The limitation of your working memory seems so obvious. Try for example to remember the phone number 202-456-6213 until you finish reading this text. You will notice! When psychologists, however, attempted to measure this capacity limitation, the “magical” number didn’t appear unequivocally. Let’s take a look a some famous inquiries.
In the classic handbook An introduction to psychology (1912), W. Wundt (1832-1920) already observed that
The number six with very minor variations denotes the maximum of simple impressions that can be grasped by attention. If we choose syllables of any form, that are not combined into words, and if we read out a row of such to an observer, and require him to repeat them, we find that a correct repetition is possible with a row such as the following : ap ku no li sa ro. Whereas it is not possible with a row like this : ra po su am na il ok pu.
R.S. Woodworth (1869-1962) tried to measure the span of attention. This is how many objects that can be clearly seen, or heard, or felt at the same time. In his monumental work Psychology. A study of mental life (1921), he gave the following example.
Place a number of marbles in a little box, take a single peek into the box and see if you know how many marbles are there. Four or five you can get in a single glance, but with more there you become uncertain. In the laboratory we have “exposure apparatus” for displaying a card for a fifth of a second or less, just enough time for a single glance. Make a number of dots or strokes on the card and see whether the subject knows the number on sight. He can tell four or five, and beyond that makes many mistakes. Expose letters not making any word and he can read about four at a glance. But if the letters make familiar words, he can read three or four words at a glance. If the words make a familiar phrase, he gets a phrase of several words, containing as many as twenty letters, at a single glance. Expose a number of little squares of different colors, and a well-trained subject will report correctly as many as five colors, though he cannot reach this number every time.
Both examples are typical for the decades of research on memory and attention span. In his famous The magical number seven, plus or minus two: Some limits on our capacity for processing information, G.A. Miller (1920-2012) reported also on both phenomena and tried to connect them. He first discussed absolute judgements of uni- and multidimensional stimuli which resembles the attention span of Woodworth. For example, how many tones can you identify by assigning numerals to them? Miller came to the conclusion that you can distinguish about 6.5 categories. We can however identify many more multidimensional stimuli like faces and words. Why it should be easier to identify multidimensional stimuli is left to the imagination of the reader and a small reference to evolution theory (“better to have a little information about a lot of things than to have a lot of information about a small segment of the environment.” ( p. 88-89) . Then Miller continued with the measurement of the span of immediate memory.
Up to this point we have presented a single stimulus and asked the observer to name it immediately thereafter. We can extend this procedure by requiring the observer to withhold his response until we have given him several stimuli in succession. At the end of the sequence of stimuli he then makes his response. […] Everybody [sic] knows that there is a finite span of immediate memory and that for a lot of different materials this span is about seven items in length. […] In spite of the coincidence that the magical number seven appears in both places, the span of absolute judgment and the span of immediate memory are quite different kinds of limitations that are imposed on our ability to process information. Absolute judgment is limited by the amount of information. Immediate memory is limited by the number of items. In order to capture this distinction in somewhat picturesque terms, I have fallen into the custom of distinguishing between bits of information and chunks of information.
Miller remained awkwardly vague about the exact nature of a chunk (“grouping the input into familiar units“) and compared it with recoding, at that time very popular among information theory scientists. For example, you can recode a 20-bit binary number into a 10-item chunk by replacing the four possible combinations “00”, “01”, “10” and “11” with 0,1, 2 and 3. The 20-item binary number 11 01 00 10 10 00 11 00 10 01 becomes then a 10-item chunk 3 1 0 2 2 0 3 0 2 1. By applying more and more sophisticated recoding rules, you can reduce the number of chunks, e.g. recode “000” by 0; “001” by 1; “010” by 2, …
Figure 1. Recoding binary numbers with chunksize = 2
Of course, when we do not know in advance what kind of chunking rules a subject will apply, there is no way to measure the immediate memory span. Ericson et al. (1980) trained a subject S.F. until the limit (?) of 79 decimal digits. Undergraduate student S.F. could only accomplish this after extensive training (more than 230 hours of practice) and by using chunking rules as 3492 = 3 minutes and 49 point 2 seconds, near world-record mile time. Is the memory span of S.F. increased? According to Ericsson et al., it is not.
After all this practice, can we conclude that S.F. increased his short-term memory capacity? There are several reasons to think not. [..] These data suggest that the reliable working capacity of short-term memory is about three or four units, […] and that it is not possible to increase the capacity of short-term memory with extended practice.
Baddeley (1994) however challenged this constant chunk-hypothesis by pointing at the word length effect. When you ask a subject to remember a list of words, they typically can recall more words of lists that use short words (e.g. CAT) than long words (e.g. TIGER).
The fact that span is strongly influenced by the spoken duration of the words suggests a system that is time based rather than chunk based. The concept of a phonological loop involving a time-based store and an articulatory rehearsal process that operates in real time offers a simple account of this and other related findings.
Longer words however could also implicate more chunks. According to Baddeley, this is unlikely but since we do not know the chunking rules it remains a possible explanation. A strong proponent of the constant memory capacity hypothesis is Nelson Cowan. In numerous studies, he comes to the conclusion that our working memory store is limited to 3 to 5 meaningful items (e.g. chunks).
To memorize verbal materials, one can try to repeat them in one’s mind (rehearse them covertly). One can also try to form chunks from multiple words. For example, to remember to buy bread, milk, and pepper, one can form an image of bread floating in peppery milk. To memorize a sequence of spatial locations, one can envision a pathway formed from the locations. Although we cannot yet make precise predictions about how well working memory will operate in every possible task, we can measure storage-specific capacity by preventing or controlling processing strategies. That is how one can observe a capacity limit of three to five separate items (Cowan, 2001). In many such studies with rehearsal and grouping curtailed, information was presented (a) in a brief, simultaneous spatial array; (b) in an unattended auditory channel, with attention to the sensory memory taking place only after the sounds ended; (c) during the overt, repetitive pronunciation of a single word by the participant; or (d) in a series with an unpredictable ending, as in running span. In such task conditions, one can observe that a handful of concepts can be held in the conscious mind.
The logic behind Cowan’s reasoning is that, if we can prevent a subject to process the material, for example by presenting the info at the unattended ear, then we have a robust and uncontaminated measure of the naked working memory. But, of course, the rationale for a working memory is precisely the capacity for processing. While it seems very unlikely that a subject would recode (on the fly) a binary number, as Miller proposed, it seems equally unlikely that a subject can refrain from processing while hearing the items “CAT” and “MILK”.
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