The Neural Code of Intelligence

The only numerical measures of intelligence are test scores. They are theoretically based on psychometric g, which is an empirical outcome of factor analysis that accounts for a large proportion of variance in individuals’ mental tests (Spearman, 1927). In other words, individuals who perform well on one mental task tend to perform well on most others. The higher the g-loading of a test is, the more it is considered to include the essence of intelligence. Although this is one of the most often replicated findings in social science, it cannot conceal that intelligence is what the test is testing (Boring, 1923). Therefore IQ scores are heavily criticized and demonized, especially when researchers try to answer questions which oppose the current Zeitgeist, such as, are there differences in cognitive abilities between populations or between genders? Sometimes the answers may even lead to violence, as was the case for Jensen’s (1969) statement that compensatory education in the US failed to produce lasting beneficial effects on children’s IQ. Consequently he had to be escorted by security guards when moving around campus.

One has to admit that based on IQ test scores, these two questions have no answer that would withstand scientific rigor. To give just an example for the second sex-related question. As noted by Ackerman (2006), whether males or females differ in general intelligence depends on the test used to assess cognitive ability.  Test designers had two options, either to use separate norms for males and females, as it is done in some personality questionnaires, or to remove items that show sex bias.

 When Terman (1916) provided test norms for the Binet-Simon Intelligence test, the sex differences were in his opinion negligible and therefore ignored, thus the same IQ scale for boys and girls was adopted. In later years when the scale was refined, items that showed greater sex differences were eliminated.  The same holds true for the third revision of WAIS.

As put forward by Irwing (2012), the WAIS-III manual documents state that extensive procedures were used in the construction of the test in order to eliminate sex bias. For instance, the test does not include 3-D mental rotation tasks, for which a large male advantage was found (Miller & Halperen, 2014).
It is therefore not surprising that research into neural underpinnings of intelligence has most often tried to find an IQ biomarker. This attempt makes sense because from a brain perspective, intelligence is just a specific sequence of action potentials. Some promising candidates in the past were string length and individual alpha frequency (IAF), which were later replaced by more sophisticated measures derived from mathematics – chaos and graph theories. The disappointing part is that they still do not explain much more than about 10% of IQ test score variance.

The string length
The string length measure was introduced by Hendrickson and Hendrickson (1980) based on Rhodes’ et al. (1969) excursion measure, which they determined using a map-reading wheel following the ERP curve. They reported a high correlation of 0.77 between the string measure and IQ (Eureka!). It seemed as though a useful biomarker of IQ was discovered. The theoretical explanation was that differences in intelligence reflect the rate at which errors are produced during the train of neural transmissions underlying problem solving.

High IQ individuals make fewer errors than low IQ individuals, thus the individual epochs are less variable from trial to trial, preserving more detail of the single evoked response, and therefore producing a more complex ERP (Hendrickson and Hendrickson, 1980). High correlations were also reported by Stough et al. (1990). Others found modest correlations (e.g.,  Haier et al., 1983), correlations near zero (e.g., Barrett and Eysenck, 1994), and even negative correlations (e.g., Bates and Eysenck, 1993). Negative correlations between the string measure and verbal IQ, and positive correlations with performance IQ were observed by Batt et al. (1999).

These contradictory observations provoked numerous theories which have attempted to explain the ERP-IQ relationship. Bates and Eysenck (1993) proposed that the relationship between the string measure and IQ depends on the attentional demands of the task. Tasks which demand focused attention produce a negative correlation between IQ and string length, because the string measure is supposed to index the efficiency of the brain.

In unattended conditions, however, the string measure indexes brain capacity and therefore the correlation is expected to be positive. Studies by Burns et al. (1997) and Batt et al. (1999) did not confirm this hypothesis. The bitter end for the string length measure came with the conclusion by Burns et al. (1997), stating that it is not a valid measure of the ERP.
Nonlinear Dynamical Systems and Chaos Theory
Nonlinear EEG analysis started in 1985, when Rapp et al. (1985) used chaos theory to analyze spontaneous neural activity in the motor cortex of a monkey. The first studies employing chaos theory and nonlinear measures (e.g. Lyapunov exponent L1, correlation dimension D2, or Kolmogorov entropy K2) to explain the brain-intelligence relationship were done in our lab.
During problem solving, less chaotic EEG patterns have been observed in more intelligent individuals (Jaušovec, 1998; Anokhin et al., 1999) and in more creative ones (Mölle et al., 1999).

