![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||
|
Remove Farrington link in intro?
Or spot on? In the section: Other cognitive numeric limits - "Cowan also noted a number of other limits of cognition that point to a 'magical number four'" made, for me, an immediate connection to a masterful performance that totally demonstrates the concept: https://www.youtube.com/watch?v=Tym0MObFpTI .
Rather looks to me like she wrote that herself. A minor paper with only 7 citations doesn't justify the use of the word 'demonstrated'.Suggested' may be better, but if this has to be included at it should be in some later section. In fact, I 'd say the paper doesn't really warrant a ref at all. If we included every minor fluff and fart with 7 cites on this topic the page would be 25k words.
I've read the article over... Exactly what is 7 +- 2? It doesn't say.
I have recently sat a psychology exam in Cognitive and Developmental psychology. I am very intreaged by Miller's Magic Number Seven, and think that it is a very successful theory. —The preceding unsigned comment was added by 80.189.20.240 ( talk • contribs) .
!!Why should it be merged with chunking? This should be a historical article, explaining that the paper was the original presentation of a theory
The chunking article explains the modern day useage and interpretation of a theory that has some derivation from Miller's one. I think they should be kept seperate Christianpunk 10:27, 13 February 2007 (UTC)
I have a theory that this has much to do with the way information is stored in our brains.
We don't store information in terms of bits and bytes. We store information in terms of items or atomic elements. An item may be a number, a word, a picture, a sound, a feeling, or any single object.
For example, the set A can be treated as a simple item. A description of the set A (such as "A is the set of all prime digits") is another item. An enumeration of the set A: {2, 3, 5, 7} are four items linked together in a group or set.
Take a look at the following diagrams:
In all of them, there's a central item, which is the main focus of our attention, and there are 6±2 other items, that are related to the central item.
The diagram in the middle has 7 elements. They're neatly ordered in a 3D cross-like figure, just as we would expect a set of 7 neurons to be arranged. The other two diagrams are just diagrams where there are less or more related items.
Of course, when you add too much links, things start to become unmanageable. The diagram with nine items already looks overcrowded. Try adding just one more item: you won't be able to do so without forgetting another item.
That's my theory about the whole Hrair limit. LGM ᚂ 16:07, 2 August 2006 (UTC)
Does the term 'hrair' appear in Ed Yourdon's book? If somebody has access to a copy can they check. Is a term that appears in Watershipdown really of sufficient import to be mentioned in this kind of article? Derek farn 12:25, 11 September 2006 (UTC)
I've read Watership Down, and the book mentions the word and concept a significant number of times, and the reference could show acceptance or inspiration. I don't know if Watership Down or the paper came first, but one is likely based on the other and this would either show history or a popular view of the idea.
joe conflo (
talk)
00:10, 26 January 2008 (UTC)
I've read Miller's paper multiple times, but I cannot find where he actually obtains a result of 7+-2. Some of the data he refers to falls far outside this range. I've even recall reading a slightly sarcastic analysis of Miller's paper saying 7+-2 should actually be 9+-4 from the data Miller presents. -- Ronz 21:03, 7 February 2007 (UTC)
The reason you cannot find this result in his paper is that Miller never meant to stipulate a magical number. He has used this number only as a rhetorical device for the talk on which his 1956-paper is based (see Miller, G.A. (1989). George A. Miller. In G. Lindzey (Ed.), A history of psychology in autobiography (Vol. VIII, pp. 391-418). Stanford, CA: Stanford University Press). Therefore I would argue that “It supposedly [clarification needed] argues that the number of objects an average human can hold in working memory is 7 ± 2.” should read: “It is often misinterpreted as arguing that the number of objects…” I discuss this misinterpretation (including many references to peer-reviewed work) in more detail here: http://www.centigrade.de/en/blog/article/the-number-seven-is-not-magical-part-1/ -- HRLfeld ( talk) 12:00, 20 April 2012 (UTC)
I'm just reading Tufte's book Beautiful Evidence now, and he sums up Miller's paper by saying "people had a hard time remembering more than about 7 unrelated pieces of really dull data all at once." Tufte emphasises that the experiment was about remembering nonsense data, and goes on to say that you can only reach the conclusion of "only 7 items belong on a list" if you don't read Miller's paper. This suggests that the current wiki-article's statement of "remarkable coincidences between the channel capacity of a number of human cognitive and perceptual tasks" -- to say that Miller is talking about cognitive capacity in general, and not just cognitive capacity when it comes to meaningless data -- is adding too many interpretations to this subject. Thanks. Chira 20:46, 30 March 2007 (UTC)
Is this the study that is frequently cited for why US phone numbers were seven characters (and later, digits) long? -- Mdwyer ( talk) 21:00, 29 January 2008 (UTC)
This article says (tail of the initial summary paragraph):
Miller hypothesized that these may all be due to some common but unknown underlying mechanism.
