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Marco Wolf
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David Gilden

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David Gilden
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This 14 page Class Notes was uploaded by Marco Wolf on Monday September 7, 2015. The Class Notes belongs to PSY 355 at University of Texas at Austin taught by David Gilden in Fall. Since its upload, it has received 5 views. For similar materials see /class/181796/psy-355-university-of-texas-at-austin in Psychlogy at University of Texas at Austin.


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Date Created: 09/07/15
From httppsychclassicsyorkucaMiller Classics Editor39s Note Footnotes are in square brackets references in round brackets The Magical Number Seven Plus or Minus Two Some Limits on our Capacity for Processing Info rmationi George A Miller 1956 Harvard University First published in Psychological Review 63 8197 My problem is that I have been persecuted by an integer For seven years this number has followed me around has intruded in my most private data and has assaulted me from the pages of our most public journals This number assumes a variety of disguises being sometimes a little larger and sometimes a little smaller than usual but never changing so much as to be unrecognizable The persistence with which this number plagues me is far more than a random accident There is to quote a famous senator a design behind it some pattern governing its appearances Either there really is something unusual about the number or else I am suffering from delusions of persecution I shall begin my case history by telling you about some experiments that tested how accurately people can assign numbers to the magnitudes of various aspects of a stimulus In the traditional language of psychology these would be called experiments in absolute judgment Historical accident however has decreed that they should have another name We now call them experiments on the capacity of people to transmit information Since these experiments would not have been done without the appearance of information theory on the psychological scene and since the results are analyzed in terms of the concepts of information theory I shall have to preface my discussion with a few remarks about this theory Information Measurement The quotamount of informationquot is exactly the same concept that we have talked about for years under the name of quotvariancequot The equations are different but if we hold tight to the idea that anything that increases the variance also increases the amount of information we cannot go far astray The advantages of this new way of talking about variance are simple enough Variance is always stated in terms of the unit of measurement inches pounds volts etc whereas the amount of information is a dimensionless quantity Since the information in a discrete statistical distribution does not depend upon the unit of measurement we can extend the concept to situations where we have no metric and we would not ordinarily think of using p 82 the variance And it also enables us to compare results obtained in quite different experimental situations where it would be meaningless to compare variances based on different metrics So there are some good reasons for adopting the newer concept The similarity of variance and amount of information might be explained this way When we have a large variance we are very ignorant about what is going to happen If we are very ignorant then when we make the observation it gives us a lot of information On the other hand if the variance is very small we know in advance how our observation must come out so we get little information from making the observation If you will now imagine a communication system you will realize that there is a great deal of variability about what goes into the system and also a great deal of variability about what comes out The input and the output can therefore be described in terms of their variance or their information If it is a good communication system however there must be some systematic relation between what goes in and what comes out That is to say the output will depend upon the input or will be correlated with the input If we measure this correlation then we can say how much of the output variance is attributable to the input and