Tuesday, March 25, 2014

Zero power and selflessness: What meditation and conscious perception have in common

Zero power and selflessness:  What meditation and conscious perception have in common

                          Sean O Nuallain
Published in cognitive Sciences 4(2)

University of Ireland, Ca and  
and Nous Research, Dublin, Ireland


This paper attempts to reconstrue the art and science of meditation in the context of an overall theory of cognition, and with reference to evidence from simulated and real data analysed in a neurodynamical framework. First, we discuss the phenomenology of meditation and its relation to the known evidence. It is argued that meditation is on a continuum with the types of conscious mental activity characterized by gamma waves, particularly synchronized gamma. Specifically, it is suggested that gamma synchrony in meditation allows the normally prominent background noise of the brain momentarily to subside in like synchrony. Secondly, a set of experiments using both simulated and real data and interpreted in a neurodynamical context that bear on the issue of meditation is described. The isomorphism between the similar and real data is established before a set of ECOG data involving a single brain in epileptic seizure, resting and performing a task is adduced. It is argued that seizure, above all,  reveals the desirability of intervals of “zero power”. Thirdly, the theoretical and experimental frameworks are brought together into a brief sketch of an overall perspective that impacts on cognition as on applied experientialism.

1. Introduction

The neurophysiological literature on meditation is vast and confusing. It ranges from the borders of the New Age (Murphy et al, 1988) to more hardcore science (Wallace et al, 1972) to the hallowed PNAS (Lutz et al, 2004).  The benefits of meditation have plausibly been proven to be perceptual (Tloczynski et al, 2000), anti-ageing due to gross cortical changes (Lazar et al, 2005), and finally enormous in that links between the nervous and immune systems are exploited to implement improvements in health (Davidson et al, 2003). One recent paper has implicitly challenged the consensus that gamma synchrony is at the core of the successful meditative experience; yet Chang et al's (2005) paper shows no sign of having tested for gamma, which they do not even explicitly mention. In their paper, it is handled, if at all, as high beta, and in fact can be encompassed within the theoretical framework about to be outlined here.

Perhaps a more important contrarian voice, from an anthology of his writings on the subject,  is that of J. Krishnamurti (1999);

“Meditation is one of the greatest arts in life.....it has no technique, and therefore no authority” (P. 2)

“Meditation according to a system is the avoidance of the fact of what you are; it is far more important to understand yourself” (p. 55)

Following classical practical spirituality (described, inter alia, in Ó Nualláin (2006)), Krishnamurti emphasises self-observation as the key to that experience he calls “meditation”;

“Every system, method, binds thought to time, but choiceless awareness of every thought and feeling.....is the beginning of meditation” (41)

“Meditation is not something different from daily life.....Watching all that, realizing your part in it, all that is part of meditation” (12)

The enemy, again as in classical spirituality, is what is normally known as the “self”

“Without knowing the activities of the self, meditation becomes sensuous excitement and therefore of very little significance”(7)

“In that attention there is no frontier, there is no center, as the 'me' who is aware or attentive. That attention, that silence, is a state of meditation” (21)

While disabusing the initiate of the notion that there will be spectacular visions,  Krishnamurti is eager to emphasise that the experience of the senses will be sharpened and heightened ;

“Perception without the word .....is more acute,not only with the brain but also with all the senses. ....It can be called a total perception, and is part of meditation” (25)

So we now have an echo of Tloczynski et al (2000) in that sense-perception is made more acute as a result of meditation. However, much more can be said

“As you watched, a great stillness came into you. The brain itself became very still....the quality of that silence, that stillness, is not felt by the brain; it is beyond the brain” (63-64)

“Meditation which began at unknown depths, and went on with increasing intensity and sweep, carved the brain into total silence, scooping out the depths of thought, uprooting feeling” (79)

Again, this must be in some sense an egoless state, with “thought” and the empirical self now explicitly being identified;

“And it was meditation without the meditator. The meditator interferes with his stupidities and vanities,  ambitions and greed. The meditator is thought” (ibid.)

