Short Dictionary of Heuristic” with more than 60 specific recommendations for what he calls heuristic reasoning.
Polya counsels us to be wary, “if you go into detail, you may lose yourself in the details.” His “heuristic”18 is similar to, though not quite the same as, the heuristics that we talked about in Chapters 11 and 12.
For example, his first heuristic is Analogy: make an analogy between a difficult problem that you’re trying to solve and a simpler one that you know more about. I’ve mentioned (Chapter 2) the experiment in which Paul Fatt and Bernard Katz were trying to figure out how synaptic transmission at the neuromuscular synapse worked. In essence, they made an analogy between heart muscles and skeletal muscles in the body and hypothesized that the way that nerves signaled to heart muscles—by releasing a chemical signal—was the way that nerves signaled to skeletal muscles. They also followed another Polya rule to Decompose a complicated problem into separate parts and deal with them separately. I don’t know if Fatt and Katz had read Polya (his book is copyrighted 1945), but, in breaking down the stream of small electrical signals that they observed in skeletal muscles into two groups—“bursts” versus the low- frequency, regular ones—and ignoring the bursts, they were doing exactly what he recommended.14.E.3 Fast and Frugal Hypotheses
In Chapter 12, I introduced Gerd Gigerenzer’s view of heuristics as adaptive cognitive tools that help us cope quickly and efficiently with complexity. Heuristics are “fast-and-frugal” procedures—quickly applied and sparing of time and effort—and, while they often act as stand-alone solutions to difficult problems, they can also be used to build up the more elaborate devices that are hypotheses.
In reviewing the bias-variance dilemma (see Box 12.1), I noted that bias, perhaps in the form of a straight line through a mass of data points, preserves the general trend of the data and offers predictive power at the cost of losing the information contained in the variance of the data points. This is a key element of Gigerenzer’s vision of “less is more”19 (i.e., that less detail sometimes yields more information). The bias-variance dilemma also shows how the philosophy of less is more generates a hypothesis. The straight line that fits the data relating height to age embodied a hypothesis.
There is no line in the raw data; you express your interpretation of how age and height are related when you draw one. The line does not mean that height is explained by age but suggests that there is a common mechanism that relates them linearly. The process of line fitting could even lead to multiple hypotheses if, in examining the graph, we decided to try fitting the points more closely with another function. We’d give up some of the straight-line bias in favor of paying greater attention to the variance. Experienced experimenters recognize complicated trends in data— exponentials, polynomials—that lead to different hypotheses about underlying mechanisms.Gigerenzer wants to understand how we form heuristics; how, at a fundamental level, we come up with the “straight-line hypothesis.” To appreciate his approach, let's start with the observation by Herbert Simon that “intuition is nothing more and nothing less than recognition”20 (e.g., the expert intuition of a chess master of what would be a good move in a chess game). The chess master's intuition results from having studied and practiced chess for tens of thousands of hours and does not necessarily represent native genius. His vast experience allows him to recognize positions on the board and their outcomes at a glance.
The overarching motif of Gigerenzer's school of thought is that we have a storehouse of mental constructs—he calls them probabilistic mental models—that serve us well and that we successfully rely on for many tasks.21 As products of evolution and experience, the constructs are adaptable cognitive tools that we often use unconsciously. There are many rules for “one-reason decision-making” that, operating on the basis of limited information, often provide workable solutions to problems by satisficing rather than optimizing. These rules can be incorporated into algorithmic process models; however, even in their simplest form, heuristics can lead to practical hypotheses.
Heuristics, Gigerenzer and colleagues point out, allow you to make choices based on familiar patterns.