how much is due to random uctuations or quotnoisequot introduced by the system during transmission So we see that the measure of transmitted information is simply a measure of the inputoutput correlation There are two simple rules to follow Whenever I refer to quotamount of informationquot you will understand quotvariancequot And whenever I refer to quotamount of transmitted informationquot you will understand quotcovariancequot or quotcorrelationquot The situation can be described graphically by two partially overlapping circles Then the left circle can be taken to represent the variance of the input the right circle the variance of the output and the overlap the covariance of input and output I shall speak of the left circle as the amount of input information the right circle as the amount of output information and the overlap as the amount of transmitted information In the experiments on absolute judgment the observer is considered to be a communication channel Then the left circle would represent the amount of information in the stimuli the right circle the amount of information in his responses and the overlap the stimulusresponse correlation as measured by the amount of transmitted information The experimental problem is to increase the amount of input information and to measure the amount of transmitted information If the observer39s absolute judgments are quite accurate then nearly all of the input information will be transmitted and will be recoverable from his responses If he makes errors then the transmitted information may be considerably less than the input We expect that as we increase the amount of input information the observer will begin to make more and more errors we can test the limits of accuracy of his absolute judgments If the human observer is a reasonable kind of communication system then when we increase the amount of input information the transmitted information will increase at first and will eventually level off at some asymptotic value This asymptotic value we take to be the channel capacity of the observer it represents the greatest amount of information that he can give us about the stimulus on the basis of an absolute judgment The channel capacity is the upper limit on the extent to which the observer can match his responses to the stimuli we give him Now just a brief word about the bit p 83 and we can begin to look at some data One bit of information is the amount of information that we need to make a decision between two equally likely alternatives If we must decide whether a man is less than six feet tall or more than six feet tall and if we know that the chances are 5050 then we need one bit of information Notice that this unit of information does not refer in any way to the unit of length that we use feet inches centimeters etc However you measure the man39s height we still need just one bit of information Two bits of information enables us to decide among four equally likely alternatives Three bits of information enable us to decide among eight equally likely alternatives Four bits of information decide among 16 alternatives five among 32 and so on That is to say if there are 32 equally likely alternatives we must make five successive binary decisions worth one bit each before we know which alternative is correct So the general rule is simple every time the number of alternatives is increased by a factor of two one bit of information is added There are two ways we might increase the amount of input information We could increase the rate at which we give information to the observer so that the amount of information per unit time would merease confusxons begm to occur Confusions wul appear near the pomtthatwe are ea1hng hxs channel capaex Ahsnlute Judgments nr Unidimensinnal Stimuli v u 1m asked Fr an n t nthmt steps eorreetxdenn eauon ofthe tone With fourteen durehent tones the hstenehs made many mistakes These data are plottedm Fxg 1 Along the bottom 15 the amount ofmputmformanon tn xspers hnu1us As the number ofaltematzve tones was increasedfrom 2to 14 the e mputmfor manon increased from 1 to 3 8 bxts on the ordmatexsplott dthe amo 1 s mueh the way we would expect a communication ehanne1 rimsw sb w39n39wa y to about 2 bxts and then bends off toward an asymptote at about 2 5 bxts Thxs value 2 5 bxts therefore us what we are eallmg the ehanne1 eapaeuty ofthe hstenerfor absolute m m