- Email: [email protected]
Dimensional Complexity and Power Spectral Measures of the EEG during Functional versus Predicative Problem Solving
Brain and Cognition 44, 547–563 (2000) doi:10.1006/brcg.2000.1215, available online at http://www.idealibrary.com on
Dimensional Complexity and Power Spectral Measures of the EEG during Functional versus Predicative Problem Solving Matthias Mo¨lle,* Inge Schwank,† Lisa Marshall,* Anke Klo¨hn,* and Jan Born*,‡ *Clinical Neuroendocrinology, Medical University of Lu¨beck, Lu¨beck, Germany; †Institute for Cognitive Mathematics, University of Osnabru¨ck, Osnabru¨ck, Germany; and ‡Physiological Psychology, University of Bamberg, Bamberg, Germany Published online August 18, 2000 Electroencephalograms were recorded in 22 men while solving tasks of visualpattern completion and during mental relaxation. They were primed (by foregoing trials) to solve these tasks either in a predicative or functional mode of thinking. Predicative thinking required that in order to complete the pattern the subject had to get involved with the logic of the static structure of the pattern and therefore had to recognize the recurrence of certain features of the elements (e.g., shape, color, and size). Functional thinking required involvement in a dynamic reading of the logic of the pattern and therefore to search for operations and actions to be performed on the pattern elements (e.g., pushing, mirroring, and rotating). The EEG complexity during predicative thinking decreased in comparison to functional thinking and mental relaxation, with this reduction being most pronounced over the right parietal cortex. A reduction in dimensional complexity during functional thinking as compared to mental relaxation, which was concentrated over the left central cortex, although significant, was less clear. The reduced EEG complexity during predicative thought, dominant over the right hemisphere, could reflect increased competitive inhibition among respective cortical neuron assemblies in association with the visual analysis of static element features, converging upon those predicates relevant for the solution. 2000 Academic Press
INTRODUCTION
Today, as the material basis of human thinking, the cerebral cortex is essentially considered to house a large amount of memory associations. Almost Address correspondence and reprint requests to Matthias Mo¨lle, Klinische Forschergruppe, Haus 23a, Universita¨t Lu¨beck, Ratzeburger Allee 160, 23538 Lu¨beck, Germany. Fax: ⫹49 ⫹451 500 3640. E-mail: [email protected]. We thank Professor W. Lutzenberger for providing the software for nonlinear analysis of the EEG and A.K. Ju¨rß and A. Otterbein for technical assistance. Supported by a grant from the DFG to J.B. 547 0278-2626/00 $35.00 Copyright 2000 by Academic Press All rights of reproduction in any form reserved.
548
¨ LLE ET AL. MO
all abilities of the brain are assumed to be based on the simultaneous and successive activity of many different cortical networks (neuronal cell assemblies), which are considered as single processing units, i.e., as representational units of thoughts and ideas (Hebb, 1949; Elbert, Ray, Kowalik, Skinner, Graf, & Birbaumer, 1994; Pulvermu¨ller, 1996). However, abstract thinking not only consists of pure forming of associations but also of the integration and processing of information according to certain ‘‘logical’’ principles. Particularly, this ability to control the formation of associations of mental representations and imaginations along certain rules appears to distinguish human intelligence from the intelligence of nonhuman animals. But still not much is known about the concrete mechanisms regulating the flow of thoughts and ideas within cortical neuronal networks active during human information processing. By means of the electroencephalographic activity recorded from the scalp this study aimed to differentiate two modes of thinking: predicative versus functional thinking (Schwank, 1986, 1993). The concept of predicative/functional thinking originated in cognitive mathematics. Qualitative experimental studies in subjects of different ages, sexes, intellectual levels, and cultures indicated recurrent basic features in the way ideas were arranged during concept formation on mathematical problems (for summary, Xu, 1994; Schwank, 1995). Two fundamentally different ways of logical orientation were extracted: one taking into account manifold features and relationships, resulting in a static structural view on things, and another taking into account various efficacious actions and construction procedures resulting in a dynamic view on things. Analogous to concepts in mathematical logic, the first is called predicative thinking, the latter functional thinking. In some cases no inner mathematical constraints determine that the chance of success is unbalanced: both predicative and functional thinking are doing well. But in other cases for successful problem solving one should behave either in a functional or in a predicative way. Although the terms predicative and functional thinking were originally used to indicate a type of thinking that occurs when human beings think about mathematical content, one would not expect that the cognitive mechanisms involved in this type of thinking are used exclusively in the case of a mathematical content. In fact the idea of a more static or a more dynamic view on things, leading to different mathematical problem solutions, is a very fundamental one. A prototype for the functional mode of thinking is expressed in the concept of a ‘‘switch,’’ which Bateson presented in his philosophical analysis (Bateson, 1980, pp. 120–121): We do not notice that the concept ‘‘switch’’ is of quite a different order from the concepts ‘‘stone,’’ ‘‘table,’’ and the like. Closer examination shows that the switch, considered as a part of an electric circuit, does not exist when it is in the on position. From point of view of the circuit, it is not different from the conducting wire which leads to it and the wire which leads away from it. It is merely ‘‘more conductor.’’ Conversely, but similarly, when the switch is off, it does not exist form the point
EEG DURING MODES OF THINKING
549
of view of the circuit. It is nothing, a gap between two conductors which, themselves exist only as conductors when the switch is on. In other words, the switch is not except at the moments of its change of setting, and the concept ‘‘switch’’ has thus a special relation to time. It is related to the notion ‘‘change’’ rather than to the notion ‘‘object.’’
It seems that in the general scientific discourse functional thinking is less appreciated and in any case less explored. Reasons could be that it is easier to use static experimental material as well as the assumed close relation of thinking to language. Nevertheless, functional thinking appears to have a profound impact on progress in mathematics. For example van der Waerden (1954) discussing the style of creating a special mathematical curve by Pascal showed that this one had an absolutely clear concept in terms of motoric actions of his new idea before he invented its name. Van der Waerden claims that the motoric idea is essential in mathematical thinking: If you have forgotten it, you do not have the concept of the curve any longer, even if you know what it looks like—or if you just know the (artificial) name/wordmark. There are further hints in this direction by Einstein (Hadamard, 1954). While various studies showed that the discrimination between functional versus predicative problem solving can be successfully transferred from mathematical thinking to more real-life problem solving (e.g., to decision making in business reengineering; Cohors-Fresenborg, 1996), it is presently unknown whether these modes of thinking can be distinguished also on a neurophysiological level. The present study asked whether the different ‘‘logical orientations’’ involved in these modes express themselves in different types of EEG activity. Several studies proved that EEG measures can provide a useful tool to discriminate complex processes of thought (Petsche, Lacroix, Lindner, Rappelsberg, & Schmidt-Henrich, 1992; Hollander, Petsche, Dimitrov, Filz, & Wenger, 1997). A measure of particular sensitivity in this context appears to be the dimensional complexity of the EEG. In foregoing studies, we showed that EEG activity during creative thinking is associated with a generally enhanced dimensional complexity, as compared to convergent thinking (Mo¨lle, Marshall, Pietrowsky, Lutzenberger, Fehm, & Born, 1996; Mo¨lle, Marshall, Wolf, Fehm, & Born, 1998). Also, mental imagery of a moving object (pendulum) resulted in increased prefrontal dimensional complexity of the EEG in comparison to the actual perception of the same object (Schupp, Lutzenberger, Birbaumer, Miltner, & Braun, 1994) and the EEG over frontal cortical regions during emotional imagery was accompanied by higher dimensional complexity than during mental arithmetic tasks (Birbaumer, Lutzenberger, Elbert, Flor, & Rockstroh, 1993). All these results can be explained by the concept of dimensional complexity representing a measure which estimates the number of simultaneously activated oscillating neuron assemblies within the cortex (Lutzenberger, Preissl, & Pulvermu¨ller, 1995). Modes of focused thinking, i.e., mental processing which is directed and converging toward a distinct aim, result in
550
¨ LLE ET AL. MO
an inhibition of neuronal networks and thus in a smaller number of competitive neuronal cell assemblies. On the other hand, modes of divergent thinking, i.e., cortical processing which is characterized by a loosening of rigid attentional sets, show an enhanced number of simultaneously activated oscillating neuron assemblies. Considering thinking as a form of covert attention to internal ideas (Posner, 1980), a parallel distinction in the EEG’s dimensional complexity has been demonstrated between focusing and dividing attention (Mo¨lle, Marshall, Pietrowsky, Lutzenberger, Fehm, & Born, 1995; Mo¨lle, Albrecht, Marshall, Fehm, & Born, 1997). In this study the EEG’s dimensional complexity and spectral power within traditional frequency bands were measured while subjects solved tasks of visual pattern completion, i.e., tasks of convergent thinking, using different modes of ‘‘logical orientation.’’ Subjects were primed by instructions (on several foregoing tasks, where the mode of logical analysis and the solution process were demonstrated) to solve a given task on one condition in a predicative way and on another condition in a functional way. It was hypothesized that these two modes of thinking would also show differences in their ongoing electrocortical activity, especially with regard to their topographical distribution. Multiple evidence exists pointing to preferential execution of visuo-spatial analysis, as performed during the predicative thinking, in the right as compared to the left hemisphere (Hellige, 1990; Springer & Deutsch, 1993). In a recent study, Goebel, Linden, Sireteanu, Lanfermann, Zanella, Singer, and Goebel (1997), using functional magnetic resonance imaging (fMRI), observed distinctly greater activation in the right frontal and parietal cortex than in respective left cortical areas during an active visual search. In our terms this is a predicative visual search task because it requires the conjunction of features to find a target (e.g., a red vertical bar among red horizontal and green vertical bars). Based on these similarities, for the present experiment we expected a stronger right than left hemispheric activation during the predicative mode of thinking. In contrast, the operations and actions to be performed on pattern elements with functional thinking may be linked more closely to a motor type of processing. Considering evidence from clinical studies in patients with ideomotor apraxia (Heilman & Valenstein, 1993) and also from recent PET studies (Decety, Grezes, Costes, Perani, Jeannerod, Procyk, Grassi, & Fazio, 1997; Grafton, Fagg, & Arbib, 1998) indicating that the organization of action preferentially involves left and more anterior cortical areas, it was supposed that in comparison with predicative thinking the functional mode of thinking is associated with increased activation in left anterior cortical areas. However, since the processing of visual task patterns also relies always on more elementary visuospatial operations, functional problem solving (like predicative thinking) was expected to induce also signs of right-hemispheric activation. An additional aim of the study was to compare differences in EEG activity during primed functional versus predicative thinking with differences in indi-
EEG DURING MODES OF THINKING
551
vidual habits (‘‘style’’) of thinking. For this purpose, prior to the conditions of primed functional and predicative thinking, subjects were required to spontaneously solve tasks of pattern completion (i.e., without prior priming). Here, it was expected that depending on whether a subject’s cognitive style tended to be more functional or predicative, interindividual differences would occur comparable with those after primed functional versus predicative thinking. METHODS AND MATERIALS
Subjects and EEG Recordings Twenty-five, right-handed male subjects participated in the study. EEG data from three subjects were discarded because the subjective ratings of task difficulty differed greatly. Mean age of the remaining 22 subjects was 26.6 years (SD ⫽ 3.3; range: 21 to 37). The studies were approved by the Committee on Research Involving Human Subjects of the University of Lu¨beck. All subjects gave written informed consent before participation. EEGs were recorded from Fp1, Fp2, F3, F4, F7, F8, T3, T4, T5, T6, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz electrodes (international 10–20 system). Linked electrodes attached to the mastoids served as reference. In addition, four electrodes were used to record vertical and horizontal eye movements. A single ground electrode was attached at Fpz. The EEG was recorded using a SynAmps EEG amplifier (NeuroScan Inc.). Sample frequency was 500 Hz with 16-bit A-to-D precision. The time constant used was 1 s. The low-pass filter was set to 70 Hz.
