The Information - James Gleick [124]
For a brief period, researchers discussed the transition explicitly; later it became invisible. Donald Broadbent, an English experimental psychologist exploring issues of attention and short-term memory, wrote of one experiment in 1958: “The difference between a description of the results in terms of stimulus and response, and a description in information theory terms, becomes most marked.… One could no doubt develop an adequate description of the results in S-R terms … but such a description is clumsy compared to the information theory description.”♦ Broadbent founded an applied psychology division at Cambridge University, and a flood of research followed, there and elsewhere, in the general realm of how people handle information: effects of noise on performance; selective attention and filtering of perception; short-term and long-term memory; pattern recognition; problem solving. And where did logic belong? To psychology or to computer science? Surely not just to philosophy.
An influential counterpart of Broadbent’s in the United States was George Miller, who helped found the Center for Cognitive Studies at Harvard in 1960. He was already famous for a paper published in 1956 under the slightly whimsical title “The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information.”♦ Seven seemed to be the number of items that most people could hold in working memory at any one time: seven digits (the typical American telephone number of the time), seven words, or seven objects displayed by an experimental psychologist. The number also kept popping up, Miller claimed, in other sorts of experiments. Laboratory subjects were fed sips of water with different amounts of salt, to see how many different levels of saltiness they could discriminate. They were asked to detect differences between tones of varying pitch or loudness. They were shown random patterns of dots, flashed on a screen, and asked how many (below seven, they almost always knew; above seven, they almost always estimated). In one way and another, the number seven kept recurring as a threshold. “This number assumes a variety of disguises,” he wrote, “being sometimes a little larger and sometimes a little smaller than usual, but never changing so much as to be unrecognizable.”
Clearly this was a crude simplification of some kind; as Miller noted, people can identify any of thousands of faces or words and can memorize long sequences of symbols. To see what kind of simplification, he turned to information theory, and especially to Shannon’s understanding of information as a selection among possible alternatives. “The observer is considered to be a communication channel,” he announced—a formulation sure to appall the behaviorists who dominated the profession. Information is being transmitted and stored—information about loudness, or saltiness, or number. He explained about bits:
One bit of information is the amount of information that we need to make a decision between two equally likely alternatives. If we must decide whether a man is less than six feet tall or more than six feet tall and if we know that the chances are 50-50, then we need one bit of information.…
Two bits of information enable us to decide among four equally likely alternatives. Three bits of information enable us to decide among eight equally likely alternatives … and so on. That is to say, if there are 32 equally likely alternatives, we must make five successive binary decisions, worth one bit each, before we know which alternative is correct. So the general rule is simple: every time the number of alternatives is increased by a factor of two, one bit of information is added.
The magical number seven is really just under three bits. Simple experiments measured discrimination,