Wm WM 17 m 0 W Judgments ofpxteh amount nf ut munm that as u umuuu u hsuncrs who 39uuxkn ahgulute judzmam or on have the number25bxts What doesxt mean7 W A V my fining Fust note that 2 5 bus corresponds to about sxx equally n n he u nt wt uein emu lxkely altematzves The result meanst atwe cannot pxek j law the amml L m lmaam39 ted ininmmr more than sxx dufferent pxtehes that the hstener wxll never liun apprnhmru is f5 quot131 quot 1quot Lhmr confuse 0 stated shghtly dfferendynomatterhow many W W 7 1 P 1W wmu HFDF MM 1w th uht on agaun Judgment enables us to narrow down the pameular suhnulus to one out ofN o t Ofcourse 60 duffehent mt h F mu t t Isayxtxs fortunate e confused m rtw n tFrmth ask how reproduelble thls result ls Does rt b u 0 wl transmrtted more than a smal ferent grouplngs ofthe prtehes deereased the transmrssron but the 1 ss was small For example lf you ean dlscnmlnate ve YnANswrlEu Mn a another serres rtrs reasonable to expeet that you eould o t z 3 4 eombrne all ten rnto a srngle senes and sall tell them all apart mw wwmnow wrthout error en you try rt howeyer rt does not wor we 2 untr lrom Carnnr m on AM L n he ehannel eapaerty for prteh seems to be about slx and that me mutiny m ahwm iw39gmmm m umr 5 me bestyou can do tnry tounntss summanzedrn Flg 2 rntensrty range from 15 to 110 db He used 4 5 o 7 10 and 20 dlfferent samulus rntensrtres The r uh h w w Fl p 85 The ehannel 3 brts Srnee these two studres were done m dlfferent laboratones wrth slrghtly dlfferent teehnrques and methods of analysls we are not m agood posraon to argue whether flve Tia NFDRvnlou r te WS Probably the dlfference ls m the nght dlrecnon and absolute Judg e slrghtly te than abs g l r pg ments ofpltch ar more aeeura olute Wm 75 o some judgments ofloudness The rmportantpornt howeyer ls that E 39 the two answers are ofthe same order ofmagnrtude o l 2 3 A b The expenment has also been done for taste rntensraes 1n Flg 3 are the results obtarned by BeeberCenter Rogers and WFUY tnmamlntt Ext 3 I r 1mm Ilrtltchcnlny nugrts uvd cennnelt m absolute mum s ot mums salt solutzons The concentrations ranged from 0 3 to 34 7 gm NaCl per 100 ee tap waterrn equal subjective steps They used 3 5 9 and 17 dlfferent eoneentraaons The ehannel eapaerty ls l 9 brts whreh ls about four but agarn the order of magnrtude ls not far off on the otherhand Thelr results are shown m Flg 4 1 10 20 erreles on the graph That ls to say erreles on the graph 3 25 brts he HakerGamer expenrnenthas been repeated by Coonan g dKl rner Although they have notyet publlshed Lhelr s results they have glven rne perrnlsslon to say that they g obtatnedehannel eapaeluesrangln from 32blts for p 86 2 very short exposures of the polnter posltlon to 3 9 blts f r E l er exp T se val es sh tl th 3 t ake and Garner s so we rnust eonelude that there ar between an Thls ls the largest ehannel capaclty thathas been rneasured 2 l J for any umdlmenslonal vanable quot41 WWW m mm mm Hake and C39lmlzr a At the present urne these four expenrnents on absolute a quotR d W W quot quotNW quotAquot menu or e phylum or a nonler ur 1 m Jud rnents ofslmple unldm uh are all that mm g enslonal have appearedln the psychologlcal journals However a great deal ofwork on other surnulus vanables has notyet appearedln thejoumals For example Enksen or abou ve t u Wdlh n found 2 8 blts for slze31blts for hue and 2 3 blts for bnghmess Geldard has measured the ehannel lntenslues about ve durations and about seven loeauons vlsual dlsplays the ur m l n th A A l v 1 n A A t t and2 F r L l L m tt n bltsfor When twhen the u t u Vb length ofthe ehord was eonstant the result was only 1 6 blts Thls last value ls the lowest that anyone L A A T h uld dd h r dtrrm ll rst the ehannel p hurnan b rt r froml L L In terms of lncludesfrom4to 10 t n to 15eategorles lanun or L A t m umdtm n t n l one slrnple sensory atmbute to another p 87 Ahsnlnte Judgments hr Mlltidimensinnal Stimuli ete The why h rnolepenolently yanable attnbutes othe starnulr that are belngjudged Objects faces worols and the llke dlffer from from one anotherrn only one respeet 39 Fortunately there are a few data on what happens when we another m several ways Letus look rst atthe results Kl rnrner anol Fnck g have reported for the absolute Judgment of the posrtaon ofa olot m a square 1n Flg 5 we see news to a 9mm therrresults Nowthe ehannel eapaerty seernsto have no em