2.6 Bits of Information at a Time

An average person can process 2.6 bits of information at one time. Two to the power of 2.6 equals six. And that dimensionless number six is the cognitive limit for a human on average to process information.

Psychologists have experimented on these human senses.

1.     Sound tones: Pollack asked listeners to identify sound tones heard in equal logarithmic steps in a typical audible range. There was no confusion with four pitches. When increased beyond six pitches, confusions were frequent. The result was people cannot classify more than six sound pitches without confusion. Pollack obtained the same result when he varied the tone ranges. Now, we are only talking about an average person; a trained musician can of course do much better.

2.     Sound intensities: Garner in a different lab asked listeners to identify loudness ranging from 15 to 110 dB. The result was five different loudness were identifiable. That is 2.3 bits of information.

3.     Taste intensities: Beebe-Center, Rogers, and O'Connell used table salt water ranging from 0.3 to 34.7 gram of NaCl per 100 cc. tap water for subjects to identify saltiness. They obtained four or 1.9 bits of identifiable information.

4.     Visual positions: Hake and Garner tested subjects’ ability to a number to describe the positions of filled circles on a one-dimensional graph. The result was about nine or 3.2 bits for short exposures.

5.     Size of shapes: Eriksen and Hake tested subjects’ ability to judge sizes of squares and found five or 2.3 bits.

6.     Hue, brightness, area, direction of lines, curvature, angle inclination, etc., and the results were all ranging from five to seven.

Those experiments were with one dimensional evaluations only. So if one has a multi-dimensional analysis, such as a recognition of words or faces, the bit depths can be much higher. The scientists also found that the bits were not purely additive for multi-dimensions but rather with a diminished rate of return. That is, if one can classify 2.6 bits of tones and 2.3 bits of loudness, the combined tone-and-loudness judging ability is not 4.9 bits but lower.

The above studies were summarized in George A. Miller’s 1955 article “The Magical Number Seven, Plus or Minus Two, Some Limits on Our Capacity for Processing Information”, Psychological Review, Vol. 101, No. 2, 343-352. Is the magical number 7 an urban legend or is it a psychological truth? I think it has to do with short term memory in human beings.

As a systems engineer and program manager, this number of six or seven is a good reference for a the size of a breakdown structure at any level in systems engineering when we deal with a complex problem, be it about the decomposition of system requirements or the team organization that one has to keep track of.