# Miller’s law, chunking, and the capacity of working memory

### Problem

In 1956, George Miller asserted that the span of immediate memory and absolute judgment were both limited to around 7 pieces of information. The main unit of information is the bit, the amount of data necessary to make a choice between two equally likely alternatives. Likewise, 4 bits of information is a decision between 16 binary alternatives (4 successive binary decisions). The point where confusion creates an incorrect judgment is the channel capacity. In other words, the quantity of bits which can be transmitted reliably through a channel, within a certain amount of time.
Chunking, or clustering, is the function of grouping information together related by perceptual features. This is a form of semantic relation, such as types of fruit, parts of speech, or 1980s fashion. Chunking allows the brain to increase the channel capacity of the short term memory; however, each chunk must be meaningful to the individual. There are many other memory consolidation techniques. The peg memory system creates a mental peg from an association, such as a rhyme, letter, or shape. Another memory technique is the link system, where images are creating links, stories, or associations between elements in a list to be memorized.
A researcher wanted to challenge the limits imposed by Miller’s Law (7 plus/minus 2). In the study (n = 20, H, start subscript, 0, end subscript = 7 plus/minus 2), subjects completed a backward digit span test and other memory tests administered during each of five sessions over the course of a year. The backward digit span test consisted of five trials during each session. Each trial began with instructions and a statement of understanding from the subject. Each backward digit span test began with two digits and was read at a rate of one digit per second. The digit span length increased until there were three incorrect attempts. The digits must be repeated in reverse order by the subject (researcher – “3, comma, 5, comma, 6, comma, 2, comma, 3, comma, 1” subject – “1, comma, 3, comma, 2, comma, 6, comma, 5, comma, 3”). The results for the average longest correctly repeated string of digits over all sessions by each subject are shown in Table 1 below.
Table 1: The averaged results of the backward digit span test throughout all 25 trials (5 trials, 5 sessions) for each subject (n = 20). Mean (μ) = 4, point, 73, Confidence interval at 95, percent [4, point, 02, comma, 5, point, 45], Standard deviation (σ) = 1, point, 48, p-value 2, point, 32, times 10, start superscript, minus, 5, end superscript, and the significance criterion (α) was 5, percent.
SubjectAverage resultsSubjectAverage results
14, point, 63114, point, 18
24, point, 53124, point, 81
35, point, 12139, point, 32
43, point, 81143, point, 79
53, point, 27152, point, 67
65, point, 38164, point, 65
77, point, 75173, point, 82
85, point, 46183, point, 75
95, point, 41194, point, 19
104, point, 41204, point, 37
Adapted from: Miller, G. A. (1956). The magical number seven, plus or minus two: some limits on our capacity for processing information. Psychological review, 63(2), 81.
Which system of the working memory model was the researcher testing by utilizing the backwards digit span test?