rnereaseolto 4 o brts whreh rneans thatpeople ean ldentlfy us see urnsqu 3 4 5 a 7 quotHquot quot URW W39 The posmon of a olotrn a square ls elearly atwordlmenslonal ne 5 ttt n 1 5 5mm 55mm fur ahm utz inr z beldennfled Thus rtseerns natural to comparethe4 Srblt quot m quotIt 1mm 1 391 d m a 3 a eapaerty for a square wth the 3 25ebrt eapaerty forthe r rnerease from 3 25 to 4 o butltfalls short ofthe perfeet addlnon that wouldglve o 5 brts Another example ls provlded by BeeberCenter Rogers and O Connell When they asked people to 3brts altar n a 19we ml m n V b m eoneeryably rnrght brts bt w d l brts pltch Four V w v ll seeonol dlmenslon augments the ehannel eapaerty butnot so rnueh as rt rnrght fourth exam A pl ofequal p 88 lule n th estrrnate that there are about ll to 15 rolentrfrable eolors or m our terrns about 3 o brts Srnee these Judgment Enksen s 3 l olraw 1t ls stall along h r L NW1 provlded by faces worols ete To flll thrs gap we have only one expenrnent an audltory stuoly alone by frequency rntensrty rate oflntermpuon onrtlme fraetaon total duratron and spataal loeataon Eaeh one or 15 dtmenstons 7 2 btts up tnto the tange that otdtnaty expettenee wouldlead us to expeet p rt 6 1n amoment of tahtng V Clearly the addttton oftndependentty vanable attnbtttes to the stamtthts tneteases the channel eapaetty but at a deeteastng tate Itts tntetesttng to note that the ehanne1 eapaetty ts tneteased even when the se eta1 vanables are not 3 tomes mquot tndependent Enksen 5 tepotts that when stzebnghtness g r and hue all vary togethet tn petfeet eonetatton the g A ttansmtttedtnfotmataon ts 4 1 btts as compared wtth an 1 avetage of about 2 7 btts when these attxtbutes ate vatted one Hm at atame By confoundmg thtee attnbutes Enksen tneteased 0H7 L jig l the dtmenstonahty othe tnptttwtthottttneteastng the amoun o were cape Ft 6 to 31m quott wouldlead us to expeet z twcivdm y tmsttto nttttht or m sttmtth httt we deetease the aeeutaey fot any pamcularvanable 1n othetwotds we ean make te1attve1y etude tudgments ofseveral thtngs stmuttaneottsty 1 n tr w quott the one we seem to have made ts clearly the mote adaptave speeeh A A L ot atmosttemary tn natute Fot example abmary dtsttnetton ts made between vowels and eonsonants abmary deetston ts made between ota1 and nasal eonsonants atematy deetston ts made among front mxddle and back phonemes ete mm r t that there ts not ttme to dtseuss tthete ot about r tth tunexptoted L L tndeftnttety tn thts way In human speech there is clearly a limit to the number of dimensions that we use In this instance however it is not known whether the limit is imposed by the nature of the perceptual machinery that must recognize the sounds or by the nature of the speech machinery that must produce them Somebody will have to do the experiment to nd out There is a limit however at about eight or nine distinctive features in every language that has been studied and so when we talk we must resort to still another trick for increasing our channel capacity Language uses sequences of phonemes so we make several judgments successively when we listen to words and sentences That is to say we use both simultaneous and successive discriminations in order to expand the rather rigid limits imposed by the inaccuracy of our absolute judgments of simple magnitudes These multidimensional judgments are strongly reminiscent of the abstraction experiment of Kulpe M As you may remember Kulpe showed that observers report more accurately on an attribute for which they are set than on attributes for which they are not set For example Chapman A used three different attributes and compared the results obtained when the observers were instructed before the tachistoschopic presentation with the results obtained when they were not told until after the presentation which one of the three attributes was to be reported When the instruction was given in advance the judgments were more accurate When the instruction was given afterwards the subjects presumably had to judge all three attributes in order to report on any one of them and the accuracy was correspondingly lower This is in complete accord with the results we have just been considering where the accuracy of judgment on each attribute decreased as more dimensions were added The point is probably obvious but I shall make it anyhow that the abstraction experiments did not demonstrate