But Miller's article concludes:
What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.
This entire article covers only the "urban mythos" arising from the first quarter of Miller's paper (and widely hung on the famous line which is its title). Should we write a real article on Miller's paper, or merely recategorize this one as covering the myth? Jackrepenning ( talk) 00:16, 4 March 2008 (UTC)
Is it just me, or is this utterly irrelevant to this article? Chris Cunningham (not at work) - talk 15:51, 22 March 2008 (UTC)
Since the article no longer mentions the term, hrair should probably redirect to some other more applicable article, or risk confusing the hell out of everybody. — Gwalla | Talk 02:48, 10 November 2008 (UTC)
I agree that this citation is not the most relevant on the topic. For the misinterpretation issue, I would suggest to cite Miller himself: Miller, G.A. (1989). George A. Miller. In G. Lindzey (Ed.), A history of psychology in autobiography (Vol. VIII, pp. 391-418). Stanford, CA: Stanford University Press
As to the question of current estimates of working memory capacity limits around 4, I consider Cowan (2001) the most relevant paper. (This is already in the reference list.) Also Luck & Vogel (1997) is often cited (for example by Cowan, 2001). I think using the term „demonstrated“ for this point is fine, as a bunch of recent studies have shown working memory capacity limits around 4.
By the way, I do not think that the author really wants to say that „recent research has demonstrated that . . . the "law" [is] based on a misinterpretation of Miller's paper.“ How could research (other than historical) demonstrate that? Furthermore, there is not much left to demonstrate as Miller himself has already noted that he was misinterpreted (Miller, 1989).
--
HRLfeld (
talk)
12:33, 20 April 2012 (UTC)
Hmmm... I noticed a bit of nonsense on display in this: "The information contained in the input can be determined by the number of binary decisions that need to be made to arrive at the selected stimulus, and the same holds for the response."
I thought, 'Heck, this can't be what he said. Obviously selecting between six, or seven, or eight different stimuli is NOT about making a series of "binary decisions."' But, unfortunately, upon review of the report I find that he pretty much did say this.
He also makes reference 2.5 bits, etcetera. I think, in attempting to explain things in laymen's terms, he engaged in very fuzzy and approximate descriptions. To say, for instance, that it takes 3 bits of data to represent 8 possible states (true) is IN NO WAY the same as saying that we need to make 3 binary decisions to identify a state (false). In fact, the rendering of data into binary is just a bit of silly number fiddling that obfuscates rather than illustrates.
There's a lot of other sloppiness in his presentation. For instance, what he said about "equally likely" alternatives is a bit of nonsense, which he again probably just inherited from an information-theory study where it was relevant and transported into an analogy where it is irrelevant. For example, how many bits of information is needed to represent whether a man is six feet tall? He says, if it's a 50-50 proposition, it takes just one bit to represent this information. Actually, it would take one bit to represent this information even if it were a 30-70 proposition. Or a 0-100 proposition.
So, anyway, no need to edit based on this info. I discovered that the article represents the original report. Surprisingly so.
The comment(s) below were originally left at Talk:The Magical Number Seven, Plus or Minus Two/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I have always been tought that empirical it is 3/4 chunks of data and not 7+-2 anymore, I am sure there is some prove for that somewhere. |
Last edited at 09:11, 31 July 2007 (UTC). Substituted at 08:15, 30 April 2016 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||||||||||||||||
|
Remove Farrington link in intro?
