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Separating cognitive capacity from knowledge: a new hypothesis

Graeme S. Halford, Nelson Cowan and Glenda Andrews

TRENDS in Cognitive Sciences Vol.11 No.6 (2007)

We propose that working memory and reasoning share relatedcapacity limits. hese limits are !"anti#ed in terms of:

$i% the number of items that can be kept active inworking memory, and

$ii% the number of interrelationships between elementsthat can be kept active in reasoning.

 he latter de#nes the comple&ity of reasoning pro'lems and theprocessing loads they impose. (rincipled proced"res for meas"ring,controlling or limiting recoding and other strategies for red"cingmemory and processing loads have opened "p new researchopport"nities, and yielded orderly !"anti#cation of capacity limits in'oth memory and reasoning. We arg"e that 'oth types of limit might'e 'ased on the limited a'ility to form and preserve 'indings 'etweenelements in memory.

W)is limited to *+- ch"nks, and reasoning is limited to relations

'etween fo"r varia'les

$% We propose that the essential link 'etween W) and reasoning is inthe common re!"irement to bind elements to a coordinatesystem.

$/% W) and reasoning di0er in whether the 'inding is supplied with theinput $as in short1term serial recall% or has to 'e constructed bythe reasoner, as in syllogistic $incl"ding transitive% inference, wherepremise elements have to 'e mapped to slots in a mental model in

a way that is consistent with the premises.

$+% Coordinate systems in the W) are less likely to incl"de explicitrelational representations than those in reasoning. Use of anexplicit symbol that dierentiates dierent kinds of links is afeat"re that disting"ishes relations from associations.

$-% W) is limited to appro&imately four items that can 'e kept activewhereas representations in reasoning are limited to fourinterrelated variables

$2% Storage is modality speci#c, however, recent st"dies show that

ver'al and spatial tasks interfere with one another "nder somecirc"mstances.

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$3% The parietal lobes take part in an attention system thatintegrates information across modalities, and might correspondto the seat of attention, separate from frontal areas involved incontrolling attention. Although both areas are often activetogether in W tasks that involve the storage and manip"lation ofinformation, transcranial magnetic stim"lation $)S% to the frontallobes disrupts only the manipulation, whereas parietalstimulation disrupts storage as well.

(osner, ).4. and (eterson, S.5. $667% he attention system of the h"man 'rain.Ann". 8ev. Ne"rosci. +, /2-/

$9% he brain data seem to 'e compati'le with a central store thatreects the foc"s of attention "sed as a store ;/

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$=% We hypothesi>e that the W) limit reects capacity for attention,which determines the n"m'er of elements, whether items or ch"nks,that can 'e 'o"nd into a coordinate system. his hypothesis linksW)C directly to a theory of capacity limitations in reasoning,relational complexity !"#$ theory , considered ne&t, whichproposes that reasoning is limited 'y the n"m'er ofvaria'les or slotsthat can 'e related in a single representation. 4n 8C theory,processing load depends on the comple&ity of relations processed inany step of a task.

relational complexity (RC) theory:

Halford, G.S. et al. (1998) Procein! capacity defined "y relationalcomplexity: implication forcomparati#e, de#elopmental, andco!niti#e pycholo!y. $eha#. $rain Sci. %1, 8&'8'1

$6% Comple&ity metrics. Comple&ity can 'e de#ned 'y the n"m'er ofslots or ?arity@ of a relation that m"st 'e represented to perform aspeci#c cognitive process $for e&ample, a 'inary relation, s"ch as?larger than@ has two slots, one each for the larger and smallerentities%.

$7% %#onceptual chunking& involves recoding concepts into lesscomple& relations. Altho"gh ch"nking red"ces processing load,ch"nked varia'les cannot 'e accessed.

$% %'egmentation& entails 'reaking tasks into less comple&steps, which can 'e processed serially. Strategies and algorithms are

common ways of doing this.

There is common ground between W and reasoning:

$i% irst, 'oth are limited 'y the a'ility to map elements into coordinatesystems, which in t"rn depends on attention

$ii% Second, 'oth involve compressing material into ch"nks, mnemonic or$for reasoning% concept"al in nat"re. Concept"al ch"nks contain morerelational information than do mnemonic ch"nks 'eca"se the coordinatesystems in reasoning are e&plicit relations.

$iii% hird, the limitation is in the n"m'er of independent components,irrespective of their si>e.

$/% When a cognitive overload cannot 'e red"ced 'y concept"alch"nking or segmentation, it is likely to 'e handled 'y defa"lt to asimpler representation, "s"ally 'y ignoring one or more varia'les,leading to fragmentation of knowledge.

$+% W hen capacity is meas"red, it has 'een fo"nd to increase withage.

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• A promising hypothesis is that 'oth W) and reasoning re!"ire itemsor concepts to 'e the foc"s of attention conc"rrently. his wo"ldena'le them to 'e interassociated to form ch"nks or 'o"nd intocoordinate systems, incl"ding relational representations that ena'leinferences to 'e made.

•

(arietal regions seem to 'e most important for foc"s of attentionand storage f"nctions of W)• (refrontal regions seem to 'e more important for manip"lation

f"nctions in W) and reasoning. 4f manip"lation increases 8C, then )S $transcranial magnetic stim"lation% applied to prefrontal regionssho"ld 'e more disr"ptive as the 8C of a task increases.

• (refrontal regions are also activated in other reasoning and "idintelligence $Gf% tasks that re!"ire relational integration, incl"dingmodi#ed 8avens )atrices pro'lems ;+3,+9< and analogy pro'lems;+=