Stimuli and Procedure In each of three experimental blocks subjects were presented with four tasks of pattern completion (see Fig. 1; see Schwank, 1997 for further examples). In the first block subjects were to find the logic in the given patterns on their own, i.e., they were free to use their preferred cognitive style (spontaneous solution). In two further blocks the subjects were primed on functional (respectively predicative) thinking: in three tasks the experimenter demonstrated an ideal functional (respectively predicative) logical analysis of the pattern for constructing the solution figure. The subjects were asked to solve the fourth task in the particular demonstrated style. The subject sample was split, so that after finishing the spontaneous solution block one half received first the functional instructions and then the predicative ones, in the other half order was reversed. A functional treatment of the task in Fig. 1 would rely on functional tools, i.e., inventing a dynamic process which produces the last element in a row or column. The embedded dynamic logic to be adopted is that in each row the circle moves around, and in each column the point moves around. The object around which the movement takes place is invariant. A predicative treatment of the task in Fig. 1 would rely on predicative tools, i.e., structuring the pattern, looking for salient features, and inventing general laws of relationship among shapes and forms and their locations. The embedded static logic to be adopted is that each figure consists of three objects: a star, a point, and a circle. The star is the same in each figure. In each row the point is at the same place (left, top, right). In each column the circle is at the same place (top, right, left). It is striking that in the functional case for logical orientation typically less precise word labeling is used. Instead, when explaining their solution subjects tend to give some general, deictic statements combined with gesture, e.g., ‘‘This is moving around here.’’ For this reason videorecording is indispensable for evaluating a subject’s argumentation. In contrast, in the
552
¨ LLE ET AL. MO
FIG. 1. Example of a pattern-completion task with embedded predicative/functional logic. In our experiment, subjects were to find the missing element. A typical functional solution for this task would be: ‘‘The circle moves clockwise from tip to tip when I go from left to right in each row. Therefore, at the end it should arrive at the left tip of the middle figure. When I go from top to bottom in each column the dot also moves clockwise from tip to tip. Therefore, at the end it should arrive at the top tip of the middle figure.’’ A typical predicative solution for this task would be: ‘‘The middle figure is always the same. In each column there are three circles. In the left column they are always on the top tip of the middle figure, in the middle column always on the right tip, and the two circles in the right column are on the left tip. Therefore, I would draw the circle on the left tip. In each row there are three dots. The dots are always on the right tip in the top row, in the middle row they are always on the left tip and the two dots of the bottom row are on the top tip. Therefore, I would draw the dot on the top tip.’’
predicative case word labels play a fundamental role. They officiate as landmarks around which the static mental model covering the features, relationships, and abstract structures of the pattern is built. The tasks were presented to the subjects on a display located 100 cm in front of the subject. The pictures used had a width and a height of 7 cm (visual angle ⫽ 4°). For solving the four tasks of the first block (spontaneous solution) and the fourth tasks of the second and third blocks (functional and predicative solution) subjects were given a maximum of 2 min. While the subjects were looking at and solving the tasks they were not allowed to speak or to move and were to avoid large eye movements. After having solved the task subjects had to draw their solution (or partial solution) and to explain why their solution figure fits the pattern. Subsequently they were to rate the difficulty of the task on a scale from ⫺3 to ⫹3.
EEG DURING MODES OF THINKING
553
The EEG was recorded while subjects were solving the fourth task of each block (spontaneous solution, functional solution, and predicative solution). Before the first block, a resting EEG was recorded during which subjects performed for 1 min a task of mental relaxation (‘‘Imagine you are lying on the beach, the sun is shining, the waves are rolling softly!’’). The order of conditions within the second and third blocks was balanced across subjects. The complete experimental session was recorded on video tape.
Analysis of Argumentation of Task Solving The subjects’ logical argumentations, why their constructed figures fit well in the patterns, were analyzed using the videorecordings. Subjects used mainly the primed style. But, especially when subjects under spontaneous conditions strongly preferred one of the two styles, they tended to use also some elements of this style even if it was not primed. Therefore, the videotaped argumentations were scored according to standardized criteria. Each task was scored up to 3 points for elements of functional solution argumentation and up to 3 points for elements of predicative solution argumentation, using prototypic standard argumentation as reference. The most important criterion for a predicative mode of task solving is the prevalent use of different nouns and adjectives to distinguish the different parts of the figure. In contrast there are only few verbs occurring which are just used to describe the static positions of parts of the figure (e.g., ‘‘In the upper left corner of the big triangle there is a small black point’’). Indicators for a functional mode of task solving are a much poorer usage of language, associated with an infrequent use of nouns and an even less frequent use of adjectives. Instead of using a lot of different words the argumentation is a more or less deicitic behavior (e.g., ‘‘This is turning around there’’). But the variety of verbs used to express the dynamics seen in the pattern is much richer. Each task argumentation was scored independently by two experienced raters. The agreement between raters was greater than r ⫽ 0.71. In cases of discrepant judgements the videotaped task was reevaluated by both raters together. For further analysis a difference score for the subject’s argumentations was determined: predicative solution argumentation minus functional solution argumentation.
EEG Analysis For each recorded task a 20.48-s EEG period free of large eye movements or other artifacts was selected from the period of problem solving. The 20.48-s epochs for analysis were taken starting about 10 s after the beginning of the recorded task. Smaller ocular artifacts were corrected with the regression method using the vertical and horizontal EOG (Gratton, Coles, & Donchin, 1983). For calculating the dimensional complexity the EEG signals were digitally filtered with a low-pass filter of 35 Hz (-3 dB) and a very steep roll-off rate (-90 dB at 45 Hz) and afterward down-sampled to 100 Hz. Low-pass filtering at 35 Hz was expected to improve the signalto-noise ratio and to minimize artifacts by EMG activity. Dimensional complexity (estimated correlation dimension) was calculated by combining the singular value decomposition technique with the ‘‘average-pointwise’’ dimension procedure (Lutzenberger et al., 1995; Pritchard & Duke, 1995). The first step of this program was based on the autocovariance function with time lags ranging from 0 to 31 points. A symmetrical 32 ⫻ 32 matrix was constructed with the covariances of the EEG trace as elements. On this matrix the singular value decomposition was performed and 32 components were generated. Now a selection was made to separate signal from presumed noise. Dependent on the sizes of the eigenvalues only a subset of eigenvectors was used to reconstruct the state-space. The extracted vectors and the original time series were used in a folding operation to calculate a new and separate time series for each extracted vector. In the next step separate calculations of the dimensionality were performed for 32 equidistant points, using the method of ‘‘pointwise dimension’’ as proposed
554
¨ LLE ET AL. MO
by Farmer, Ott, and York (1983). Subsequently, the median was calculated, representing the value of dimensional complexity of the given EEG trace, so that one value of dimension was obtained for each EEG channel and epoch. Using a Fast Fourier Transformation (FFT) the 20.48-s epochs of EEG activity (not digitally filtered and not down-sampled) were transformed into the log amplitudes of the power spectrum, and values for the delta (0.5–4.4 Hz), theta (4.4–8.1 Hz), alpha (8.1–12.2 Hz), and beta (12.2–24.9 Hz) bands were obtained. The power spectrum was calculated by averaging the Fast Fourier Transforms of nine overlapping segments of 2048 points each. To reduce errors induced by edge effects the signal was tapered toward zero at the extremes of each data segment with a raised cosine window.
Statistical Evaluation Values of EEG dimensional complexity and power spectral analysis were subjected to an ANOVA with repeated-measures factors for Thinking (functional thinking, predicative thinking, and mental relaxation) and Topography (Fp1, Fp2, F3, F4, F7, F8, T3, T4, T5, T6, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz). Additional ANOVA were used to compare each of the two modes of thinking with mental relaxation and with each other. The direct comparison of the two modes of thinking included the subjective rating of task difficulty as covariate. To evaluate differences between subjects with a cognitive style of predominant functional versus predicative task solving, for each individual the average difference score for the argumentation of task solving was calculated across the first four tasks where subjects spontaneously solved the problems. The median of these average scores was taken to split the group into two equally sized groups, one with the above-median difference score (predominant predicative types) and one with the below-median difference score (predominant functional types). An ANOVA was run on the EEGs dimensional complexity during the fourth task of the first block (spontaneous solution) with repeated measures for Topography (F3, F4, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz) and a Grouping factor for the functional and predicative Types.1
RESULTS
Primed Functional versus Predicative Thinking Argumentation of task solving and rated task difficulty. The argumentation of task solving was scored with regard to the occurrence of predicative and functional explanatory elements, with the final difference score (predicative minus functional argumentation) between ⫹3 and ⫺3 indicating a prevalent predicative or functional solution, respectively. The mean score for argumentation of task solving after functional priming was ⫺.55 ⫾ .44 and after predicative priming ⫹2.50 ⫾ 0.24 (p ⬍ .001, Wilcoxon). Although this difference was highly significant, the absolute value for functional priming was distinctly lower than for predicative priming, indicating that the induction of functional thinking was less successful. Task difficulty was rated on a scale between ⫺3 (very easy) and ⫹3 (very difficult) and did not differ significantly between the primed functional task (⫹.18 ⫾ .22) and the primed predicative task (⫺.23 ⫾ .25, p ⫽ .14, Wilcoxon). 1 The most outer electrodes Fp1, Fp2, F7, F8, T3, T4, T5, and T6 were discarded in this analysis because of their great variability.
