Drunkard's Walk - Leonard Mlodinow [88]
Faraday concluded, as the doctors had, that the sitters were unconsciously pulling and pushing the table. The movement probably began as random fidgeting. Then at some point the sitters perceived in the randomness a pattern. That pattern precipitated a self-fulfilling expectation as the subjects’ hands followed the imagined leadership of the table. The value of his indicator, Faraday wrote, was thus “the corrective power it possesses over the mind of the table-turner.”5 Human perception, Faraday recognized, is not a direct consequence of reality but rather an act of imagination.6
Perception requires imagination because the data people encounter in their lives are never complete and always equivocal. For example, most people consider that the greatest evidence of an event one can obtain is to see it with their own eyes, and in a court of law little is held in more esteem than eyewitness testimony. Yet if you asked to display for a court a video of the same quality as the unprocessed data captured on the retina of a human eye, the judge might wonder what you were trying to put over. For one thing, the view will have a blind spot where the optic nerve attaches to the retina. Moreover, the only part of our field of vision with good resolution is a narrow area of about 1 degree of visual angle around the retina’s center, an area the width of our thumb as it looks when held at arm’s length. Outside that region, resolution drops off sharply. To compensate, we constantly move our eyes to bring the sharper region to bear on different portions of the scene we wish to observe. And so the pattern of raw data sent to the brain is a shaky, badly pixilated picture with a hole in it. Fortunately the brain processes the data, combining the input from both eyes, filling in gaps on the assumption that the visual properties of neighboring locations are similar and interpolating.7 The result—at least until age, injury, disease, or an excess of mai tais takes its toll—is a happy human being suffering from the compelling illusion that his or her vision is sharp and clear.
We also use our imagination and take shortcuts to fill gaps in patterns of nonvisual data. As with visual input, we draw conclusions and make judgments based on uncertain and incomplete information, and we conclude, when we are done analyzing the patterns, that our “picture” is clear and accurate. But is it?
Scientists have moved to protect themselves from identifying false patterns by developing methods of statistical analysis to decide whether a set of observations provides good support for a hypothesis or whether, on the contrary, the apparent support is probably due to chance. For example, when physicists seek to determine whether the data from a supercollider is significant, they don’t eyeball their graphs, looking for bumps that rise above the noise; they apply mathematical techniques. One such technique, significance testing, was developed in the 1920s by R. A. Fisher, one of the greatest statisticians of the twentieth century (a man also known for his uncontrollable temper and for a feud with his fellow statistics pioneer Karl Pearson that was so bitter he continued to attack his nemesis long after Pearson’s death, in 1936).
To illustrate Fisher’s ideas, suppose that a student in a research study on extrasensory perception predicts the result of some coin tosses. If in our observations we find that she is almost always right, we might hypothesize that she is somehow skilled at it, for instance, through psychic powers. On the other hand, if she is right about half the time, the data support the hypothesis that she was just guessing. But what if the data fall somewhere in between or if there isn’t much data? Where do we draw the line between accepting and rejecting the competing hypotheses? This is what significance testing does: it is a formal procedure for calculating the probability of our having observed what we observed if the hypothesis