Or spot on? In the section: Other cognitive numeric limits - "Cowan also noted a number of other limits of cognition that point to a 'magical number four'" made, for me, an immediate connection to a masterful performance that totally demonstrates the concept: https://www.youtube.com/watch?v=Tym0MObFpTI .
Rather looks to me like she wrote that herself. A minor paper with only 7 citations doesn't justify the use of the word 'demonstrated'.Suggested' may be better, but if this has to be included at it should be in some later section. In fact, I 'd say the paper doesn't really warrant a ref at all. If we included every minor fluff and fart with 7 cites on this topic the page would be 25k words.
I've read the article over... Exactly what is 7 +- 2? It doesn't say.
I have recently sat a psychology exam in Cognitive and Developmental psychology. I am very intreaged by Miller's Magic Number Seven, and think that it is a very successful theory. —The preceding unsigned comment was added by 80.189.20.240 ( talk • contribs) .
!!Why should it be merged with chunking? This should be a historical article, explaining that the paper was the original presentation of a theory
The chunking article explains the modern day useage and interpretation of a theory that has some derivation from Miller's one. I think they should be kept seperate Christianpunk 10:27, 13 February 2007 (UTC)
I have a theory that this has much to do with the way information is stored in our brains.
We don't store information in terms of bits and bytes. We store information in terms of items or atomic elements. An item may be a number, a word, a picture, a sound, a feeling, or any single object.
For example, the set A can be treated as a simple item. A description of the set A (such as "A is the set of all prime digits") is another item. An enumeration of the set A: {2, 3, 5, 7} are four items linked together in a group or set.
Take a look at the following diagrams:
In all of them, there's a central item, which is the main focus of our attention, and there are 6±2 other items, that are related to the central item.
The diagram in the middle has 7 elements. They're neatly ordered in a 3D cross-like figure, just as we would expect a set of 7 neurons to be arranged. The other two diagrams are just diagrams where there are less or more related items.
Of course, when you add too much links, things start to become unmanageable. The diagram with nine items already looks overcrowded. Try adding just one more item: you won't be able to do so without forgetting another item.
That's my theory about the whole Hrair limit. LGM ᚂ 16:07, 2 August 2006 (UTC)
Does the term 'hrair' appear in Ed Yourdon's book? If somebody has access to a copy can they check. Is a term that appears in Watershipdown really of sufficient import to be mentioned in this kind of article? Derek farn 12:25, 11 September 2006 (UTC)
I've read Watership Down, and the book mentions the word and concept a significant number of times, and the reference could show acceptance or inspiration. I don't know if Watership Down or the paper came first, but one is likely based on the other and this would either show history or a popular view of the idea.
joe conflo (
talk)
00:10, 26 January 2008 (UTC)
I've read Miller's paper multiple times, but I cannot find where he actually obtains a result of 7+-2. Some of the data he refers to falls far outside this range. I've even recall reading a slightly sarcastic analysis of Miller's paper saying 7+-2 should actually be 9+-4 from the data Miller presents. -- Ronz 21:03, 7 February 2007 (UTC)
The reason you cannot find this result in his paper is that Miller never meant to stipulate a magical number. He has used this number only as a rhetorical device for the talk on which his 1956-paper is based (see Miller, G.A. (1989). George A. Miller. In G. Lindzey (Ed.), A history of psychology in autobiography (Vol. VIII, pp. 391-418). Stanford, CA: Stanford University Press). Therefore I would argue that “It supposedly [clarification needed] argues that the number of objects an average human can hold in working memory is 7 ± 2.” should read: “It is often misinterpreted as arguing that the number of objects…” I discuss this misinterpretation (including many references to peer-reviewed work) in more detail here: http://www.centigrade.de/en/blog/article/the-number-seven-is-not-magical-part-1/ -- HRLfeld ( talk) 12:00, 20 April 2012 (UTC)
I'm just reading Tufte's book Beautiful Evidence now, and he sums up Miller's paper by saying "people had a hard time remembering more than about 7 unrelated pieces of really dull data all at once." Tufte emphasises that the experiment was about remembering nonsense data, and goes on to say that you can only reach the conclusion of "only 7 items belong on a list" if you don't read Miller's paper. This suggests that the current wiki-article's statement of "remarkable coincidences between the channel capacity of a number of human cognitive and perceptual tasks" -- to say that Miller is talking about cognitive capacity in general, and not just cognitive capacity when it comes to meaningless data -- is adding too many interpretations to this subject. Thanks. Chira 20:46, 30 March 2007 (UTC)
Is this the study that is frequently cited for why US phone numbers were seven characters (and later, digits) long? -- Mdwyer ( talk) 21:00, 29 January 2008 (UTC)
This article says (tail of the initial summary paragraph):
Miller hypothesized that these may all be due to some common but unknown underlying mechanism.