EEG DURING MODES OF THINKING
555
FIG. 2. Mean (⫾ SEM ) dimensional complexity of the EEG during functional thinking (empty bars), predicative thinking (black bars), and mental relaxation (gray bars). Asterisks indicate significant differences between any two of these modes of cortical processing (*** p ⬍ .001; **p ⬍ .01; *p ⬍ .05).
556
¨ LLE ET AL. MO
Dimensional complexity. Figure 2 summarizes the EEGs dimensional complexity during the two modes of primed task solving and mental relaxation. Global ANOVA indicated differences depending on the recording site [Thinking ⫻ Topography: F(36, 756) ⫽ 2.24; p ⬍ .05], which were to be specified in pairwise comparisons. Compared to mental relaxation, dimensional complexity during predicative task solving was lower with this effect being most pronounced in recordings from midline electrodes and right central and parietal electrode sites [Thinking ⫻ Topography: F(18, 378) ⫽ 3.09; p ⬍ .01; for contrasts Cz: p ⬍ .001, Fz, C4, Pz, P4: p ⬍ .01 and C3: p ⬍ .05]. The comparison of dimensional complexity during functional task solving with mental relaxation revealed also a Thinking x Topography interaction [F(18, 378) ⫽ 2.24; p ⬍ .05], indicating that dimensional complexity during functional task solving was diminished at C3 and Cz ( p ⬍ .05) and enhanced at O1 (p ⬍ .05) as compared with mental relaxation. Comparison of the EEG during both modes of problem solving indicated a lower dimensional complexity during predicative than during functional thinking [F(1, 20) ⫽ 5.16; p ⬍ .05]. In contrast, calculated at each electrode this effect revealed significance for recordings over parietal and right occipital cortical areas (P3, Pz, P4, O2; p ⬍ .01) as well as over right frontal and central cortical areas (F4, Cz, C4; p ⬍ .05). The covariate of rated task difficulty introduced in these analyses did not indicate a dependence of EEG dimensionality on variations in experienced difficulty of problem solving (β ⫽ 0.02; p ⫽ 0.83). The covariate of task difficulty also remained nonsignificant in analyses on single electrode sites. Power spectral analysis. In all frequency bands spectral power of the EEG during both modes of primed thinking differed significantly from that during mental relaxation. Power within the alpha and beta frequency bands was lower during thinking than during mental relaxation [Thinking ⫻ Topography: F(18, 378) ⫽ 5.98; p ⬍ .001 for the alpha band and F(18, 378) ⫽ 3.35; p ⬍ .01 for the beta band; see Fig. 3 for pairwise comparisons at single electrode sites]. Theta power during mental relaxation was slightly lower at frontal and occipital recording sites but slightly higher at central and parietal sites than during thinking [Thinking ⫻ Topography: F(18, 378) ⫽ 2.23; p ⬍ .05]. Delta power was increased during thinking as compared to mental relaxation [F(2, 42) ⫽ 6.40; p ⬍ .01]. However, ANOVA with the factors mode of Thinking (functional versus predicative) and Topography did not reveal any difference between both types of problem solving for any of the four frequency bands. Nevertheless, analyses at single electrodes indicated higher alpha and beta power during functional than during predicative thinking with this effect dominating at occipital regions (O1, O2; p ⬍ .01). Cognitive Style during Spontaneous Problem Solving Across the four tasks of the first block (spontaneous solution) the median difference score of task argumentation was ⫹0.875 ⫾ 0.25 (range: ⫺1.5 to
FIG. 3. Mean (⫾ SEM ) log power (in arbitrary units) during functional thinking (empty bars), predicative thinking (black bars), and mental relaxation (gray bars) within the delta, theta, alpha, and beta frequency bands. Asterisks indicate significant differences between any two of these modes of cortical processing (***p ⬍ .001; **p ⬍ .01; *p ⬍ .05). Results from analyses at single-electrode locations are shown only when the ANOVA indicated a significant ( p ⬍ .05) effect of Thinking or a Thinking ⫻ Topography interaction in pairwise comparisons. (Thus, significant differences in alpha and beta power between predicative and functional thinking revealed in separate analyses at O1 and O2 were not indicated.)
558
¨ LLE ET AL. MO
FIG. 4. Dimensional complexity of the EEG during spontaneous problem solving on the pattern-completion tasks. Black circles indicate dimension values for the group of predominantly functional cognitive style. Empty rectangles indicate dimension values for the group of predominantly predicative cognitive style. Values from the two lateral and the midline electrode sites were averaged and termed correspondingly ‘‘frontal,’’ ‘‘central,’’ and ‘‘parietal’’; for ‘‘occipital’’ O1 and O2 were averaged.
2.5), indicating that subjects overall tended toward predicative problem solving. The median was used to split the group into two subgroups with average difference scores of task argumentation of ⫹1.75 ⫾ 0.11 (range: 1.0 to 2.5) for predominant predicative types and of ⫺0.14 ⫾ 0.17 (range: ⫺1.5 to 0.75) for predominant functional types. Rated task difficulty for the fourth task of the first block (used for EEG analysis) averaged ⫹0.32 ⫾ 0.20 (range: ⫺2 to 2) and did not differ significantly between both groups (⫹0.36 ⫾ 0.36 versus ⫹0.27 ⫾ 0.20, p ⫽ 0.83, t test). The analysis of the EEGs dimensional complexity during spontaneous task solving revealed a significant Topography x Group interaction effect [F(10, 200) ⫽ 2.99; p ⬍ .01; Fig. 4). The predominant functional types showed a reduced EEG complexity at frontal and central recordings and an increased EEG complexity at parietal and occipital recordings in comparison to the group of predominant predicative types. DISCUSSION
This study aimed to differentiate two fundamentally different strategies of thinking, i.e., predicative versus functional thinking by means of the analysis of ongoing EEG activity. Both modes of thinking were examined while subjects performed the same type of visual-pattern completion tasks. Compared with mental relaxation both modes of thinking were accompanied by a reduced dimensional complexity of the EEG, which for predicative thinking was more pronounced over the right than the left hemisphere. Reductions
EEG DURING MODES OF THINKING
559
in the EEG’s dimensional complexity during functional thinking were found in comparison with mental relaxation over the left and midcentral cortex. Also, both modes of thinking differed in that EEG dimensionality was generally lower during predicative than functional thinking. The effect of predicative thinking on EEG dimensionality being more distinct over the midline and right hemisphere than over left cortical areas agrees with the view that visuo-spatial analysis is predominantly performed in right cortical areas. Topographical analyses with positron emission tomography (PET) have revealed consistent evidence for greater activity in the right than the left hemisphere during different types of tasks involving basic visuo-spatial analysis such as the analysis of forms, shapes, and colors or of cubes (McIntosh, Grady, Ungerleider, Haxby, Rapoport, & Horwitz, 1994; Wendt & Risberg, 1994), although the left hemisphere is also involved, particularly in more complex tasks (Nikolaev, 1995). As in the present study, effects of visuo-spatial analysis in those previous studies often concentrated over more posterior, i.e., parietal cortical areas (Wendt & Risberg, 1994; Goebel et al., 1997). The latter authors tested cortical activity by means of fMRI during a visual search task showing great similarities to the present task of primed predicative thinking in that it required identifying a target pattern by the active conjunction of static features defined by shape, color, spatial orientation, and so on. On this task a stronger activation was found in the superior parietal cortex (and the frontal eye field) in the right than in the left hemisphere. On this background, the distinct reduction in the EEG’s dimensional complexity during predicative thought processes could be considered a reflection of active visuo-spatial attentive operations associated with conjugating the different features of the pattern elements. Given that a reduced dimensional EEG complexity indicates a diminished number of simultaneously activated cortical neuron assemblies (Lutzenberger et al., 1995) these attentive operations appear to manifest themselves in a relatively reduced number of competitively oscillating assemblies. We would conclude that the process of predicative thinking is based on an active inhibition of irrelevant cortical networks in favor of an overall reduced number of active networks essential for task solving. Thus, increased competitive inhibition among neuron assemblies of respective cortical areas may increase the signalto-noise ratio of processing. This view agrees with previous studies where reduced EEG dimensional complexity was found, especially during modes of focused (selective) attention and focused (convergent) thinking. Since these modes are directed toward finding eventually the only one correct solution, predicative as well as functional processes of thought on pattern-completion tasks likewise represent modes of convergent focused thinking which manifest themselves in increased inhibitory control over network activity and, consequently, reduced EEG dimensionality within specialized cortical areas. The hypothesis that functional thinking is associated with enhanced activity over the left and more anterior cortex was not confirmed that clearly.