that people can judge only one attribute at a time They merely showed what seems quite reasonable that people are less accurate if they must judge more than one attribute simultaneously p 90 Subitizing I cannot leave this general area without mentioning however brie y the experiments conducted at Mount Holyoke College on the discrimination of number Q In experiments by Kaufman Lord Reese and Volkmann random patterns of dots were ashed on a screen for l 5 of a second Anywhere from 1 to more than 200 dots could appear in the pattern The subject s task was to report how many dots there were The first point to note is that on patterns containing up to five or six dots the subjects simply did not make errors The performance on these small numbers of dots was so different from the performance with more dots that is was given a special name Below seven the subjects were said to subitize above seven they were said to estimate This is as you will recognize what we once optimistically called quotthe span of attentionquot This discontinuity at seven is of course suggestive Is this the same basic process that limits our unidimensional judgments to about seven categories The generalization is tempting but not sound in my opinion The data on number estimates have not been analyzed in informational terms but on the basis of the published data I would guess that the subjects transmitted something more than four bits of information about the number of dots Using the same arguments as before we would conclude that there are about 20 or 30 distinguishable categories of numerousness This is considerably more information than we would expect to get from a unidimensional display It is as a matter of fact very much like a twodimensional display Although the dimensionality of the random dot patterns is not entirely clear these results are in the same range as Klemmer and Frick s for their twodimensional display of dots in a square Perhaps the two dimensions of numerousness are area and density When the subject can subitize area and density may not be the significant variables but when the subject must estimate perhaps they are significant In any event the comparison is not so simple as it might seem at first thought This is one of the ways in which the magical number seven has persecuted me Here we have two closely related kinds of experiments both of which point to the signi cance of the number seven as a limit on our capacities And yet when we examine the matter more closely there seems to be a reasonable suspicion that it is nothing more than a coincidence The Span 0f Immediate Memory Let me summarize the situation in this way There is a clear and de nite limit to the accuracy with which we can identify absolutely the magnitude of a unidimensional stimulus variable I would propose to call this limit the span of absolute judgment and I maintain that for unidimensional judgments this span is usually somewhere in the neighborhood of seven We are not completely at the mercy of this limited span however because we have a variety of techniques for getting around it and increasing the accuracy of our judgments The three most important of these devices are a to make relative rather than absolute judgments or if that is not possible b to increase the number of dimensions along which the stimuli can differ or c to arrange the task in such a way that we make a sequence of several absolute judgments in a row The study of relative judgments is one of the oldest topics in experimental psychology and I will not pause to review it now The second device increasing the dimensionality we have just considered It seems that by adding p 91 more dimensions and requiring crude binary yesno judgments on each attribute we can extend the span of absolute judgment from seven to at least 150 Judging from our everyday behavior the limit is probably in the thousands if indeed there is a limit In my opinion we cannot go on compounding dimensions inde nitely I suspect that there is also a span of perceptual dimensionality and that this span is somewhere in the neighborhood of ten but I must add at once that there is no objective evidence to support this suspicion This is a question sadly needing experimental exploration Concerning the third device the use of successive judgments I have quite a bit to say because this device introduces memory as the handmaiden of