Timing in cognition and EEG brain dynamics: discreteness versus continuity

This means that there exists a particular minimal inter-stimulus interval for which two successive events are consistently perceived as simultaneous.

Usually it is considered that things which are analog to be continuous and things which are digital to be discrete (Suber 1988; see also Eliasmith 2000). However, see Blachowitz (1997) in support of the ubiquity of this synonymizing and for an alternative to it.

Consider a typical transistor. The processes in it are indeed continuous: That is its transfer function traces out a (nonlinear, continuous) S-shaped curve—that is why they are used as both switches and amplifiers (Eliasmith 2002). Nevertheless, we treat them as if they are only ever in one of the two possible states. Consistently with this analogy, van Gelder (1995) claims that even though neurons and neuronal assemblies may be considered as discrete in state, this does not mean that they are discrete in time.

Figure 1 also illustrates the continuity and discreteness for the spatial dimension (see B). For the case of continuity, the change of neuronal activity appeared in a gradual fashion, whereas for the discrete condition, the change of neuronal activity appeared abruptly.

To illustrate this point, consider only one example, which we borrow form Llinas et al. (1998, p 1841): “We know full well that if we are tired we can fall asleep extraordinarily quickly and that if we are asleep and a strong stimulus is given to us (e.g. the havoc played by an alarm clock) we can awaken also extraordinarily fast. It is so fast, indeed, that the only substrate capable of supporting the speed of these two events must be electrical in nature given the large number of elements involved...” EEG is mainly the “product” of the cortex. With this respect, there is interesting finding: Sahraie et al. (1997) compared brain activity in a single blindsight subject (G.Y.) generated by stimuli which give rise to awareness with activity generated by stimuli (permitting similar levels of discrimination) without awareness. They found that the shift between “aware” and “unaware” modes was associated with a shift in the pattern of activity from cortical to subcortical levels. Nunez (2000) also stated that subcortical activity is only weakly correlated with cognition and behavior. However, one should acknowledge the importance of such factors as the effects of some definite neurotransmitters controlled by thalamus (Newman 1995) and the establishment of reentrant thalamocortical loops for oscillatory EEG synchronization in order to bind specific features for consciously cognitive representation of the objects that are integrated from these features (Bachmann 1984; Llinas et al. 2002).

The OA framework has its origin in the work of Kaplan and coworkers (Kaplan 1995, 1998, 1999; Kaplan et al. 1997; Kaplan and Shishkin 2000). We thoroughly endorse what they state, since our own particular perspective on the problem of brain-mind functioning does not differ substantially, although our choice of emphasis is very different in places.

This approach goes back to Hebb (1949); however, the classical neural assemblies are too slow and may be not suitable for cognitive operations (Kaplan and Borisov 2003). Modern understanding of neural assemblies stresses its functional nature, which is at scales both coarser and finer than that of the classical ones (von der Malsburg 1999). The idea is that large neuronal populations can quickly become associated or disassociated, thus giving rise to transient assemblies (Frison 2000; Triesch and von der Malsburg 2001), which thought to execute the basic operations of informational processing (Averbeck and Lee 2004). For definition of “brain operation,” see Fingelkurts and Fingelkurts (2003, 2005). It is important to note here that the cell assembly’s concept is difficult to falsify (see Appendix 2 for details).

If the data is stationary, its dynamics does not change significantly during the acquisition period, thus been stable. Therefore, quasi-stationary means almost (or near) stable.

The attributes are the following: (1) Average amplitude within each segment (μV)—as generally agreed, indicates mainly the volume or size of neuronal population: indeed, the more neurons recruited into assembly through local synchronization of their activity, the higher will be the amplitude of corresponding to this assembly oscillations in the EEG (Nunez 2000); (2) Average length of segments (ms)—illustrates the functional life-span of neuronal population or the duration of operations produced by this population: since the transient NA functions during a particular time interval, this period is reflected in EEG as a stabilized interval of quasi-stationary activity (Fell et al. 2000; Kaplan and Shishkin 2000); (3) Coefficient of amplitude variability within segments (%)—shows the stability of local neuronal synchronization within neuronal population or assembly (Truccolo et al. 2002); (4) Average amplitude relation among adjacent segments (%)—indicates the NA behavior—growth (recruiting of new neurons) or distraction (functional elimination of neurons) (Kaplan and Borisov 2003); (5) Average steepness among adjacent segments (estimated in the close area of RTP) (%)—reflects the speed of neuronal population growth or distraction (Kaplan and Borisov 2003).