560
¨ LLE ET AL. MO
This view was derived from the fact that functional thinking requires motorlike operations and actions, such as pushing, turning, and mirroring elements of the pattern, the planning of which is assumed to involve left-hemispheric functions. In fact, a lower dimensional complexity of the EEG was found during functional thinking than during mental relaxation over the left-central cortex, but this effect was much weaker than the strong reduction of the EEG dimension during predicative thinking over the right hemisphere. There could be several reasons for this. First, the analysis of the argumentation of task solving showed that the priming of the functional thinking mode was not as successful as the priming of the predicative thinking mode. After functional priming, subjects still verbalized some ‘‘predicative’’ arguments when explaining their task solution. Hence, the EEG during the primed functional thinking may have reflected a significant contribution of predicative thought processes in addition to the predominant functional thought processes. However, this view is somewhat challenged by the fact that at right central and parietal electrodes where predicative thinking induced a distinct reduction in EEG dimensionality (as compared with mental relaxation) functional thinking remained without effect. This lack of change at right centro-parietal electrode locations is even more difficult to integrate when it is assumed that some of the elementary processes of visuo-spatial feature extraction performed on the pattern are similar for both modes of thought. A second and related reason for the less distinct effect of functional thinking on the EEG’s dimensional complexity is revealed by analysis of the argumentation of task solving on the first four tasks (where subjects were not primed): most subjects spontaneously preferred the predicative strategy, i.e., the majority of our subjects displayed spontaneously a more or less pronounced predicative style of thinking. Being less familiar with the functional mode of thinking, subjects being forced to this mode of problem solving may have spent more effort in ‘‘nonspecific’’ search operations not limited to left-hemispheric function. On the other hand, experienced task difficulty did not differ for both modes of primed thinking; also, classic EEG indicators of arousal and attention such as power within the alpha and theta frequency bands did not indicate differences related to nonspecific effects of mental effort on both modes of thinking. Alternatively, the less distinct effect of primed functional thinking might reflect an inherent ‘‘divergent’’ feature of this mode of thinking. Given that the direct comparison with the mode of predicative thinking revealed primarily a generally enhanced dimensional EEG complexity with little topographical specialization, the distinguishing characteristic of this mode of thought may be a less focused nature involving a greater number of competitively oscillating neuron assemblies distributed over extended cortical areas. Thus, it could be argued that compared to predicative thinking functional thinking requires a greater extent of imagery, i.e., imagining movements and dynamic changes of pattern elements. In previous studies operations of imagery have been found to be accompanied with in-
EEG DURING MODES OF THINKING
561
creased dimensionality in the EEG. However, although plausible, this view needs to be validated in further trials employing subjects who have a lower predisposition to use the predicative style of thinking than those of the present sample. Interestingly, on the tasks of spontaneous problem solving, predominant functional types displayed reduced EEG dimensionality over anterior cortical sites, whereas predominant predicative types displayed a posterior parietal reduction in EEG dimensionality. While this pattern is consistent with a ‘‘motor-oriented’’ style of thinking in the predominant functional types, it is also noteworthy that both groups of cognitive style were not differentiated by any hemispheric lateralization in EEG activity. This could indicate that habitual processes of thought, in contrast to those enforced by priming, are more evenly distributed across both hemispheres (Hellige, 1990). Results of power spectral analysis of the EEG were complementary to results from nonlinear analysis. As has already been found in previous studies a reduced dimensional complexity appeared to be associated with enhanced activity in lower frequency bands (delta and theta) and a concurrently decreased activity in higher frequency bands (alpha and beta). Thus, the decrease in right central and parietal EEG dimensionality during predicative thinking was accompanied by reduced activity in the alpha and beta frequency bands and increased activity in the delta band over the same cortical areas. In this context, the measure of dimensional complexity appears to condense power spectral changes occurring simultaneously in different frequency bands. An exception to this rule was the EEG activity over the occipital cortex, where the difference between functional and predicative thought appeared to be stronger for alpha and beta spectral power than for the measure of dimensionality. According to a concept proposed by Klimesch (1995), increased occipital alpha activity could point to a more elaborate memory-based encoding of visual features during functional thinking. However, this view is tentative and has to be further investigated. Aside from this issue, it remains to be emphasized that the two thinking modes did not differ in any frequency band as clearly as in the dimensional complexity. This confirms the sensitivity of dimensional complexity for recognizing EEG changes during different modes of information processing. REFERENCES Bateson, G. (1980). Mind and nature—A necessary unity. Toronto: Bantam Books. Birbaumer, N., Lutzenberger, W., Elbert, T., Flor, H., & Rockstroh, B. (1993). Imagery and ¨ hman (Eds.), The structure of emotion. Toronto: brain processes. In N. Birbaumer & A. O Hogrefe & Huber. Pp. 122–138. Cohors-Fresenborg, E. (1996). Individual differences in cognitive structures and the effect on business reengineering. In J. Georgas, M. Manthouli, E. Besevegis, & A. Kokkevi (Eds.), Contemporary psychology in Europe—Theory, research, and applications. Go¨ttingen: Hogrefe & Huber. Pp. 153–160.
562
¨ LLE ET AL. MO
Decety, J., Grezes, J., Costes, N., Perani, D., Jeannerod, M., Procyk, E., Grassi, F., & Fazio, F. (1997). Brain activity during observation of actions: Influence of action content and subject’s strategy. Brain, 120, 1763–1777. Elbert, T., Ray, W. J., Kowalik, Z. J., Skinner, J. E., Graf, K. E., & Birbaumer, N. (1994). Chaos and physiology: Deterministic chaos in excitable cell assemblies. Physiological Review, 74, 1–47. Farmer, J. D., Ott, E., & York, J. A. (1983). Dimension of chaotic attractors. Physica D, 7, 153–180. Goebel, C., Linden, D. E. J., Sireteanu, R., Lanfermann, H., Zanella, F. E., Singer, W., & Goebel, R. (1997). Different attention processes in visual search tasks investigated with functional Magnetic Resonance Imaging. NeuroImage, 5, S81. Grafton, S. T., Fagg, A. H., & Arbib, M. A. (1998). Dorsal premotor cortex and conditional movement selection: A PET functional mapping study. Journal of Neurophysiology, 79, 1092–1097. Gratton, G., Coles, M. G. H., & Donchin, E. (1983). A new method for off-line removal of ocular artifact. Electroencephalography and Clinical Neurophysiology, 55, 468–484. Hadamard, J. (1954). The psychology of invention in the mathematical field. New York: Dover. Hebb, D. O. (1949). The organization of behavior: A neuropsychological theory. New York: Wiley. Heilman, K. M., & Valenstein, E. (1993). Clinical neuropsychology. New York: Oxford Univ. Press. Third ed. Hellige, J. B. (1990). Hemispheric asymmetry. Annual Review of Psychology, 41, 55–80. Hollander, I., Petsche, H., Dimitrov, L. I., Filz, O., & Wenger, E. (1997). The reflection of cognitive tasks in EEG and MRI and a method of its visualization. Brain Topography, 9, 177–189. Klimesch, W. (1995). Memory processes described as brain oscillations in the EEG-alpha and theta bands. Psychology.95.6.06.memory-brain.1.klimesch. Lutzenberger, W., Preissl, H., & Pulvermu¨ller, F. (1995). Fractal dimension of electroencephalographic time series and underlying brain processes. Biological Cybernetics, 73, 477– 482. McIntosh, A. R., Grady, C. L., Ungerleider, L. G., Haxby, J. V., Rapoport, S. I., & Horwitz, B. (1994). Network analysis of cortical visual pathways mapped with PET. Journal of Neuroscience, 14, 655–666. Mo¨lle, M., Marshall, L., Pietrowsky, R., Lutzenberger, W., Fehm, H. L., & Born, J. (1995). Dimensional complexity of the EEG indicates a right fronto-cortical locus of attentional control. Journal of Psychophysiology, 9, 45–55. Mo¨lle, M., Marshall, L., Pietrowsky, R., Lutzenberger, W., Fehm, H.L., & Born, J. (1996). Enhanced dynamic complexity in the human EEG during creative thinking. Neuroscience Letter, 208, 1–4. Mo¨lle, M., Albrecht, C., Marshall, L., Fehm, H.L., & Born, J. (1997). ACTH widens the focus of attention in humans: A nonlinear EEG analysis. Psychosomatic Medicine, 59, 497– 502. Mo¨lle, M., Marshall, L., Wolf, B., Fehm, H. L., & Born, J. (1999). EEG complexity and performance measures of creative thinking. Psychophysiology, 36, 1–10. Nikolaev, A.R. (1995). Investigation of the stage of the mental rotation of complex figures with the intracortical interaction mapping technique. Neuroscience Behavioral Physiology, 25, 228–233. Petsche, H., Lacroix, D., Lindner, K., Rappelsberger, P., & Schmidt-Henrich, E. (1992). Think-
EEG DURING MODES OF THINKING
563
ing with images or thinking with language: A pilot EEG probability mapping study. International Journal of Psychophysiology, 12, 31–39. Posner, M. I. (1980). Orienting of attention. Quarterly Journal of Experimental Psychology, 32, 3–25. Pritchard, W. S., & Duke, D. W. (1995). Measuring ‘‘chaos’’ in the brain: A tutorial review of EEG dimension estimation. Brain and Cognition, 27, 353–397. Pulvermu¨ller, F. (1996). Hebb’s concept of cell assemblies and the psychophysiology of word processing. Psychophysiology, 33, 317–333. Schupp, H. T., Lutzenberger, W., Birbaumer, N., Miltner, W., & Braun, C. (1994). Neurophysiological differences between perception and imagery. Cognitive Brain Research, 2, 77– 86. Schwank, I. (1986). Cognitive structures of algorithmic thinking. In Proceedings of the 10th International Conference for the Psychology of Mathematics Education. London: University of London. Pp. 195–200. Schwank, I. (1993). On the analysis of cognitive structures in algorithmic thinking. Journal of Mathematical Behavior, 12, 209–231. Schwank, I. (1995). The role of microworlds for constructing mathematical concepts. In M. Behara, R. Fritsch & R. Lintz (Eds.), Symposia Gaussiana, Conference A: Mathematics and theoretical physics. Berlin: Walter de Gruyter. Pp. 101–120. Schwank, I. (1997). The assumption of predicative versus functional cognitive structures. Journal for Integrated Study of Artificial Intelligence, Cognitive Science and Applied Epistemology, 14, 213–224. Springer, S. P., & Deutsch, G. (1993). Left brain, right brain. New York: Freeman. van der Waerden, B. L. (1954). Denken ohne Sprache. In G. Re´ve´sz (Ed.), Thinking and speaking. Amsterdam: North–Holland. Pp. 165–174. Wendt, P. E., & Risberg, J. (1994). Cortical activation during visual spatial processing: Relation between hemispheric asymmetry of blood flow and performance. Brain and Cognition, 24, 87–103. Xu, B. Y. (1994). Untersuchung zu pra¨dikativen und funktionalen kognitiven Strukturen chinesischer Kinder bei der Auseinandersetzung mit Grundbegriffen der Programmierung. Osnabru¨ck: Forschungsinstitut fu¨r Mathematikdidaktik.