discrimination And since mnemonic processes are at least as complex as are perceptual processes we can anticipate that their interactions will not be easily disentangled Suppose that we start by simply extending slightly the experimental procedure that we have been using 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 We still have the same sort of inputoutput situation that is required for the measurement of transmitted information But now we have passed from an experiment on absolute judgment to what is traditionally called an experiment on immediate memory Before we look at any data on this topic I feel I must give you a word of warning to help you avoid some obvious associations that can be confusing Everybody knows that there is a nite span of immediate memory and that for a lot of different kinds of test materials this span is about seven items in length I have just shown you that there is a span of absolute judgment that can distinguish about seven categories and that there is a span of attention that will encompass about six objects at a glance What is more natural than to think that all three of these spans are different aspects of a single underlying process And that is a fundamental mistake as I shall be at some pains to demonstrate This mistake is one of the malicious persecutions that the magical number seven has subjected me to My mistake went something like this We have seen that the invariant feature in the span of absolute judgment is the amount of information that the observer can transmit There is a real operational p If h Vth m um of lnformauon For example declmal dlglts are worth 3 3 bus aplece We ean reeall about seven ofthem for atotal of 23 bus ofrnformauon Isolated Engllsh words are worth about 10 bus aplece Ifthe total lnu M n hmquot t deflmtlve kmds oftestmatenals blnary dlgltsdeclma1 dlglts letters ofthe alphabet letters plus declmal dlglts wuh l Woodworth was useolto seore the responses The results are shown by the lled clrcles m Flg 7 Here 1 5D f the olotteolhne rndleates what the span shoulol have been lf h am unt on form hon m span were eonstant Z r e no r solld euryes represent the data Hayes repeated e a t WWW expenment uslng test yoeabulanes of dlfferent slzes but all urosumuo w eontarnrng only Engll sh monosyllables open clrcles m Flg Z l 7 Thls more homogeneous test matenal dwlnot ehange the V pleture slgnlfeantly wuh bmary uems the span ls about t 2 mute and although u olrops to about ye wuh monosyllablc 3 Enghsh words the dlfference ls far less than the hypothesls W V of e nstant lnformatlon would requlre 0 Jam rg e F t There ls notlung wrong wuh Hayes s experrment beeause wFoRMAYvoV um ta nus Pollack m repeateolu mueh more elaborately and got km mm W 0 m m Fr 7 Dru essenually the sameresult Pollaektook pams tomeasure of numerunto annury plotiul as n undiun r h 39 per hem In th o t e the tradluonal proeeolure for seorlng the responses Hls 3 Mi 5v rt 8 tnbthnl b a A by the amount ofrnformauon Immedlate memory ls hmueol by the number ofltems 1n oroler to eapture ThenI e rmmedlate memory W bus per ehunk atleast oyerthe range thathas been examrneolto olate Th ontrast othe terms hr and chunk a1so serves to h ghhght the faetthatwe are not very defxmte about what am e at eonstrtutes a ehunk ofmformanon For ex pl the memory f1 o1thatH s ba d henea ordw 2 m s 1000 ghsh monosy11ab1es g mxghtjust as appropnate1y have been ea11 d me s 5 of 15 ph 1 e eaeh word had about three phonemes 1rnrt 1nturtave1yrtrs 1 arth subjects were re an e e at the vewords not 15phonemes but the not 1mme ate1y apparent We are de roeess o rgamzmg or groupmg the rnputrnto famxlxar ts or ehunks and agreat deal ofleammg has gone rnto the f ts e mg 1ogrea1 dutmcuon 15 almg here wrth a p u 1 formauon ofthese amxharum wot a 0 0115 m 5 mm mm mm 16 rm at mnunL n m ornmtnn ctt ncrl ntter 01 nnmtatmn wound a n funcumx hi on Reendmg nmuuni n1 mfmmnlmn per ttrrn hr the to WM In order to speak more preerse1y therefore we must h 1 Smce the mdlarger before Soon he L Then the ehunks F L dunng the 1 mm or T mcrease the brts per ehunk e A but V tn wd39hwrmmhr the new name rather than the ongmal rnput events 1want to ten xplmt w t w h m Thrs P h 1 1 Assoerataon m 1954 64915 at tt we bmary dAgnS LnTab1e1 of18b1nary at tt 1m n t 0115 renamed 1 1015 renamed 2 and 11 15 p 94 renamed 3 That 15 to say we reeode from abaseetwo so we gwe eaeh