Although the concept of metastability has been around in physics for a long time, the specific interpretation of metastability in the context of a theoretical model of the coordination dynamics in the brain has been developed by Kelso (1991). Metastability is a theory of how global integrative and local segregative tendencies in the brain coexist (Kelso 1995; Friston 1997; Kaplan 1998). In the metastable regime of brain functioning, the individual parts of the brain exhibit tendencies to function autonomously at the same time as they exhibit tendencies for coordinated activity (Bressler and Kelso 2001; see also Fingelkurts and Fingelkurts 2001, 2004). The synchronized operations of distributed neuronal assemblies are metastable spatial-temporal patterns because intrinsic differences in activity between the neuronal assemblies are sufficiently large that they do their own job, while still retaining a tendency to be coordinated together.

OM means that the set of the neuronal assemblies synchronously participated in the same cognitive act during the analyzed period. The criterion for defining an OM is a sequence of the same synchro-complexes (SC). Whereby, SC is a set of EEG channels in which each channel forms a paired combination (with high values of index of structural synchrony) with all other EEG channels in the same set (Fig. 3a); meaning that all pairs of channels in an SC have to have significant index of structural synchrony (Fingelkurts et al. 2004b). For the properties of OM see Fingelkurts and Fingelkurts (2005).

The index of structural synchrony (ISS) is estimated through synchronization of rapid transition processes (RTP)—boundaries between quasi-stationary segments—between different EEG channels. This procedure reveals the functional (operational) interrelationships between cortical sites as distinct from those measured using correlation, coherence and phase analysis (Kaplan et al. 2005).

These values coincide precisely with the mean microstate duration of entire neocortex (82 ± 4 ms) obtained for healthy young adults using Lehmann approach (Koenig et al. 2002), which is essentially different from our method. Thus, these data cross-validate each other.

It has been demonstrated that if two areas of cortex are operationally synchronized, then they tend to be also synchronized with some other areas (Fingelkurts 1998). Calculations showed that the power-law statistics governs the probability that a number of cortical areas are recruited into an OM. This ubiquitous dependency is characterized by a fractal relation between different levels of resolution of the data, a property also called self-organized criticality (Bak et al. 1987).

Isomorphism is generally defined as a mapping of one entity into another having the same elemental structure, whereby the behaviors of the two entities are identically describable (Warfield 1977). A functional isomorphism on the other hand requires the functional connectivity between its component entities (Lehar 2003). It is an extension to Müller's psychophysical postulate (Müller 1896), and Chalmers' principle of structural coherence (Chalmers 1995).

Indeed, experimental evidence suggests that the behavioral or cognitive continuum is a succession of discrete behavioral/cognitive acts performed by an individual (Alexandrov 1999; Madison 2001). Each separate act is the integration of a certain number of operations, which are important and appropriate for the realization of this act. The change from one behavioral/cognitive act to another is embedded in a rapid “transitional process” (Alexandrov 1999). The same is true for the phenomenological structure of human consciousness which consists of stable nuclei (or thoughts) and transitive fringes (or periods)—as it is described by James’ metaphor of “Stream of Thoughts” (James 1890). It seems that metastability provides a mechanism of the functional isomorphism realization (Fingelkurts and Fingelkurts 2004).

In this effect normal listeners report hearing audio-visually fusion syllables as some combination of the auditory and visual syllables (e.g., auditory /ba/ + visual /ga/ are perceived as /va/) or as a syllable dominated by the visual syllable (e.g., auditory /ba/ + visual /va/ are perceived as /va/). The vast majority of people (but not all) experience the McGurk illusion. It was also shown that the McGurk illusion exists between other sensory modalities.

Here there are no restrictions for the relations between frequency bands, because the method we used for assessing the OMs is not associated with the phase relation as the usual techniques estimating synchrony (Kaplan et al. 2005).

This point has been emphasized many times during history of psychophysiology science as a “limited capacity of conscious state” (James 1890; Kahneman 1978; Posner 1987; Baars 1988; von der Malsburg 1997).

Complexity hierarchy enables the system to build complex representations from primitive ones so that the semantic value of the complex representation is determined by, and dependent on, the semantic values of the primitives (Fingelkurts and Fingelkurts 2003).

It should be stressed that the concepts “state” and “contents” of consciousness should be differentiated from each other. The “contents” of consciousness refer to the patterns of subjective experience at the phenomenal level: percepts, emotions, sensations, mental images, etc. (Block 1995), while the term “state” of consciousness refers to the underlying context in the brain in which the phenomenal contents of consciousness are realized. Thus, the “state” does not refer to the subjective experiences themselves (Kallio and Revonsuo 2003).

The use of a posthypnotic suggestion would minimize the need for suggestions of relaxation, drowsiness, etc. which are typically used in a hypnotic induction (Kallio and Revonsuo 2003).