Dimensional Complexity and Power Spectral Measures of the EEG during Functional versus Predicative Problem Solving Matthias Mo¨lle,* Inge Schwank,† Lisa Marshall,* Anke Klo¨hn,* and Jan Born*,‡ *Clinical Neuroendocrinology, Medical University of Lu¨beck, Lu¨beck, Germany; †Institute for Cognitive Mathematics, University of Osnabru¨ck, Osnabru¨ck, Germany; and ‡Physiological Psychology, University of Bamberg, Bamberg, Germany Published online August 18, 2000 Electroencephalograms were recorded in 22 men while solving tasks of visualpattern completion and during mental relaxation. They were primed (by foregoing trials) to solve these tasks either in a predicative or functional mode of thinking. Predicative thinking required that in order to complete the pattern the subject had to get involved with the logic of the static structure of the pattern and therefore had to recognize the recurrence of certain features of the elements (e.g., shape, color, and size). Functional thinking required involvement in a dynamic reading of the logic of the pattern and therefore to search for operations and actions to be performed on the pattern elements (e.g., pushing, mirroring, and rotating). The EEG complexity during predicative thinking decreased in comparison to functional thinking and mental relaxation, with this reduction being most pronounced over the right parietal cortex. A reduction in dimensional complexity during functional thinking as compared to mental relaxation, which was concentrated over the left central cortex, although significant, was less clear. The reduced EEG complexity during predicative thought, dominant over the right hemisphere, could reflect increased competitive inhibition among respective cortical neuron assemblies in association with the visual analysis of static element features, converging upon those predicates relevant for the solution. 2000 Academic Press
INTRODUCTION
Today, as the material basis of human thinking, the cerebral cortex is essentially considered to house a large amount of memory associations. Almost Address correspondence and reprint requests to Matthias Mo¨lle, Klinische Forschergruppe, Haus 23a, Universita¨t Lu¨beck, Ratzeburger Allee 160, 23538 Lu¨beck, Germany. Fax: ⫹49 ⫹451 500 3640. E-mail: [email protected]. We thank Professor W. Lutzenberger for providing the software for nonlinear analysis of the EEG and A.K. Ju¨rß and A. Otterbein for technical assistance. Supported by a grant from the DFG to J.B. 547 0278-2626/00 $35.00 Copyright 2000 by Academic Press All rights of reproduction in any form reserved.
548
¨ LLE ET AL. MO
all abilities of the brain are assumed to be based on the simultaneous and successive activity of many different cortical networks (neuronal cell assemblies), which are considered as single processing units, i.e., as representational units of thoughts and ideas (Hebb, 1949; Elbert, Ray, Kowalik, Skinner, Graf, & Birbaumer, 1994; Pulvermu¨ller, 1996). However, abstract thinking not only consists of pure forming of associations but also of the integration and processing of information according to certain ‘‘logical’’ principles. Particularly, this ability to control the formation of associations of mental representations and imaginations along certain rules appears to distinguish human intelligence from the intelligence of nonhuman animals. But still not much is known about the concrete mechanisms regulating the flow of thoughts and ideas within cortical neuronal networks active during human information processing. By means of the electroencephalographic activity recorded from the scalp this study aimed to differentiate two modes of thinking: predicative versus functional thinking (Schwank, 1986, 1993). The concept of predicative/functional thinking originated in cognitive mathematics. Qualitative experimental studies in subjects of different ages, sexes, intellectual levels, and cultures indicated recurrent basic features in the way ideas were arranged during concept formation on mathematical problems (for summary, Xu, 1994; Schwank, 1995). Two fundamentally different ways of logical orientation were extracted: one taking into account manifold features and relationships, resulting in a static structural view on things, and another taking into account various efficacious actions and construction procedures resulting in a dynamic view on things. Analogous to concepts in mathematical logic, the first is called predicative thinking, the latter functional thinking. In some cases no inner mathematical constraints determine that the chance of success is unbalanced: both predicative and functional thinking are doing well. But in other cases for successful problem solving one should behave either in a functional or in a predicative way. Although the terms predicative and functional thinking were originally used to indicate a type of thinking that occurs when human beings think about mathematical content, one would not expect that the cognitive mechanisms involved in this type of thinking are used exclusively in the case of a mathematical content. In fact the idea of a more static or a more dynamic view on things, leading to different mathematical problem solutions, is a very fundamental one. A prototype for the functional mode of thinking is expressed in the concept of a ‘‘switch,’’ which Bateson presented in his philosophical analysis (Bateson, 1980, pp. 120–121): We do not notice that the concept ‘‘switch’’ is of quite a different order from the concepts ‘‘stone,’’ ‘‘table,’’ and the like. Closer examination shows that the switch, considered as a part of an electric circuit, does not exist when it is in the on position. From point of view of the circuit, it is not different from the conducting wire which leads to it and the wire which leads away from it. It is merely ‘‘more conductor.’’ Conversely, but similarly, when the switch is off, it does not exist form the point
EEG DURING MODES OF THINKING
549
of view of the circuit. It is nothing, a gap between two conductors which, themselves exist only as conductors when the switch is on. In other words, the switch is not except at the moments of its change of setting, and the concept ‘‘switch’’ has thus a special relation to time. It is related to the notion ‘‘change’’ rather than to the notion ‘‘object.’’
It seems that in the general scientific discourse functional thinking is less appreciated and in any case less explored. Reasons could be that it is easier to use static experimental material as well as the assumed close relation of thinking to language. Nevertheless, functional thinking appears to have a profound impact on progress in mathematics. For example van der Waerden (1954) discussing the style of creating a special mathematical curve by Pascal showed that this one had an absolutely clear concept in terms of motoric actions of his new idea before he invented its name. Van der Waerden claims that the motoric idea is essential in mathematical thinking: If you have forgotten it, you do not have the concept of the curve any longer, even if you know what it looks like—or if you just know the (artificial) name/wordmark. There are further hints in this direction by Einstein (Hadamard, 1954). While various studies showed that the discrimination between functional versus predicative problem solving can be successfully transferred from mathematical thinking to more real-life problem solving (e.g., to decision making in business reengineering; Cohors-Fresenborg, 1996), it is presently unknown whether these modes of thinking can be distinguished also on a neurophysiological level. The present study asked whether the different ‘‘logical orientations’’ involved in these modes express themselves in different types of EEG activity. Several studies proved that EEG measures can provide a useful tool to discriminate complex processes of thought (Petsche, Lacroix, Lindner, Rappelsberg, & Schmidt-Henrich, 1992; Hollander, Petsche, Dimitrov, Filz, & Wenger, 1997). A measure of particular sensitivity in this context appears to be the dimensional complexity of the EEG. In foregoing studies, we showed that EEG activity during creative thinking is associated with a generally enhanced dimensional complexity, as compared to convergent thinking (Mo¨lle, Marshall, Pietrowsky, Lutzenberger, Fehm, & Born, 1996; Mo¨lle, Marshall, Wolf, Fehm, & Born, 1998). Also, mental imagery of a moving object (pendulum) resulted in increased prefrontal dimensional complexity of the EEG in comparison to the actual perception of the same object (Schupp, Lutzenberger, Birbaumer, Miltner, & Braun, 1994) and the EEG over frontal cortical regions during emotional imagery was accompanied by higher dimensional complexity than during mental arithmetic tasks (Birbaumer, Lutzenberger, Elbert, Flor, & Rockstroh, 1993). All these results can be explained by the concept of dimensional complexity representing a measure which estimates the number of simultaneously activated oscillating neuron assemblies within the cortex (Lutzenberger, Preissl, & Pulvermu¨ller, 1995). Modes of focused thinking, i.e., mental processing which is directed and converging toward a distinct aim, result in
550
¨ LLE ET AL. MO
an inhibition of neuronal networks and thus in a smaller number of competitive neuronal cell assemblies. On the other hand, modes of divergent thinking, i.e., cortical processing which is characterized by a loosening of rigid attentional sets, show an enhanced number of simultaneously activated oscillating neuron assemblies. Considering thinking as a form of covert attention to internal ideas (Posner, 1980), a parallel distinction in the EEG’s dimensional complexity has been demonstrated between focusing and dividing attention (Mo¨lle, Marshall, Pietrowsky, Lutzenberger, Fehm, & Born, 1995; Mo¨lle, Albrecht, Marshall, Fehm, & Born, 1997). In this study the EEG’s dimensional complexity and spectral power within traditional frequency bands were measured while subjects solved tasks of visual pattern completion, i.e., tasks of convergent thinking, using different modes of ‘‘logical orientation.’’ Subjects were primed by instructions (on several foregoing tasks, where the mode of logical analysis and the solution process were demonstrated) to solve a given task on one condition in a predicative way and on another condition in a functional way. It was hypothesized that these two modes of thinking would also show differences in their ongoing electrocortical activity, especially with regard to their topographical distribution. Multiple evidence exists pointing to preferential execution of visuo-spatial analysis, as performed during the predicative thinking, in the right as compared to the left hemisphere (Hellige, 1990; Springer & Deutsch, 1993). In a recent study, Goebel, Linden, Sireteanu, Lanfermann, Zanella, Singer, and Goebel (1997), using functional magnetic resonance imaging (fMRI), observed distinctly greater activation in the right frontal and parietal cortex than in respective left cortical areas during an active visual search. In our terms this is a predicative visual search task because it requires the conjunction of features to find a target (e.g., a red vertical bar among red horizontal and green vertical bars). Based on these similarities, for the present experiment we expected a stronger right than left hemispheric activation during the predicative mode of thinking. In contrast, the operations and actions to be performed on pattern elements with functional thinking may be linked more closely to a motor type of processing. Considering evidence from clinical studies in patients with ideomotor apraxia (Heilman & Valenstein, 1993) and also from recent PET studies (Decety, Grezes, Costes, Perani, Jeannerod, Procyk, Grassi, & Fazio, 1997; Grafton, Fagg, & Arbib, 1998) indicating that the organization of action preferentially involves left and more anterior cortical areas, it was supposed that in comparison with predicative thinking the functional mode of thinking is associated with increased activation in left anterior cortical areas. However, since the processing of visual task patterns also relies always on more elementary visuospatial operations, functional problem solving (like predicative thinking) was expected to induce also signs of right-hemispheric activation. An additional aim of the study was to compare differences in EEG activity during primed functional versus predicative thinking with differences in indi-
EEG DURING MODES OF THINKING
551
vidual habits (‘‘style’’) of thinking. For this purpose, prior to the conditions of primed functional and predicative thinking, subjects were required to spontaneously solve tasks of pattern completion (i.e., without prior priming). Here, it was expected that depending on whether a subject’s cognitive style tended to be more functional or predicative, interindividual differences would occur comparable with those after primed functional versus predicative thinking. METHODS AND MATERIALS
Subjects and EEG Recordings Twenty-five, right-handed male subjects participated in the study. EEG data from three subjects were discarded because the subjective ratings of task difficulty differed greatly. Mean age of the remaining 22 subjects was 26.6 years (SD ⫽ 3.3; range: 21 to 37). The studies were approved by the Committee on Research Involving Human Subjects of the University of Lu¨beck. All subjects gave written informed consent before participation. EEGs were recorded from Fp1, Fp2, F3, F4, F7, F8, T3, T4, T5, T6, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz electrodes (international 10–20 system). Linked electrodes attached to the mastoids served as reference. In addition, four electrodes were used to record vertical and horizontal eye movements. A single ground electrode was attached at Fpz. The EEG was recorded using a SynAmps EEG amplifier (NeuroScan Inc.). Sample frequency was 500 Hz with 16-bit A-to-D precision. The time constant used was 1 s. The low-pass filter was set to 70 Hz.