The main problem related to the nonlinear analysis of EEG data is a mathematical one. Most of the measures used to determine low deterministic chaos were not designed to be used with relatively short and noisy data sets such as EEG. Hence, approximate entropy (ApEn) was introduced as a quantification of regularity in time-series data.

It has been shown that ApEn can distinguish a wide variety of systems ranging from multi periodic, to stochastic and mixed systems; furthermore, it is applicable to noisy, medium-sized data sets. Mathematically, ApEn measures the likelihood that runs of patterns that are close in one observation remain close on the following incremental comparisons (Pincus, 1995).
In a second study conducted in our lab (Jaušovec and Jaušovec, 2000a), several experiments using visual and auditory oddball tasks were used to clarify the relation between ERP complexity and  intelligence. The correlations indicated that in the attended conditions, more intelligent individuals showed more regular ERP waveforms than less intelligent individuals.

These trends were observed both in auditory and visual oddball paradigms. The negative correlations between ApEn and different intelligence measures obtained in the study suggest that high intelligent individuals have more spatially and temporarily coordinated electro cortical activity when engaged in cognitive tasks – they are less chaotic thinkers.
IAF, a never-ending story
Peak alpha frequency or individual alpha frequency (IAF) is the frequency with the highest magnitude in FFT-derived estimates of spectral power (maximum alpha power in a 7 to 14 Hz window – see figure below).

IAF is assumed to be related to the characteristics of white matter structure, like fiber density, axonal diameter, and myelination, and captures different neural processes than alpha power (e.g., Jann et al., 2010).
The idea that brains that run faster are also smarter is appealing, however the research evidence is rather weak. Some early research conducted before 1960 reported positive correlations. Considering the technical possibilities at that time, it is questionable whether the findings can be compared to those obtained with EEG acquisition systems available today. For instance, Mundy-Castle (1960) reported a positive correlation (r = 0.34) between what he called alpha frequency and IQ. For a detailed review of research on the relation between EEG measures and intelligence done before 1964 see Vogel and Broverman (1964).

Studies performed on more sophisticated EEG acquisition systems and software provided mixed findings. The study by Anokhin and Vogel (1996) showed positive correlations between peak alpha frequency (eyes closed) and test scores obtained on Raven’s matrices (correlations between .20 to .36). On the other hand, two large scale studies conducted in our lab (Jaušovec and Jaušovec, 2000b) and by Posthuma and colleagues (2001) showed no significant correlations between IAF and IQ (WAIS). Recently, Grandy et al. (2013) used structural equation modelling to estimate the association between IAF and intellectual functioning.

The correlation between g (Berlin Intelligence Structure test – BIS) and composed eyes open/closed IAF was .40 (n = 85). However, the correlations reported ranged between .06 and .37; the highest correlations were reported for the memory tests, followed by tests of perceptual speed, and were not significant for the reasoning part of BIS. Among the 12 correlations determined (eyes: open/close; subtests: speed, memory and reasoning; respondents: young/old) only 5 were significant at a p < .05 level. Hence, none would have survived a correction for multiple comparison.

In yet another study from our lab (Pahor and Jaušovec, 2016), three experiments were conducted in order to investigate this relationship: two correlational studies and a third study in which we experimentally induced changes in IAF by means of transcranial alternating current stimulation (tACS). (1) In a large scale study (n=417), no significant correlations between IAF and IQ were observed. However, in males IAF positively correlated with mental rotation and shape manipulation and with an attentional focus on detail.  (2) The second study showed sex-specific correlations between IAF (obtained during task performance) and scope of attention in males and between IAF and reaction time in females.

(3) In the third study, individuals’ IAF was increased with tACS. The induced changes in IAF had a disrupting effect on male performance on Raven’s matrices, whereas a mild positive effect was observed for females. Neuro-electric activity after verum tACS showed increased desynchronization in the upper alpha band and dissociation between fronto-parietal and right temporal brain areas during performance on Raven’s matrices.
You can download the presentation from: https://www.youtube.com/watch?v=Na6f2LwJHhQ&t=41s&list=PLQ8yHMSBC8UCwGZBosBXT6msaCvzN8P4S&index=7
Small-World Networks, Hubs, Local and Global Efficiency – Graph Theory
Sporns and Betzel (2016) see the developing network-based perspective on brain function as a result of two strands of research: (1) improved capabilities in brain imaging and recording and (2) the availability of new tools and methods for representing and analyzing networks – graph theory. Some basic terminology is shown in the figure below:

A networks consist of nodes and edges. The number of edges that are attached to each node correspond to its degree (k = 3). Highly connected nodes are hubs. Networks consist of modules which connect within or between them. When hubs connect with other nodes in the same module they are named provincial hubs, in contrast, connector hubs connect with nodes that belong to different modules.
The few research findings analyzing network differences related to intelligence do not allow for a generalization, although most research seems to support a specialization model of intelligence with emphasis on the frontal-parietal lobes and global efficient allocation of resources in a small-world model of the brain (Thatcher et. al., 2016).