Finally, Krishnamurti (4) presages much of the discussion about to take place with one comment;

“Meditation is to find out whether the brain, with all its activities, all its experiences, can be absolutely quiet...that quietness is not sleep but is tremendously active and therefore quiet.... A big dynamo that is working perfectly hardly makes a sound; it is only when there is friction that there is noise”

Let us anticipate the major argument in this paper. By using the Hilbert transform, we can calculate, moment to moment, the power of the background activity of the brain, which itself is a major consumer of the total energy of the entire organism. When superimposed over by any oscillation, the phenomena of “beats” occurs and the power of the background activity is momentarily zero. The faster the superimposing wave, the more frequent the occurrence of zero power (and thus amplitude, which explains the apparently anomalous findings of Chang et al (2005)). So gamma oscillations will cause the greatest number of zero power moments. Obviously, while totally synchronized gamma is observationally impossible (given the relative crudity of the measures like calcium ions that are used), the impressively synchronized observations of Lutz et al (2004) will produce many moments of zero power. So the observations of Chang et al and Lutz et al can be synthesised; high gamma leads to a frequent incidence of zero power moments.

Elsewhere (O Nualláin, 2008, and forthcoming) , this author has argued that self is essentially an artefact of the necessary maintenance of differentiation between subject and object.  In the safe environments in which meditation happens, these distinctions can, at least momentarily, be let go. It is possible that, through Buddhist and other meditative training, the self can be identified with observation itself, with choiceless awareness. Not only that; the brain is now maximally sensitive (Freeman 2002, 2003, 2005a and b).

By the end of this paper, the reader will hopefully be convinced of the plausibility of this scenario vis a vis “formal” Buddhist meditation. However, we have seen Krishnamurti argue that this type of ritual is unnecessary; meditation starts with self-observation, and can be experienced anywhere. Moreover, there is an extremely well-attested body of work by Singer et al (1995) indicating that beta and gamma synchrony accompany conscious perception. Can we weave together a narrative in which all these strands cohere?

With respect to such a narrative,Singer (2007) emphasises temporal codes in the brain, and argues that gamma synchrony is ubiquitous in cognition. Elsewhere (O Nualláin et al, in press) our group at Nous Research has produced a theoretical model that can explain how an oscillation like gamma can affect the firing of individual neurons. For the central purposes of the current paper, the recent work by Melloni, Singer et al (2007) is critical, wherein it is showed that conscious perception depends on prior gamma synchrony

Consequently, both meditation and conscious perception seem intimately related to gamma activity. After perusing section 2 below,  the  reader will hopefully be open to the argument that the major role of gamma, and in particular gamma that is synchronized and/or high amplitude, may well be its capacity to induce moments of zero power on the overall activity of the brain.

On a phenomenal level, there is a consensus that the meditative state is in some way selfless ( Ó Nualláin, 2006). Gazzaniga (2008) summarises his life's work by re-emphasising the theme that our experience has a narrative imposed on it by an “interpreter” in the left hemisphere. This is consistent with the famous Libet (1994) observation that the action potential for a voluntary act has been in preparation for fully tenths of seconds before we become aware of it. Our narratives to ourselves impose continuity on discontinuity, and attribute agency to ourselves when utterly inappropriate. Agency as a concept needs to be correspondingly attenuated; when the intending of an act presents itself to consciousness, it is experienced as a cause; consciousness of the consequences thereof are experienced as effects. This vastly consequential idea is consistent with  Libet's classic work and amplified in the Freeman opera (ibid.).

Once an action is lined up, the brain prepares the system for the sensory consequences of this action in what is called the preafference process. According to Freeman, globally coherent brain activity may be an objective correlate of consciousness through preafference.  Preafference, in turn, enters once the more veridical notion of circular causality is substituted for the stimulus-response act.  The consequences for consciousness qua process are enormous. It functions similarly to an organizer in a thermostat. Hume was right; there is no conscious will, but there does exist a conscious “won't”.

Meditation occurs in contexts in which the organism is expecting minimal sensory consequences of its actions.  If it is the case that regular states of “Zero power” and maximum sensitivity occur, the self may well be able to identify with and thus make a phenomenal state of that zero power process. Consciousness may be due either to the globally coherent activity, or to the fact that the brain has entered a zero power state through which consciousness can now transparently act.  This issue is possibly  unresolvable even in principle; we explore it a little more in conclusion.