Stimuli and Procedure In each of three experimental blocks subjects were presented with four tasks of pattern completion (see Fig. 1; see Schwank, 1997 for further examples). In the first block subjects were to find the logic in the given patterns on their own, i.e., they were free to use their preferred cognitive style (spontaneous solution). In two further blocks the subjects were primed on functional (respectively predicative) thinking: in three tasks the experimenter demonstrated an ideal functional (respectively predicative) logical analysis of the pattern for constructing the solution figure. The subjects were asked to solve the fourth task in the particular demonstrated style. The subject sample was split, so that after finishing the spontaneous solution block one half received first the functional instructions and then the predicative ones, in the other half order was reversed. A functional treatment of the task in Fig. 1 would rely on functional tools, i.e., inventing a dynamic process which produces the last element in a row or column. The embedded dynamic logic to be adopted is that in each row the circle moves around, and in each column the point moves around. The object around which the movement takes place is invariant. A predicative treatment of the task in Fig. 1 would rely on predicative tools, i.e., structuring the pattern, looking for salient features, and inventing general laws of relationship among shapes and forms and their locations. The embedded static logic to be adopted is that each figure consists of three objects: a star, a point, and a circle. The star is the same in each figure. In each row the point is at the same place (left, top, right). In each column the circle is at the same place (top, right, left). It is striking that in the functional case for logical orientation typically less precise word labeling is used. Instead, when explaining their solution subjects tend to give some general, deictic statements combined with gesture, e.g., ‘‘This is moving around here.’’ For this reason videorecording is indispensable for evaluating a subject’s argumentation. In contrast, in the
552
¨ LLE ET AL. MO
FIG. 1. Example of a pattern-completion task with embedded predicative/functional logic. In our experiment, subjects were to find the missing element. A typical functional solution for this task would be: ‘‘The circle moves clockwise from tip to tip when I go from left to right in each row. Therefore, at the end it should arrive at the left tip of the middle figure. When I go from top to bottom in each column the dot also moves clockwise from tip to tip. Therefore, at the end it should arrive at the top tip of the middle figure.’’ A typical predicative solution for this task would be: ‘‘The middle figure is always the same. In each column there are three circles. In the left column they are always on the top tip of the middle figure, in the middle column always on the right tip, and the two circles in the right column are on the left tip. Therefore, I would draw the circle on the left tip. In each row there are three dots. The dots are always on the right tip in the top row, in the middle row they are always on the left tip and the two dots of the bottom row are on the top tip. Therefore, I would draw the dot on the top tip.’’
predicative case word labels play a fundamental role. They officiate as landmarks around which the static mental model covering the features, relationships, and abstract structures of the pattern is built. The tasks were presented to the subjects on a display located 100 cm in front of the subject. The pictures used had a width and a height of 7 cm (visual angle ⫽ 4°). For solving the four tasks of the first block (spontaneous solution) and the fourth tasks of the second and third blocks (functional and predicative solution) subjects were given a maximum of 2 min. While the subjects were looking at and solving the tasks they were not allowed to speak or to move and were to avoid large eye movements. After having solved the task subjects had to draw their solution (or partial solution) and to explain why their solution figure fits the pattern. Subsequently they were to rate the difficulty of the task on a scale from ⫺3 to ⫹3.
EEG DURING MODES OF THINKING
553
The EEG was recorded while subjects were solving the fourth task of each block (spontaneous solution, functional solution, and predicative solution). Before the first block, a resting EEG was recorded during which subjects performed for 1 min a task of mental relaxation (‘‘Imagine you are lying on the beach, the sun is shining, the waves are rolling softly!’’). The order of conditions within the second and third blocks was balanced across subjects. The complete experimental session was recorded on video tape.
Analysis of Argumentation of Task Solving The subjects’ logical argumentations, why their constructed figures fit well in the patterns, were analyzed using the videorecordings. Subjects used mainly the primed style. But, especially when subjects under spontaneous conditions strongly preferred one of the two styles, they tended to use also some elements of this style even if it was not primed. Therefore, the videotaped argumentations were scored according to standardized criteria. Each task was scored up to 3 points for elements of functional solution argumentation and up to 3 points for elements of predicative solution argumentation, using prototypic standard argumentation as reference. The most important criterion for a predicative mode of task solving is the prevalent use of different nouns and adjectives to distinguish the different parts of the figure. In contrast there are only few verbs occurring which are just used to describe the static positions of parts of the figure (e.g., ‘‘In the upper left corner of the big triangle there is a small black point’’). Indicators for a functional mode of task solving are a much poorer usage of language, associated with an infrequent use of nouns and an even less frequent use of adjectives. Instead of using a lot of different words the argumentation is a more or less deicitic behavior (e.g., ‘‘This is turning around there’’). But the variety of verbs used to express the dynamics seen in the pattern is much richer. Each task argumentation was scored independently by two experienced raters. The agreement between raters was greater than r ⫽ 0.71. In cases of discrepant judgements the videotaped task was reevaluated by both raters together. For further analysis a difference score for the subject’s argumentations was determined: predicative solution argumentation minus functional solution argumentation.
EEG Analysis For each recorded task a 20.48-s EEG period free of large eye movements or other artifacts was selected from the period of problem solving. The 20.48-s epochs for analysis were taken starting about 10 s after the beginning of the recorded task. Smaller ocular artifacts were corrected with the regression method using the vertical and horizontal EOG (Gratton, Coles, & Donchin, 1983). For calculating the dimensional complexity the EEG signals were digitally filtered with a low-pass filter of 35 Hz (-3 dB) and a very steep roll-off rate (-90 dB at 45 Hz) and afterward down-sampled to 100 Hz. Low-pass filtering at 35 Hz was expected to improve the signalto-noise ratio and to minimize artifacts by EMG activity. Dimensional complexity (estimated correlation dimension) was calculated by combining the singular value decomposition technique with the ‘‘average-pointwise’’ dimension procedure (Lutzenberger et al., 1995; Pritchard & Duke, 1995). The first step of this program was based on the autocovariance function with time lags ranging from 0 to 31 points. A symmetrical 32 ⫻ 32 matrix was constructed with the covariances of the EEG trace as elements. On this matrix the singular value decomposition was performed and 32 components were generated. Now a selection was made to separate signal from presumed noise. Dependent on the sizes of the eigenvalues only a subset of eigenvectors was used to reconstruct the state-space. The extracted vectors and the original time series were used in a folding operation to calculate a new and separate time series for each extracted vector. In the next step separate calculations of the dimensionality were performed for 32 equidistant points, using the method of ‘‘pointwise dimension’’ as proposed
554
¨ LLE ET AL. MO
by Farmer, Ott, and York (1983). Subsequently, the median was calculated, representing the value of dimensional complexity of the given EEG trace, so that one value of dimension was obtained for each EEG channel and epoch. Using a Fast Fourier Transformation (FFT) the 20.48-s epochs of EEG activity (not digitally filtered and not down-sampled) were transformed into the log amplitudes of the power spectrum, and values for the delta (0.5–4.4 Hz), theta (4.4–8.1 Hz), alpha (8.1–12.2 Hz), and beta (12.2–24.9 Hz) bands were obtained. The power spectrum was calculated by averaging the Fast Fourier Transforms of nine overlapping segments of 2048 points each. To reduce errors induced by edge effects the signal was tapered toward zero at the extremes of each data segment with a raised cosine window.
Statistical Evaluation Values of EEG dimensional complexity and power spectral analysis were subjected to an ANOVA with repeated-measures factors for Thinking (functional thinking, predicative thinking, and mental relaxation) and Topography (Fp1, Fp2, F3, F4, F7, F8, T3, T4, T5, T6, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz). Additional ANOVA were used to compare each of the two modes of thinking with mental relaxation and with each other. The direct comparison of the two modes of thinking included the subjective rating of task difficulty as covariate. To evaluate differences between subjects with a cognitive style of predominant functional versus predicative task solving, for each individual the average difference score for the argumentation of task solving was calculated across the first four tasks where subjects spontaneously solved the problems. The median of these average scores was taken to split the group into two equally sized groups, one with the above-median difference score (predominant predicative types) and one with the below-median difference score (predominant functional types). An ANOVA was run on the EEGs dimensional complexity during the fourth task of the first block (spontaneous solution) with repeated measures for Topography (F3, F4, C3, C4, P3, P4, O1, O2, Fz, Cz, and Pz) and a Grouping factor for the functional and predicative Types.1
RESULTS
Primed Functional versus Predicative Thinking Argumentation of task solving and rated task difficulty. The argumentation of task solving was scored with regard to the occurrence of predicative and functional explanatory elements, with the final difference score (predicative minus functional argumentation) between ⫹3 and ⫺3 indicating a prevalent predicative or functional solution, respectively. The mean score for argumentation of task solving after functional priming was ⫺.55 ⫾ .44 and after predicative priming ⫹2.50 ⫾ 0.24 (p ⬍ .001, Wilcoxon). Although this difference was highly significant, the absolute value for functional priming was distinctly lower than for predicative priming, indicating that the induction of functional thinking was less successful. Task difficulty was rated on a scale between ⫺3 (very easy) and ⫹3 (very difficult) and did not differ significantly between the primed functional task (⫹.18 ⫾ .22) and the primed predicative task (⫺.23 ⫾ .25, p ⫽ .14, Wilcoxon). 1 The most outer electrodes Fp1, Fp2, F7, F8, T3, T4, T5, and T6 were discarded in this analysis because of their great variability.