A possible scenario for future research was recently outlined by Santarnecchi and Rossi (2016). It includes several steps: (1) Network nodes and connections essential for intelligent performance are identified (e.g., Santarnecchi, et al., 2015; Pineda-Pardo, et al., 2016; Ponsoda et al., 2016). (2) The identified networks serve as targets for subsequent rTMS stimulation.

This step would further include loading  participants’  functional connectivity data into a frameless stereotactic optical tracking neuronavigation system, which would permit key nodes for intelligent performance to be reliably stimulated within subsequent rTMS sessions (neuronavigated brain stimulation).  (3) The use of fcMRI to asses for possible changes in brain networks targeted during rTMS. (4) Analysis of behavioral measures (IQ tests) to establish possible beneficial/disruptive effects of rTMS. This part could be further accompanied with fMRI or other measures of brain imaging.

Perspectives for future research
Whenever writing about scientific predictions, the first landing on the Moon pops into my mind. Why? Because it is a scholarly example of false predictions. In 1969 it was seriously estimated that by the end of the century we will face lunar colonies living in bases build on the Moon, and missions to orbit or even land on Mars. At that time one would be probably diagnosed insane if predicting that in 2016 a mission to Moon would be regarded a mission impossible, not to speak about Mars.

In my opinion the brain-intelligence enigma can only be unraveled by analyzing brain oscillations. An attempt in this direction is the project put forward by Arturo Tozzi:  “Is there a modular function underlying physical and biological phenomena?”

In recent research it was found that the real part of the modular function j, central in the assessment of abstract mathematical problems, can be in more than 85% of cases spotted in the resting electric activity (EEG) of the human brain.

We hypothesized that the recurring j-oscillations are disrupted during pathology, but could also be otherwise altered in relation to personality or intelligence paving the way to novel approaches for a better understanding of humans.

The only numerical measures of intelligence are test scores. They are theoretically based on psychometric g, which is an empirical outcome of factor analysis that accounts for a large proportion of variance in individuals’ mental tests (Spearman, 1927). In other words, individuals who perform well on one mental task tend to perform well on most others. The higher the g-loading of a test is, the more it is considered to include the essence of intelligence.

Although this is one of the most often replicated findings in social science, it cannot conceal that intelligence is what the test is testing (Boring, 1923). Therefore IQ scores are heavily criticized and demonized, especially when researchers try to answer questions which oppose the current Zeitgeist, such as, are there differences in cognitive abilities between populations or between genders? Sometimes the answers may even lead to violence, as was the case for Jensen’s (1969) statement that compensatory education in the US failed to produce lasting beneficial effects on children’s IQ. Consequently he had to be escorted by security guards when moving around campus.

One has to admit that based on IQ test scores, these two questions have no answer that would withstand scientific rigor. To give just an example for the second sex-related question. As noted by Ackerman (2006), whether males or females differ in general intelligence depends on the test used to assess cognitive ability.  Test designers had two options, either to use separate norms for males and females, as it is done in some personality questionnaires, or to remove items that show sex bias.

When Terman (1916) provided test norms for the Binet-Simon Intelligence test, the sex differences were in his opinion negligible and therefore ignored, thus the same IQ scale for boys and girls was adopted. In later years when the scale was refined, items that showed greater sex differences were eliminated.

The same holds true for the third revision of WAIS. As put forward by Irwing (2012), the WAIS-III manual documents state that extensive procedures were used in the construction of the test in order to eliminate sex bias. For instance, the test does not include 3-D mental rotation tasks, for which a large male advantage was found (Miller & Halperen, 2014).

It is therefore not surprising that research into neural underpinnings of intelligence has most often tried to find an IQ biomarker. This attempt makes sense because from a brain perspective, intelligence is just a specific sequence of action potentials. Some promising candidates in the past were string length and individual alpha frequency (IAF), which were later replaced by more sophisticated measures derived from mathematics – chaos and graph theories. The disappointing part is that they still do not explain much more than about 10% of IQ test score variance.

