# Is The magical number 7 still valid?

George A. Miller published "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information" in 1956 and is one of the most highly cited papers in psychology. It supposedly argues that the number of objects an average human can hold in working memory is 7 ± 2. This is frequently referred to as Miller's Law.[1]

I've learned this in school as well, and I often use the magic number seven when it comes to grouping of elements in more logical units. However recent research question Miller's Law stating that the correct number a human being can hold in working memory is three or four[2]. In my daily life, I can see that this is more likely. When I go shopping, I need to write a shopping list if there are more than four things I need to buy and by this not forget what it was I'm supposed to buy. One could argue that my working memory is worse than average, but I would never agree to such a statement.

But the question remains and is puzzling my mind... Is The magical number 7 still valid?

[1] Wikipedia article on Miller's Law

[2] Jeanne Farrington EdD, "Seven plus or minus two"

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No, this has been largely rejected, especially as a "magic number". I'll try and find some good sources later – Ben Brocka Mar 31 '12 at 14:35

As far as I recall, the "magic" of the number seven is that George Miller had to give a 1h-presentation while not having enough research on one particular topic to talk about this long. So he tried to connect unrelated lines of research, with the only connection between them being that they show cognitive limitations of similar magnitude ("7+/-2 items"). However, the comparison was not very serious and mostly rhetorical. So I guess the short answer is: No it is not valid, and it has never really been.

Here is an short article that answers your question in more detail:

Cowan, N., Morey, C.C., & Chen, Z. (2007). The legend of the magical number seven. In S. Della Sala (Ed.), Tall tales about the mind & brain: Separating fact from fiction (pp. 45-59). Oxford, U.K.: Oxford University Press.

And here is Millers original article, it's actually fun to read:

Miller, G. A. (1956). "The magical number seven, plus or minus two: Some limits on our capacity for processing information". Psychological Review 63 (2): 81–97.

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+1 for another reference to the same conclusion: three or four items. – Benny Skogberg Mar 31 '12 at 20:09
Agree with this answer. I think the problem is the scope of the object "item" How many properties does the item itself contain? How intricate or complex is each item? How has each person encoded it in their association scheme and world model? Some people, via coincidental experience, might be able to include 3 or 4 items as 1 item if they have an association to "wrap up" the items in (like we know a human has two legs, two arms, and a head, so if "items" have the appropriate property relationships, we could compress 5 items into 1 "human") EDIT: also, see EM23's answer, just noticecd it. – Keegan Keplinger Jun 9 '12 at 20:46
In "The legend of the magical number seven" article - "Perhaps there is something deep and profound behind all of these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.” The results of absolute judgement, span of attention and intermediate memory all gave results in the 7+-2 range, but of course, given how many different tasks can be concocted, it is unsurprising that some of them provide almost the same result – Casebash Jun 14 '12 at 4:01

While their answer may not be any more useful in everyday life and while the results are within the specific domain of visual short-term memory, Sims, Jacobs, & Knill, 2011 provide a more detailed (and less arbitrary) answer than either "7 +/- 2" or "about 4" items by using rate distortion theory to model optimal lossy compression.

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Pavel has already given a pretty good answer, and I agree that not even Miller was very serious about 7 +/- 2 being a useful or accurate conclusion. As for the limit of three or four items that was suggested in the question, I'm not entirely certain about that myself, as it still isn't entirely clear what constitutes an "item", nor is it clear how information on items is stored in working memory.

I'd recommend looking at the current debate between the "Discrete-Slots" and "Distributed Resources" models of Working Memory (which is far from being resolved) to get a better understanding of the issue. Some good examples include work by:

• Luck and Vogel "The capacity of visual working memory for features and conjunctions" (1997, Nature)
• Bays and Husain "Dynamic Shifts of Limited Working Memory Resources in Human Vision" (2008, Science)
• Awh, Barton, and Vogel "Visual working memory represents a fixed number of items regardless of complexity" (2007, Psychological Science)
• Bays, Catalao, and Husain "The precision of visual working memory is set by allocation of a shared resource" (2009, Journal of Vision)
• Gorgoraptis, Catalao, Bays, and Husain "Dynamic updating of working memory resources for visual objects" (2011, The Journal of Neuroscience)
• Rouder, Morey, Cowan, Zwilling, Morey, and Pratte "An assessment of fixed-capacity models of visual working memory" (2008, Proceedings of the National Academy of Sciences)
• Wheeler and Treisman "Binding in short-term visual memory" (2002, Journal of Experimental Psychology: General)
• Wilken and Ma "A detection theory account of change detection" (2004, Journal of Vision)
• Zhang and Luck "Discrete fixed-resolution representations in visual working memory" (2008, Nature)

That being said, measures of "effective" capacity, such as Cowan's K (Cowan "The magical number 4 in short-term memory: A reconsideration of mental storage capacity", 2001, Behavioral and Brain Sciences) suggest that the capacity of visual working memory is about 4.

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Most others have already pointed to some great papers on this and the fact that the literature has moved on from these claims now (as usual, 'bold' claims so often end up being false), but there's a great and very recent review on visual memory by Brady etal (2011) that gives a great deal of detail and is available via open access online here :

To quote the abstract:

Traditional memory research has focused on identifying separate memory systems and exploring different stages of memory processing. This approach has been valuable for establishing a taxonomy of memory systems and characterizing their function but has been less informative about the nature of stored memory representations. Recent research on visual memory has shifted toward a representation-based emphasis, focusing on the contents of memory and attempting to determine the format and structure of remembered information. The main thesis of this review will be that one cannot fully understand memory systems or memory processes without also determining the nature of memory representations. Nowhere is this connection more obvious than in research that attempts to measure the capacity of visual memory. We will review research on the capacity of visual working memory and visual long-term memory, highlighting recent work that emphasizes the contents of memory. This focus impacts not only how we estimate the capacity of the system—going beyond quantifying how many items can be remembered and moving toward structured representations—but how we model memory systems and memory processes.

### References

• Brady, T.F., Konkle, T. & Alvarez, G.A. (2011). A review of visual memory capacity: Beyond individual items and toward structured representations. Journal of Vision, 11. FULL TEXT
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