EEG DURING MODES OF THINKING
555
FIG. 2. Mean (⫾ SEM ) dimensional complexity of the EEG during functional thinking (empty bars), predicative thinking (black bars), and mental relaxation (gray bars). Asterisks indicate significant differences between any two of these modes of cortical processing (*** p ⬍ .001; **p ⬍ .01; *p ⬍ .05).
556
¨ LLE ET AL. MO
Dimensional complexity. Figure 2 summarizes the EEGs dimensional complexity during the two modes of primed task solving and mental relaxation. Global ANOVA indicated differences depending on the recording site [Thinking ⫻ Topography: F(36, 756) ⫽ 2.24; p ⬍ .05], which were to be specified in pairwise comparisons. Compared to mental relaxation, dimensional complexity during predicative task solving was lower with this effect being most pronounced in recordings from midline electrodes and right central and parietal electrode sites [Thinking ⫻ Topography: F(18, 378) ⫽ 3.09; p ⬍ .01; for contrasts Cz: p ⬍ .001, Fz, C4, Pz, P4: p ⬍ .01 and C3: p ⬍ .05]. The comparison of dimensional complexity during functional task solving with mental relaxation revealed also a Thinking x Topography interaction [F(18, 378) ⫽ 2.24; p ⬍ .05], indicating that dimensional complexity during functional task solving was diminished at C3 and Cz ( p ⬍ .05) and enhanced at O1 (p ⬍ .05) as compared with mental relaxation. Comparison of the EEG during both modes of problem solving indicated a lower dimensional complexity during predicative than during functional thinking [F(1, 20) ⫽ 5.16; p ⬍ .05]. In contrast, calculated at each electrode this effect revealed significance for recordings over parietal and right occipital cortical areas (P3, Pz, P4, O2; p ⬍ .01) as well as over right frontal and central cortical areas (F4, Cz, C4; p ⬍ .05). The covariate of rated task difficulty introduced in these analyses did not indicate a dependence of EEG dimensionality on variations in experienced difficulty of problem solving (β ⫽ 0.02; p ⫽ 0.83). The covariate of task difficulty also remained nonsignificant in analyses on single electrode sites. Power spectral analysis. In all frequency bands spectral power of the EEG during both modes of primed thinking differed significantly from that during mental relaxation. Power within the alpha and beta frequency bands was lower during thinking than during mental relaxation [Thinking ⫻ Topography: F(18, 378) ⫽ 5.98; p ⬍ .001 for the alpha band and F(18, 378) ⫽ 3.35; p ⬍ .01 for the beta band; see Fig. 3 for pairwise comparisons at single electrode sites]. Theta power during mental relaxation was slightly lower at frontal and occipital recording sites but slightly higher at central and parietal sites than during thinking [Thinking ⫻ Topography: F(18, 378) ⫽ 2.23; p ⬍ .05]. Delta power was increased during thinking as compared to mental relaxation [F(2, 42) ⫽ 6.40; p ⬍ .01]. However, ANOVA with the factors mode of Thinking (functional versus predicative) and Topography did not reveal any difference between both types of problem solving for any of the four frequency bands. Nevertheless, analyses at single electrodes indicated higher alpha and beta power during functional than during predicative thinking with this effect dominating at occipital regions (O1, O2; p ⬍ .01). Cognitive Style during Spontaneous Problem Solving Across the four tasks of the first block (spontaneous solution) the median difference score of task argumentation was ⫹0.875 ⫾ 0.25 (range: ⫺1.5 to
FIG. 3. Mean (⫾ SEM ) log power (in arbitrary units) during functional thinking (empty bars), predicative thinking (black bars), and mental relaxation (gray bars) within the delta, theta, alpha, and beta frequency bands. Asterisks indicate significant differences between any two of these modes of cortical processing (***p ⬍ .001; **p ⬍ .01; *p ⬍ .05). Results from analyses at single-electrode locations are shown only when the ANOVA indicated a significant ( p ⬍ .05) effect of Thinking or a Thinking ⫻ Topography interaction in pairwise comparisons. (Thus, significant differences in alpha and beta power between predicative and functional thinking revealed in separate analyses at O1 and O2 were not indicated.)
558
¨ LLE ET AL. MO
FIG. 4. Dimensional complexity of the EEG during spontaneous problem solving on the pattern-completion tasks. Black circles indicate dimension values for the group of predominantly functional cognitive style. Empty rectangles indicate dimension values for the group of predominantly predicative cognitive style. Values from the two lateral and the midline electrode sites were averaged and termed correspondingly ‘‘frontal,’’ ‘‘central,’’ and ‘‘parietal’’; for ‘‘occipital’’ O1 and O2 were averaged.
2.5), indicating that subjects overall tended toward predicative problem solving. The median was used to split the group into two subgroups with average difference scores of task argumentation of ⫹1.75 ⫾ 0.11 (range: 1.0 to 2.5) for predominant predicative types and of ⫺0.14 ⫾ 0.17 (range: ⫺1.5 to 0.75) for predominant functional types. Rated task difficulty for the fourth task of the first block (used for EEG analysis) averaged ⫹0.32 ⫾ 0.20 (range: ⫺2 to 2) and did not differ significantly between both groups (⫹0.36 ⫾ 0.36 versus ⫹0.27 ⫾ 0.20, p ⫽ 0.83, t test). The analysis of the EEGs dimensional complexity during spontaneous task solving revealed a significant Topography x Group interaction effect [F(10, 200) ⫽ 2.99; p ⬍ .01; Fig. 4). The predominant functional types showed a reduced EEG complexity at frontal and central recordings and an increased EEG complexity at parietal and occipital recordings in comparison to the group of predominant predicative types. DISCUSSION
This study aimed to differentiate two fundamentally different strategies of thinking, i.e., predicative versus functional thinking by means of the analysis of ongoing EEG activity. Both modes of thinking were examined while subjects performed the same type of visual-pattern completion tasks. Compared with mental relaxation both modes of thinking were accompanied by a reduced dimensional complexity of the EEG, which for predicative thinking was more pronounced over the right than the left hemisphere. Reductions
EEG DURING MODES OF THINKING
559
in the EEG’s dimensional complexity during functional thinking were found in comparison with mental relaxation over the left and midcentral cortex. Also, both modes of thinking differed in that EEG dimensionality was generally lower during predicative than functional thinking. The effect of predicative thinking on EEG dimensionality being more distinct over the midline and right hemisphere than over left cortical areas agrees with the view that visuo-spatial analysis is predominantly performed in right cortical areas. Topographical analyses with positron emission tomography (PET) have revealed consistent evidence for greater activity in the right than the left hemisphere during different types of tasks involving basic visuo-spatial analysis such as the analysis of forms, shapes, and colors or of cubes (McIntosh, Grady, Ungerleider, Haxby, Rapoport, & Horwitz, 1994; Wendt & Risberg, 1994), although the left hemisphere is also involved, particularly in more complex tasks (Nikolaev, 1995). As in the present study, effects of visuo-spatial analysis in those previous studies often concentrated over more posterior, i.e., parietal cortical areas (Wendt & Risberg, 1994; Goebel et al., 1997). The latter authors tested cortical activity by means of fMRI during a visual search task showing great similarities to the present task of primed predicative thinking in that it required identifying a target pattern by the active conjunction of static features defined by shape, color, spatial orientation, and so on. On this task a stronger activation was found in the superior parietal cortex (and the frontal eye field) in the right than in the left hemisphere. On this background, the distinct reduction in the EEG’s dimensional complexity during predicative thought processes could be considered a reflection of active visuo-spatial attentive operations associated with conjugating the different features of the pattern elements. Given that a reduced dimensional EEG complexity indicates a diminished number of simultaneously activated cortical neuron assemblies (Lutzenberger et al., 1995) these attentive operations appear to manifest themselves in a relatively reduced number of competitively oscillating assemblies. We would conclude that the process of predicative thinking is based on an active inhibition of irrelevant cortical networks in favor of an overall reduced number of active networks essential for task solving. Thus, increased competitive inhibition among neuron assemblies of respective cortical areas may increase the signalto-noise ratio of processing. This view agrees with previous studies where reduced EEG dimensional complexity was found, especially during modes of focused (selective) attention and focused (convergent) thinking. Since these modes are directed toward finding eventually the only one correct solution, predicative as well as functional processes of thought on pattern-completion tasks likewise represent modes of convergent focused thinking which manifest themselves in increased inhibitory control over network activity and, consequently, reduced EEG dimensionality within specialized cortical areas. The hypothesis that functional thinking is associated with enhanced activity over the left and more anterior cortex was not confirmed that clearly.