But Miller's article concludes:
What about the seven-point rating scale, the seven categories for absolute judgment, the seven objects in the span of attention, and the seven digits in the span of immediate memory? For the present I propose to withhold judgment. Perhaps there is something deep and profound behind all these sevens, something just calling out for us to discover it. But I suspect that it is only a pernicious, Pythagorean coincidence.
This entire article covers only the "urban mythos" arising from the first quarter of Miller's paper (and widely hung on the famous line which is its title). Should we write a real article on Miller's paper, or merely recategorize this one as covering the myth? Jackrepenning ( talk) 00:16, 4 March 2008 (UTC)
Is it just me, or is this utterly irrelevant to this article? Chris Cunningham (not at work) - talk 15:51, 22 March 2008 (UTC)
Since the article no longer mentions the term, hrair should probably redirect to some other more applicable article, or risk confusing the hell out of everybody. — Gwalla | Talk 02:48, 10 November 2008 (UTC)
I agree that this citation is not the most relevant on the topic. For the misinterpretation issue, I would suggest to cite Miller himself: Miller, G.A. (1989). George A. Miller. In G. Lindzey (Ed.), A history of psychology in autobiography (Vol. VIII, pp. 391-418). Stanford, CA: Stanford University Press
As to the question of current estimates of working memory capacity limits around 4, I consider Cowan (2001) the most relevant paper. (This is already in the reference list.) Also Luck & Vogel (1997) is often cited (for example by Cowan, 2001). I think using the term „demonstrated“ for this point is fine, as a bunch of recent studies have shown working memory capacity limits around 4.
By the way, I do not think that the author really wants to say that „recent research has demonstrated that . . . the "law" [is] based on a misinterpretation of Miller's paper.“ How could research (other than historical) demonstrate that? Furthermore, there is not much left to demonstrate as Miller himself has already noted that he was misinterpreted (Miller, 1989).
--
HRLfeld (
talk)
12:33, 20 April 2012 (UTC)
Hmmm... I noticed a bit of nonsense on display in this: "The information contained in the input can be determined by the number of binary decisions that need to be made to arrive at the selected stimulus, and the same holds for the response."
I thought, 'Heck, this can't be what he said. Obviously selecting between six, or seven, or eight different stimuli is NOT about making a series of "binary decisions."' But, unfortunately, upon review of the report I find that he pretty much did say this.
He also makes reference 2.5 bits, etcetera. I think, in attempting to explain things in laymen's terms, he engaged in very fuzzy and approximate descriptions. To say, for instance, that it takes 3 bits of data to represent 8 possible states (true) is IN NO WAY the same as saying that we need to make 3 binary decisions to identify a state (false). In fact, the rendering of data into binary is just a bit of silly number fiddling that obfuscates rather than illustrates.
There's a lot of other sloppiness in his presentation. For instance, what he said about "equally likely" alternatives is a bit of nonsense, which he again probably just inherited from an information-theory study where it was relevant and transported into an analogy where it is irrelevant. For example, how many bits of information is needed to represent whether a man is six feet tall? He says, if it's a 50-50 proposition, it takes just one bit to represent this information. Actually, it would take one bit to represent this information even if it were a 30-70 proposition. Or a 0-100 proposition.
So, anyway, no need to edit based on this info. I discovered that the article represents the original report. Surprisingly so.
The comment(s) below were originally left at Talk:The Magical Number Seven, Plus or Minus Two/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
I have always been tought that empirical it is 3/4 chunks of data and not 7+-2 anymore, I am sure there is some prove for that somewhere. |
Last edited at 09:11, 31 July 2007 (UTC). Substituted at 08:15, 30 April 2016 (UTC)