2.     Experimental evidence

Freeman, O'Nuallain and Rodriguez(in press) include much of the detail of the work about to be presented here.  O Nuallain (in preparation)specifies some of the programming detail left out in that paper.
In summary, phase slippage and beat phenomena are ubiquitous in any form of wave superposition. Likewise, it is trivially true that cumulative summation of individual random events gives rise to Brownian motion simulation. Freeman et al (ibid.) proposes a simulation environment in which these phenomena are interrelated with cortical function. In particular, we have found that phase slippage for brown noise filtered at frequencies corresponding to beta and gamma EEG gives null power spike effects. These null spikes, in turn, occur at rates similar to those that we have experimentally found in test subjects. We compared data from our simulation with those taken from a human experimental subject undergoing neurosurgery for epileptic seizure; the protocol is described in Freeman (2006).

2.1 Methodology

We begin from the assumption that neuronal activity in the resting brain  can be simulated by white noise. Specifically, the average firing and refractory periods suggest a Nyquist frequency of 250 Hz, with a nominal timestep of 2 ms. There is therefore nothing remarkable about the white noise, as indicated in Figure 1a. The facts that true randomness cannot of course be algorithmically generated, and that there would be numerical, as distinct from mathematical inexactitude, had some consequences  in that the null spikes we describe below occasionally did not in fact go to zero. 

Figure 1a; pseudo-white noise, simulating random firing of neurons with the brain in a resting state.

White noise is simply a sum over excitatory neurons, stabilized by refractory periods rather than inhibition. Rather, inhibition provides a bandpass filter. In the case where we have a short delay and feedback, gamma oscillations ensue; for longer such, it is beta. “Real” white noise, as represented in 1b, shows internal correlation, as would be expected;

We then considered populations of neurons, which we terms the “mesoscopic” level of analysis (Freeman 2000).  This, again, is construed as a cumulative summation of the white noise. Alternatively, of course, we could have chosen to sum the later-applied filter directly to the white noise; our investigation in this direction indicated that the results were exactly the same.  The frequency profile was as suggested in Schroeder(1991).

2.2 Findings

Freeman (1975, 2002, 2003) provides the interpretive context for this work. In  a neurodynamics approach, he argues that 3-7 times a second, the brain approaches a limit attractor cycle at which any external signal is amplified as the noise abates at the singularity. Consequently,  there is no need to invoke stochastic resonance to explain how extremely weak signals get detected. At this point, the phase is undefined and background noise is  minimised. Freeman (2006) features experimental data showing this phase slippage occurring in experimental subjects at the intervals predicted.

Let us first look at the log of analytic power plotted against time at both the   theta and gamma frequencies (Figs 2a and 2b) for the simulated data.  Observations of EEG show frame rates in the range of 3-7 Hz; at the low end for beta, and the high end for gamma. The results here support this, and below we have a comparison with real data. Freeman (2005a) has suggested that the cortex can change with great rapidity from one complex state into another since it has effectively got a fractal structure. Self-similarity is therefore a crucial theme; our work shows that the analysis of the brownian motion at various filters shows similarity in the graph form

Figure 2a; Log of analytic power graphed against time, theta frequency.

Figure 2b; Log of analytic power graphed against time, gamma frequency.

We include a figure (Figure 3a)showing that the power is occasionally less during the null spikes than the peak by a factor of up to ten thousand; this is encouragingly similar in the “real data” version in Figure 3b

Figures 3a and 3b

Text Box:

Under analysis, the real data showed almost identical null spiking behaviour, as indicated in figures 4a and 4b. As the data were collected under a different regime, and in order to demonstrate the generality of the method, we use a different Nyquist frequency for the simulated data