560
¨ LLE ET AL. MO
This view was derived from the fact that functional thinking requires motorlike operations and actions, such as pushing, turning, and mirroring elements of the pattern, the planning of which is assumed to involve left-hemispheric functions. In fact, a lower dimensional complexity of the EEG was found during functional thinking than during mental relaxation over the left-central cortex, but this effect was much weaker than the strong reduction of the EEG dimension during predicative thinking over the right hemisphere. There could be several reasons for this. First, the analysis of the argumentation of task solving showed that the priming of the functional thinking mode was not as successful as the priming of the predicative thinking mode. After functional priming, subjects still verbalized some ‘‘predicative’’ arguments when explaining their task solution. Hence, the EEG during the primed functional thinking may have reflected a significant contribution of predicative thought processes in addition to the predominant functional thought processes. However, this view is somewhat challenged by the fact that at right central and parietal electrodes where predicative thinking induced a distinct reduction in EEG dimensionality (as compared with mental relaxation) functional thinking remained without effect. This lack of change at right centro-parietal electrode locations is even more difficult to integrate when it is assumed that some of the elementary processes of visuo-spatial feature extraction performed on the pattern are similar for both modes of thought. A second and related reason for the less distinct effect of functional thinking on the EEG’s dimensional complexity is revealed by analysis of the argumentation of task solving on the first four tasks (where subjects were not primed): most subjects spontaneously preferred the predicative strategy, i.e., the majority of our subjects displayed spontaneously a more or less pronounced predicative style of thinking. Being less familiar with the functional mode of thinking, subjects being forced to this mode of problem solving may have spent more effort in ‘‘nonspecific’’ search operations not limited to left-hemispheric function. On the other hand, experienced task difficulty did not differ for both modes of primed thinking; also, classic EEG indicators of arousal and attention such as power within the alpha and theta frequency bands did not indicate differences related to nonspecific effects of mental effort on both modes of thinking. Alternatively, the less distinct effect of primed functional thinking might reflect an inherent ‘‘divergent’’ feature of this mode of thinking. Given that the direct comparison with the mode of predicative thinking revealed primarily a generally enhanced dimensional EEG complexity with little topographical specialization, the distinguishing characteristic of this mode of thought may be a less focused nature involving a greater number of competitively oscillating neuron assemblies distributed over extended cortical areas. Thus, it could be argued that compared to predicative thinking functional thinking requires a greater extent of imagery, i.e., imagining movements and dynamic changes of pattern elements. In previous studies operations of imagery have been found to be accompanied with in-
EEG DURING MODES OF THINKING
561
creased dimensionality in the EEG. However, although plausible, this view needs to be validated in further trials employing subjects who have a lower predisposition to use the predicative style of thinking than those of the present sample. Interestingly, on the tasks of spontaneous problem solving, predominant functional types displayed reduced EEG dimensionality over anterior cortical sites, whereas predominant predicative types displayed a posterior parietal reduction in EEG dimensionality. While this pattern is consistent with a ‘‘motor-oriented’’ style of thinking in the predominant functional types, it is also noteworthy that both groups of cognitive style were not differentiated by any hemispheric lateralization in EEG activity. This could indicate that habitual processes of thought, in contrast to those enforced by priming, are more evenly distributed across both hemispheres (Hellige, 1990). Results of power spectral analysis of the EEG were complementary to results from nonlinear analysis. As has already been found in previous studies a reduced dimensional complexity appeared to be associated with enhanced activity in lower frequency bands (delta and theta) and a concurrently decreased activity in higher frequency bands (alpha and beta). Thus, the decrease in right central and parietal EEG dimensionality during predicative thinking was accompanied by reduced activity in the alpha and beta frequency bands and increased activity in the delta band over the same cortical areas. In this context, the measure of dimensional complexity appears to condense power spectral changes occurring simultaneously in different frequency bands. An exception to this rule was the EEG activity over the occipital cortex, where the difference between functional and predicative thought appeared to be stronger for alpha and beta spectral power than for the measure of dimensionality. According to a concept proposed by Klimesch (1995), increased occipital alpha activity could point to a more elaborate memory-based encoding of visual features during functional thinking. However, this view is tentative and has to be further investigated. Aside from this issue, it remains to be emphasized that the two thinking modes did not differ in any frequency band as clearly as in the dimensional complexity. This confirms the sensitivity of dimensional complexity for recognizing EEG changes during different modes of information processing. REFERENCES Bateson, G. (1980). Mind and nature—A necessary unity. Toronto: Bantam Books. Birbaumer, N., Lutzenberger, W., Elbert, T., Flor, H., & Rockstroh, B. (1993). Imagery and ¨ hman (Eds.), The structure of emotion. Toronto: brain processes. In N. Birbaumer & A. O Hogrefe & Huber. Pp. 122–138. Cohors-Fresenborg, E. (1996). Individual differences in cognitive structures and the effect on business reengineering. In J. Georgas, M. Manthouli, E. Besevegis, & A. Kokkevi (Eds.), Contemporary psychology in Europe—Theory, research, and applications. Go¨ttingen: Hogrefe & Huber. Pp. 153–160.
562
¨ LLE ET AL. MO
Decety, J., Grezes, J., Costes, N., Perani, D., Jeannerod, M., Procyk, E., Grassi, F., & Fazio, F. (1997). Brain activity during observation of actions: Influence of action content and subject’s strategy. Brain, 120, 1763–1777. Elbert, T., Ray, W. J., Kowalik, Z. J., Skinner, J. E., Graf, K. E., & Birbaumer, N. (1994). Chaos and physiology: Deterministic chaos in excitable cell assemblies. Physiological Review, 74, 1–47. Farmer, J. D., Ott, E., & York, J. A. (1983). Dimension of chaotic attractors. Physica D, 7, 153–180. Goebel, C., Linden, D. E. J., Sireteanu, R., Lanfermann, H., Zanella, F. E., Singer, W., & Goebel, R. (1997). Different attention processes in visual search tasks investigated with functional Magnetic Resonance Imaging. NeuroImage, 5, S81. Grafton, S. T., Fagg, A. H., & Arbib, M. A. (1998). Dorsal premotor cortex and conditional movement selection: A PET functional mapping study. Journal of Neurophysiology, 79, 1092–1097. Gratton, G., Coles, M. G. H., & Donchin, E. (1983). A new method for off-line removal of ocular artifact. Electroencephalography and Clinical Neurophysiology, 55, 468–484. Hadamard, J. (1954). The psychology of invention in the mathematical field. New York: Dover. Hebb, D. O. (1949). The organization of behavior: A neuropsychological theory. New York: Wiley. Heilman, K. M., & Valenstein, E. (1993). Clinical neuropsychology. New York: Oxford Univ. Press. Third ed. Hellige, J. B. (1990). Hemispheric asymmetry. Annual Review of Psychology, 41, 55–80. Hollander, I., Petsche, H., Dimitrov, L. I., Filz, O., & Wenger, E. (1997). The reflection of cognitive tasks in EEG and MRI and a method of its visualization. Brain Topography, 9, 177–189. Klimesch, W. (1995). Memory processes described as brain oscillations in the EEG-alpha and theta bands. Psychology.95.6.06.memory-brain.1.klimesch. Lutzenberger, W., Preissl, H., & Pulvermu¨ller, F. (1995). Fractal dimension of electroencephalographic time series and underlying brain processes. Biological Cybernetics, 73, 477– 482. McIntosh, A. R., Grady, C. L., Ungerleider, L. G., Haxby, J. V., Rapoport, S. I., & Horwitz, B. (1994). Network analysis of cortical visual pathways mapped with PET. Journal of Neuroscience, 14, 655–666. Mo¨lle, M., Marshall, L., Pietrowsky, R., Lutzenberger, W., Fehm, H. L., & Born, J. (1995). Dimensional complexity of the EEG indicates a right fronto-cortical locus of attentional control. Journal of Psychophysiology, 9, 45–55. Mo¨lle, M., Marshall, L., Pietrowsky, R., Lutzenberger, W., Fehm, H.L., & Born, J. (1996). Enhanced dynamic complexity in the human EEG during creative thinking. Neuroscience Letter, 208, 1–4. Mo¨lle, M., Albrecht, C., Marshall, L., Fehm, H.L., & Born, J. (1997). ACTH widens the focus of attention in humans: A nonlinear EEG analysis. Psychosomatic Medicine, 59, 497– 502. Mo¨lle, M., Marshall, L., Wolf, B., Fehm, H. L., & Born, J. (1999). EEG complexity and performance measures of creative thinking. Psychophysiology, 36, 1–10. Nikolaev, A.R. (1995). Investigation of the stage of the mental rotation of complex figures with the intracortical interaction mapping technique. Neuroscience Behavioral Physiology, 25, 228–233. Petsche, H., Lacroix, D., Lindner, K., Rappelsberger, P., & Schmidt-Henrich, E. (1992). Think-
EEG DURING MODES OF THINKING
563
ing with images or thinking with language: A pilot EEG probability mapping study. International Journal of Psychophysiology, 12, 31–39. Posner, M. I. (1980). Orienting of attention. Quarterly Journal of Experimental Psychology, 32, 3–25. Pritchard, W. S., & Duke, D. W. (1995). Measuring ‘‘chaos’’ in the brain: A tutorial review of EEG dimension estimation. Brain and Cognition, 27, 353–397. Pulvermu¨ller, F. (1996). Hebb’s concept of cell assemblies and the psychophysiology of word processing. Psychophysiology, 33, 317–333. Schupp, H. T., Lutzenberger, W., Birbaumer, N., Miltner, W., & Braun, C. (1994). Neurophysiological differences between perception and imagery. Cognitive Brain Research, 2, 77– 86. Schwank, I. (1986). Cognitive structures of algorithmic thinking. In Proceedings of the 10th International Conference for the Psychology of Mathematics Education. London: University of London. Pp. 195–200. Schwank, I. (1993). On the analysis of cognitive structures in algorithmic thinking. Journal of Mathematical Behavior, 12, 209–231. Schwank, I. (1995). The role of microworlds for constructing mathematical concepts. In M. Behara, R. Fritsch & R. Lintz (Eds.), Symposia Gaussiana, Conference A: Mathematics and theoretical physics. Berlin: Walter de Gruyter. Pp. 101–120. Schwank, I. (1997). The assumption of predicative versus functional cognitive structures. Journal for Integrated Study of Artificial Intelligence, Cognitive Science and Applied Epistemology, 14, 213–224. Springer, S. P., & Deutsch, G. (1993). Left brain, right brain. New York: Freeman. van der Waerden, B. L. (1954). Denken ohne Sprache. In G. Re´ve´sz (Ed.), Thinking and speaking. Amsterdam: North–Holland. Pp. 165–174. Wendt, P. E., & Risberg, J. (1994). Cortical activation during visual spatial processing: Relation between hemispheric asymmetry of blood flow and performance. Brain and Cognition, 24, 87–103. Xu, B. Y. (1994). Untersuchung zu pra¨dikativen und funktionalen kognitiven Strukturen chinesischer Kinder bei der Auseinandersetzung mit Grundbegriffen der Programmierung. Osnabru¨ck: Forschungsinstitut fu¨r Mathematikdidaktik.