For instance, you use the take-the-best heuristic to make choices based on a property—a cue value—that you know about. Suppose you need to guess which of two cities is larger. The take-the-best method is to rank order cues that might be relevant: Does it have an airport? A major-sports team? Then compare the cities according to each cue in order, stop as soon as you find a cue that discriminates between the cities, and pick the city with the higher cue value. This uncomplicated strategy is surprisingly successful where you have at least some relevant information. (You're at random chance otherwise. Heuristics are not magic.) Scientists can develop their own intuitive insights based on heuristics like this.Take-the-best, for instance, will often generate parsimonious hypotheses. For instance, when my colleagues and I first noticed the disappearing I-cell signals, we thought that some change in the P cell itself must be responsible. There was already a great deal of information about seemingly similar effects that took place in P cells, and, knowing what we knew then, we quickly took the best of the known explanations. As it so happened, that hypothesis was false, but the fact that it was simple, concrete, and testable told us where not to look for answers and gave us a good place to start from.
While heuristics assist in generating hypotheses, they cannot take the place of reasoning about or testing hypotheses. We should keep in mind the Russian proverb that President Ronald Reagan liked to quote: “trust, but verify”; that is, be willing to believe, but don't be naive. We should consciously welcome the attempts of our unconscious minds to understand the world while remaining skeptical of its trustworthiness. Your brilliant inspiration notwithstanding, you must still subject your ideas to critical scrutiny as you continue to consult your intuition for new ones.
14.E.4 Develop Your Insight
In The Art of Insight in Science and Engineering: Mastering Complexity Sanjoy Mahajan substantially expands on the theme of discovering solutions from practice and approximation.
For Mahajan, the great challenge is that, as scientists, we need to develop insight if we are not to “drown in complexity.” He quotes William James's remark that “the art of being wise is the art of knowing what to overlook.” Mahajan teaches how to organize, as well as discard, complexity via a series of nine thinking tools for simplifying complex problems and getting plausible, approximate answers to problems where the exact answer might be hard or impossible to come by.If you had to estimate the volume of a dollar bill, how would you go about it? Use the divide-and-conquer strategy to break the problem down into manageable bits: you can easily make good guesses as to the bill's width and length (~ 6 cm x 15 cm, say), but what about its thickness? A dollar bill is a piece of paper and you know, roughly, how thick a ream (500 sheets) of paper is (~5 cm), so divide 5 cm by 500 and you get 0.01 cm for its thickness. Put your guesses together and—Voila!— the volume of a dollar bill is approximately 1 cm3. By simplifying a problem and estimating an approximate solution, you will often be able to find a hypothesis. Neuroscientists do this when they try to understand a neuron's electrical activity by collapsing its complex structure into a spherical cell body with a single tapering branch representing all the dendrites sticking out of it. Its easy to calculate the volume of the ball-and-stick model, and it is good enough for many purposes.
Or consider that often the first step in generating a hypothesis is noticing something unusual that needs explaining. This means that you need a sense of how things normally are. There isn't always a lot of background information around for comparison, so it's good to have ways of guesstimating what to expect. Suppose you're studying neurons in the mouse brain and you come across a neuron firing steadily along at a rate of 20 action potentials per second (20 Hz). Is it unusual or not? You might start by recalling that firing at 100 Hz is considered quite fast—only a few cells do that; on the other hand, you might sense that a cell's firing once every 10 seconds, 0.1 Hz, would seem slow.
Should you take the average between them for comparison? The usual arithmetic mean of 0.1 and 100 Hz is about 50 Hz, but you know the arithmetic mean tends to follow the extremes. In such a case, Mahajan would recommend picking the geometric mean: the square root of the product of the extremes. The geometric mean here is (0.1 x 100)1/2 = (10)1/2 ~ 3 Hz. This suggests that, at 20 Hz, your new neuron is firing considerably faster than what you'd expect for an average neuron and that therefore you may have found a phenomenon that needs to be explained.As a scientist, you should know how to do approximations like this and to “talk to your gut” to develop imprecise but insightful ways of thinking about complex problems. Mahajan has many illustrations of how to do this, although his homey examples—how to estimate the number gas stations in the United States or the total land area of the United Kingdom—soon give way to cases in that require detailed background knowledge and technical expertise. For instance, his explanation of how to estimate the power output of a trained human athlete is neat23; you'll want to have all of your college physics right at hand to follow it closely, however. The main point is that there are many times when the sheer complexity of the problem you face will seem daunting, and Mahajan's program can give you the optimism you need to tackle it.
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