A 1 15andfrom 0to31 mm 1 1mm be beeuutso 5M2le or Hunk MW n n 41 o u 1 t 1 2391 cunter l 10 ut u no 11 10 but 1mg 0 1 o o 31 Chunks It DUO 00 In 11mm 5 0 4 n 41 Chunks 1010 0010 10 kccmlmg m 2 51 Chunla 1011 mom 1 Mounts 211 9 61915 b oeta1s c b 10 mmutes wh1le they tnedto use the recodmg sehemes they had studmd pant r ydAgns m eyery trans1ata on othe 1ast group Smce the 4 V L F1 predmt on the basrs ofh1s span for oeta1 dAgnS He eou1o1remember 12 oeta1 dAgnS th the 2 1 reeodmg these 12 ehunks were worth 24 bmary dAg1ts th th 3 1 recodmg they were worth 36 bmary dAg1ts Wrth the 4 1 and 5 1 reeodmgs they were worth about 40 bmary dAgnS rrrH r e The pomt 15 deal wrth In one form or anotherwe use recodmg eonstant1y m our dar1y behayror eode When there 15 a story or an argument or an rdeathatwe want to remember we usua11y try to rephrase rt m our own words When we wrtness some event we want to remember we make ayerba1 verbalxzan on Upon recall we recreate by secondary elabor n the detads that seem consistenthth the vs 40 35531233 pameular verbal recodmg we happen to have made The Wk Wellrknown enpenment by Canmchael Hogan dWalter g on them uenee thatnames have on the recall ofvxsual gures is one demonstration oftheprocess The maeeunaey ofthe testamony of eyewnnesses is well known m legal psychology but the distortions oftesumony are recodingtha the Witness used an ep cularrecodmg he used depends uponhxswhole hfehstory Ourlanguagexs mnc m m ehunks neh m mformauon Isuspeet that imagery ls aform F dw V operationally andto study expenmentany Lhanthemore 5 g u hunted In a unrucn o the 39 The pnde 4mm aquot n nmnanen by v minlymx he mm m mats b 2 s n to m mumquot ium hash had b39 p m nspmzmhv ymbohe kmds ofrecodm F t t V enough H m w m elustenng m the recall ofwords is especially mteresung m this respect Summary summanzmg remarks Fust L or win m mh r we manage to break or at least stretch this mformauonal botueneek Second Tun m m r hmtn n h ep91 Vhme nrhh because Tmazes the N nh r nun uneharted wilderness ofmdmdual differences 739 A h F mm rt rm Infomauon can be useful in the study of concept formation A lot of questions that seemed fruitless twenty or thirty years ago may now be worth another look In fact I feel that my story here must stop just as it begins to get really interesting And nally what about the magical number seven What about the seven wonders of the world the seven seas the seven deadly sins the seven daughters of Atlas in the Pleiades the seven ages of man the seven levels of hell the seven primary colors the seven notes of the musical scale and the seven days of the week What about the sevenpoint 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 Footnotes 1 This paper was first read as an Invited Address before the Eastern Psychological Association in Philadelphia on April 15 1955 Preparation of the paper was supported by the Harvard PsychoAcoustic Laboratory under Contract N5ori76 between Harvard University and the Office of Naval Research Us Navy Project NR142201 Report PNR174 Reproduction for any purpose ofthe Us Government is permitted References 1 BeebeCenter J G Rogers M S amp O39Connell D N Transmission of information about sucrose and saline solutions through the sense oftaste J Psychol 1955 39 157160 2 Bousfield W A amp Cohen B H The occurrence of clustering in the recall of randomly arranged words of different frequenciesofusage J gen Psychol 1955 52 8395 3 Carmichael L Hogan H P amp Walter A A An experimental study of the effect of language on the reproduction of visually perceived form J exp Psychol 1932 15 7386 4 Chapman D W Relative effects of determinate and indeterminate Aufgaben Amer J Psychol 1932 44 163174 5 Eriksen C W Multidimensional stimulus differences and accuracy of discrimination USAF WADC Tech Rep 1954 No 54165 6 Eriksen C W amp Hake H W Absolute judgments as a function of the stimulus range and the number of stimulus and response categories J exp Psychol 1955 49 323332 7 Garner W R An informational analysis of absolute judgments of loudness J exp Psychol 1953 46 373380 8 Hake H W amp Garner W R The effect of presenting various numbers of discrete steps on scale reading accuracy J exp Psychol 1951 42 358366 9 Halsey R M amp Chapanis A Chromaticityconfusion contours in a complex viewing situation J Opt Soc Amer 1954 44 442454


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