Figure 4a null spike pattern, gamma  frequency, simulated data

Figure 4b Null spike pattern, gamma frequency, real data

However, the gross power consumption of the brain is the issue that we are most concerned with here. The hypothesis is that, by gamma wave superposition on the background noise, which “noise” actually comprises a significant proportion of the organism's metabolic energy, meditation and indeed fully  conscious perception results in less energy consumption by the organism. Figure 5a shows one extreme case, that of brown noise during an epileptic seizure, where the lack of stabilization by refractory periods results in massive metabolic requirements. It is worth pointing out that, although the negative exponential suggested by 5b does not always occur in the case of the resting brain, all data sets involving seizure show this monotonic upward trend;

This can be contrasted with the metabolic requirement of a brain at rest in 5b, which conforms with the classical Freeman requirement of a negative exponent, to which he attributes the self-similarity in 2a and 2b;

For the removal of doubt, it should be said that the scaling is exactly the same in each. Finally, 5c shows the same spectrum for a brain doing a cognitive task;

2.3 Interpretation of the experimental evidence

The general hypothesis that there exists periods of self-organised criticality in which brain activity is essentially “reset” is supported by this work. Moreover, it can indeed be argued that this vital aspect of brain activity is a result of a general mathematical property of the  filtering of brown noise at certain fractions of the Nyquist frequency. A narrative emerges; beta and gamma are artifacts of the operation of inhibitory neurons. These frequencies, superimposed on the brown noise provided by the mass action of groups of neurons, introduce a “shutter” in the brain's operations. Just as we need microsaccades in order to see anything, it seems to be the case  that we need null spikes in activity for cognition to continue. We intend to explore this aspect in future papers.

We are happy to make the code and data available to any researchers who want to replicate the work. There is one specific finding that we find intriguing, and may act as a motivating factor. Can it be the case that brown noise filtered at frequencies corresponding in Nyquist terms to gamma produces phase slips in the upper end of the 3-7 times per second that we have observed as the canonical rate of phase transition in the brain? If that is the case, the brain is exploiting a general mathematical law in order to maximise its sensitivity at a certain predetermined rate (which, again intriguingly, is of the same order as the “conscious moment” of a tenth of a second, the minimum time from which we can consciously access a perceived scene)

Buttressing this idea, the convergence of the behaviour of our simulation with real data is a helpful result. We intend,  in collaboration with others, to extend the analysis to rabbit data from the visual and auditory cortices that were gathered at a Nyquist of 250. That will allow attestation of the notion that the brain maximises its sensitivity by exploiting the filtering of brown noise at certain frequencies as well as grounding in real experimental data.

3. Pansychism or internal process? - some final speculation on consciousness

 What is being asserted, then,  is that conscious states comprise a sparse sample of the wave packets propagating through the brain (Freeman, 2002) that embody motor commands, corollary discharges, and pre-perceptions that we conceive as unconscious. The   idea, pioneered by Piaget (1954, P. 434) that  “thought in its various aspects reproduces on its own plane the processes....in the case of sensorimotor intelligence and the structure of the initial practical universe” is accepted. Wave packets embodying motor commands are the substratum for mathematical and other abstract thought. Furthermore, focal consciousness samples at far too slow a rate to give veridical access to the contents of our cortices, and nature has gifted us various mechanisms to get around this, some of which are mentioned in my 2008 paper.

The meditative context inevitably facilitates attenuation of wave packet behaviour; it is normally a safe, stimulation-poor environment. Meditators are encouraged not to think of worldly concerns; even better, to simply observe such thoughts rising and falling. The attested health benefits of meditation may be partly due to the context itself  -  after all, it is quite a boon to be free of worries sufficiently as to be able just to sit for a while -  and, intriguingly, the fact that the power use of the brain will be lessened for a while, freeing metabolic energy up for such matters as getting glucose into cells.

However, many a reader will feel cheated by what looks like a philistinical exercise. What of the feelings of blessedness that even Chang et al (2005) speak of? Let us return to the issue of the self in meditation. From the Advaita Vedanta context which Krishnamurti has brilliantly popularised in the West, the self is conscious awareness. It is also identical with Brahman, reality, consciousness, being, bliss. It will always be open to scientist to reduce the meditative experience to the brain process that induces it as it well be open to the meditator to claim that her experience as a result of this process puts her in touch with a further experience of self which transcends everyday experience. It is this writer's guess that this final observation is the most certain statement in this largely technical paper.


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