The string length
The string length measure was introduced by Hendrickson and Hendrickson (1980) based on Rhodes’ et al. (1969) excursion measure, which they determined using a map-reading wheel following the ERP curve. They reported a high correlation of 0.77 between the string measure and IQ (Eureka!). It seemed as though a useful biomarker of IQ was discovered.

The theoretical explanation was that differences in intelligence reflect the rate at which errors are produced during the train of neural transmissions underlying problem solving.

High IQ individuals make fewer errors than low IQ individuals, thus the individual epochs are less variable from trial to trial, preserving more detail of the single evoked response, and therefore producing a more complex ERP (Hendrickson and Hendrickson, 1980). High correlations were also reported by Stough et al. (1990).

Others found modest correlations (e.g.,  Haier et al., 1983), correlations near zero (e.g., Barrett and Eysenck, 1994), and even negative correlations (e.g., Bates and Eysenck, 1993). Negative correlations between the string measure and verbal IQ, and positive correlations with performance IQ were observed by Batt et al. (1999). These contradictory observations provoked numerous theories which have attempted to explain the ERP-IQ relationship. Bates and Eysenck (1993) proposed that the relationship between the string measure and IQ depends on the attentional demands of the task.

Tasks which demand focused attention produce a negative correlation between IQ and string length, because the string measure is supposed to index the efficiency of the brain. In unattended conditions, however, the string measure indexes brain capacity and therefore the correlation is expected to be positive. Studies by Burns et al. (1997) and Batt et al. (1999) did not confirm this hypothesis. The bitter end for the string length measure came with the conclusion by Burns et al. (1997), stating that it is not a valid measure of the ERP.

Nonlinear Dynamical Systems and Chaos Theory
Nonlinear EEG analysis started in 1985, when Rapp et al. (1985) used chaos theory to analyze spontaneous neural activity in the motor cortex of a monkey. The first studies employing chaos theory and nonlinear measures (e.g. Lyapunov exponent L1, correlation dimension D2, or Kolmogorov entropy K2) to explain the brain-intelligence relationship were done in our lab.

During problem solving, less chaotic EEG patterns have been observed in more intelligent individuals (Jaušovec, 1998; Anokhin et al., 1999) and in more creative ones (Mölle et al., 1999).

The main problem related to the nonlinear analysis of EEG data is a mathematical one. Most of the measures used to determine low deterministic chaos were not designed to be used with relatively short and noisy data sets such as EEG. Hence, approximate entropy (ApEn) was introduced as a quantification of regularity in time-series data.

It has been shown that ApEn can distinguish a wide variety of systems ranging from multi periodic, to stochastic and mixed systems; furthermore, it is applicable to noisy, medium-sized data sets. Mathematically, ApEn measures the likelihood that runs of patterns that are close in one observation remain close on the following incremental comparisons (Pincus, 1995).

In a second study conducted in our lab (Jaušovec and Jaušovec, 2000a), several experiments using visual and auditory oddball tasks were used to clarify the relation between ERP complexity and  intelligence. The correlations indicated that in the attended conditions, more intelligent individuals showed more regular ERP waveforms than less intelligent individuals.

These trends were observed both in auditory and visual oddball paradigms. The negative correlations between ApEn and different intelligence measures obtained in the study suggest that high intelligent individuals have more spatially and temporarily coordinated electro cortical activity when engaged in cognitive tasks – they are less chaotic thinkers.

IAF, a never-ending story
Peak alpha frequency or individual alpha frequency (IAF) is the frequency with the highest magnitude in FFT-derived estimates of spectral power (maximum alpha power in a 7 to 14 Hz window – see figure below).

IAF is assumed to be related to the characteristics of white matter structure, like fiber density, axonal diameter, and myelination, and captures different neural processes than alpha power (e.g., Jann et al., 2010).

The idea that brains that run faster are also smarter is appealing, however the research evidence is rather weak. Some early research conducted before 1960 reported positive correlations. Considering the technical possibilities at that time, it is questionable whether the findings can be compared to those obtained with EEG acquisition systems available today. For instance, Mundy-Castle (1960) reported a positive correlation (r = 0.34) between what he called alpha frequency and IQ. For a detailed review of research on the relation between EEG measures and intelligence done before 1964 see Vogel and Broverman (1964).


