Magic+Numbers

=Come One, Come All! Who wants to witness the MAGIC Number Seven?=

Scott Levine
As humans with minds developed only so far (except for some), we seem to have limits on our capacity for short term memory and information processing. This numeric limit is often referred to as "Working Memory Capacity." Cognitive psychologist George A. Miller from Princeton's Department of Psychology explained this phenomena in his landmark paper "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information" in 1956. In the paper, he explores human perceptual and cognitive tasks and the relationships between each channel capacity per task.

But the question is, what is "channel capacity?” Well, in this experiment, Miller explains that the subjects are considered “communication channels,” vessels to track and retain information to potentially calculate the maximum amount of information (or data bits) stored in short term memory. The term “channel capacity” is seemingly stolen from the electrical engineering field, where it is considered the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel. The channel, in this context is a medium between a transmitter and a receiver. A handy explanation of this can be found on none other than Wikipedia! []

Miller tests multiple cognitive tasks looking for a correlation of the effective channel capacities, finding that in fact there is a steady value across the board. What was that value? Miller found that the average channel capacity is 5 and 9 equally weighted error-less choices: on average, about 2.5 bits of information. Now let’s not get ahead of ourselves, this was just a hypothesis that maybe our average upper limit for retaining information was around 7. No conclusions, just an idea.

We can call this capacity our “working memory capacity,” which is used across fields, even towards the end of medical rehabilitation for ailments such as Alzheimer’s. Even “home memory health” websites use this term: [] However, our findings about working memory capacity don’t stop at just the discovery of the magical number seven. Later research uncovered that that memory span also depends on the category in which the information is tested (for example the span is around seven for digits, around six for letters, and around five for words), and as well depends on features of the information within a category. For example, the variance is lower for longer than it is for shorter words.

As a more general finding, memory variance for verbal information strongly depends on the time it takes to speak the contents aloud, and whether the contents are words that the person knows or not. Other unknown factors also affect a person's measured span or variance, which means that it can be tough to dial down the exact capacity of short-term or working memory to a number of chunks and/or information.

There have also been a good amount of urban legends and misconceptions generated by the 7±2 “rule” after Miller’s paper. Such well known falsities include things like software engineer’s limits on programming subroutines at or around 7±2. There is a quite blunt and aggressive pamphlet made for the MISRA-C (Motor Industry Software Reliability Association) Conference in 2002. It’s a pretty interesting read: []