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Table 1. Difference between the addition operation without carry (Level 1) and with
carry (Level 2)
Level 1: no-carry (e.g. 24+34=58)
Level 2: carry (e.g. 13+28=41)
module
module
time declarative imaginal
procedual
time declarative imaginal
procedual
6.435
4+4=?
start-addition 6.435
3+8=?
start-addition
6.485
add-ones
6.485 11=10+?
add-ones
6.685
one=8
6.685
one=1
6.735
2+3=?
add-tens
6.735
1+2=?
add-tens
6.935
ten=5
6.935
ten=3
6.985
6.985 3+carry=?
add-carry
7.035
ans=58
7.035
7.085
7.085
ans=41
Table 1 shows the results of ACT-R simulation with respect to Level 1 (with-
out carry) and Level 2 (with carry). Comparing the processes, we can see that
the declarative memory is accessed in the case with carry, and the delay about
50 msec appears (step-11 in the ACT-R result). This is because a carry is caused
by the addition operation of “3” and “8”of the units digit, and the carry will be
operated with “3” of the sum of the tens digit, which is more complex than the
computation in Level 1.
5Con lu on
In this paper, we presented an approach of combining EEG/ERP analysis and
ACT-R simulation to understand deeply a two digit mental computation prob-
lem as a case study for investigating human computation mechanism. It was
confirmed that the retardation phenomenon of the reaction appears in the addi-
tion operation with carry, compared with the addition operation without carry.
And individual difference in performance was also discussed. The preliminary
results show the usefulness of our approach.
Our future work includes extending our approach to combine with fMRI since
EEG topographies have limitation in spatial resolution and need to combine with
fMRI data analysis for identifying the activated areas more accurately. Thus,
combining EEG/ERP, fMRI and ACT-R will provides an powerful approach to
help us to investigate the spatiotemporal feature and flow of HIPS, and its neural
structures and neurobiological processes related to the activated areas.
References
1. Anderson, J.R., Bothell, D., Byrne, M.D., Douglass, S., Lebiere, C., Qin, Y.: An
Intergrated Theory of the Mind. Psychological Review 111(4), 1036-1060 (2004)
2. Anderson, J.R.: How can the Human Mind Occur in the Physical Universe. Oxford
University Press, Oxford (2007)
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