Studies performed on more sophisticated EEG acquisition systems and software provided mixed findings. The study by Anokhin and Vogel (1996) showed positive correlations between peak alpha frequency (eyes closed) and test scores obtained on Raven’s matrices (correlations between .20 to .36). On the other hand, two large scale studies conducted in our lab (Jaušovec and Jaušovec, 2000b) and by Posthuma and colleagues (2001) showed no significant correlations between IAF and IQ (WAIS). Recently, Grandy et al.

(2013) used structural equation modelling to estimate the association between IAF and intellectual functioning.

The correlation between g (Berlin Intelligence Structure test – BIS) and composed eyes open/closed IAF was .40 (n = 85). However, the correlations reported ranged between .06 and .37; the highest correlations were reported for the memory tests, followed by tests of perceptual speed, and were not significant for the reasoning part of BIS. Among the 12 correlations determined (eyes: open/close; subtests: speed, memory and reasoning; respondents: young/old) only 5 were significant at a p < .05 level. Hence, none would have survived a correction for multiple comparison.

In yet another study from our lab (Pahor and Jaušovec, 2016), three experiments were conducted in order to investigate this relationship: two correlational studies and a third study in which we experimentally induced changes in IAF by means of transcranial alternating current stimulation (tACS). (1) In a large scale study (n=417), no significant correlations between IAF and IQ were observed. However, in males IAF positively correlated with mental rotation and shape manipulation and with an attentional focus on detail.

(2) The second study showed sex-specific correlations between IAF (obtained during task performance) and scope of attention in males and between IAF and reaction time in females. (3) In the third study, individuals’ IAF was increased with tACS. The induced changes in IAF had a disrupting effect on male performance on Raven’s matrices, whereas a mild positive effect was observed for females. Neuro-electric activity after verum tACS showed increased desynchronization in the upper alpha band and dissociation between fronto-parietal and right temporal brain areas during performance on Raven’s matrices.


Small-World Networks, Hubs, Local and Global Efficiency – Graph Theory
Sporns and Betzel (2016) see the developing network-based perspective on brain function as a result of two strands of research: (1) improved capabilities in brain imaging and recording and (2) the availability of new tools and methods for representing and analyzing networks – graph theory. Some basic terminology is shown in the figure below:

A networks consist of nodes and edges. The number of edges that are attached to each node correspond to its degree (k = 3). Highly connected nodes are hubs. Networks consist of modules which connect within or between them. When hubs connect with other nodes in the same module they are named provincial hubs, in contrast, connector hubs connect with nodes that belong to different modules.

The few research findings analyzing network differences related to intelligence do not allow for a generalization, although most research seems to support a specialization model of intelligence with emphasis on the frontal-parietal lobes and global efficient allocation of resources in a small-world model of the brain (Thatcher et. al., 2016). A possible scenario for future research was recently outlined by Santarnecchi and Rossi (2016).

 It includes several steps: (1) Network nodes and connections essential for intelligent performance are identified (e.g., Santarnecchi, et al., 2015; Pineda-Pardo, et al., 2016; Ponsoda et al., 2016). (2) The identified networks serve as targets for subsequent rTMS stimulation.

This step would further include loading  participants’  functional connectivity data into a frameless stereotactic optical tracking neuronavigation system, which would permit key nodes for intelligent performance to be reliably stimulated within subsequent rTMS sessions (neuronavigated brain stimulation).

(3) The use of fcMRI to asses for possible changes in brain networks targeted during rTMS. (4) Analysis of behavioral measures (IQ tests) to establish possible beneficial/disruptive effects of rTMS. This part could be further accompanied with fMRI or other measures of brain imaging.

Whenever writing about scientific predictions, the first landing on the Moon pops into my mind. Why? Because it is a scholarly example of false predictions.

 In 1969 it was seriously estimated that by the end of the century we will face lunar colonies living in bases build on the Moon, and missions to orbit or even land on Mars. At that time one would be probably diagnosed insane if predicting that in 2016 a mission to Moon would be regarded a mission impossible, not to speak about Mars.

In my opinion the brain-intelligence enigma can only be unraveled by analyzing brain oscillations. An attempt in this direction is the project put forward by Arturo Tozzi:  “Is there a modular function underlying physical and biological phenomena?”

In recent research it was found that the real part of the modular function j, central in the assessment of abstract mathematical problems, can be in more than 85% of cases spotted in the resting electric activity (EEG) of the human brain.

We hypothesized that the recurring j-oscillations are disrupted during pathology, but could also be otherwise altered in relation to personality or intelligence paving the way to novel approaches for a better understanding of humans.