The lectures are at http://universityofireland.com/course-neuroscience-and-experience/ and it costs $75 payable at foundationsofmind.org to get access to them. What follows is commentary on them;

The introductory lecture at http://universityofireland.com/neuro-lecture-sampler/ was self-explanatory

Lecture 1: On single neurons

We now begin the first technical lecture;

p/word as before

We will stay with this material until everyone is comfortable with it.

This is why we're doing this work;

Current theme; Single neurons - classical and quantum

Since our original work, quantum coherence at physiological temperatures has been demonstrated for biological systems in photosynthesis at the 3nm level characteristic of gap junctions in neurons (Hoyer et al, 2011). This finding converges with a controversy about quantum effects in neurons related to consciousness. While, in related work, we question the assumption in the later that “phase coherence” has in fact been demonstrated in the brain, there is a long-attested corpus of observations suggestive of entropically minimal states several times a second there.

We therefore speculate that gap junctions might allow a quantum superposition of states of the membrane potential of each neuron to be communicated to thousands of others. This will lead to entanglement of a scale that would allow the Fourier decomposition we envisage for the classical case be extended to a quantum description. This is the only currently physiologically plausible story about Quantum effects in the brain

In fact, we have data to indicate that much of the statistical inferences in classical EEE/ECOG evince premature closure, and that this approach is certainly not ready – pace, the ORCH OR proponents – for the non-classical world.

The existence of phase coherence in gamma waves in the brain, and the relation of this phenomenon to consciousness, is a point of much consensus, with only the recent work of Pockett and her colleagues contradicting it. It has been further argued that the entropically minimal state resulting from this phase coherence might yield an environment conducive to quantum coherence.

While we believe that the work of Walter Freeman indeed is indicative of entropically minimal states in th brain occurring several times a second, we believe that the EEG/ECOG signal is too coarse to indicate synchrony. Indeed, we have findings from PCA , among other methods, indicating that a 64-electrode grid produces at most two signals. As for phase coherence, the stated electronic specifications of the equipment use expressly prohibit any such inference, as the error range of the equipment is too large. So this study of single neurons over the next few classes is REALLY important

O Nuallain, S CSLI, Stanford and T. Doris(2004) http://bcats.stanford.edu/previous_bcats/bcats04/html/nuallain.html

Hoyer et al, (2011) http://arxiv.org/pdf/1106.2911.pdf

See also (2010) http://www.sciencemag.org/content/329/5999/1671

The critical paper on neural resonance is appended below

WHAT IS NEURAL RESONANCE FOR?

SEAN O NUALLAIN, University of Ireland USA AND TOM DORIS

ABSTRACT. Vast amounts of research, both theoretical and experimental, are being carried out about neural resonance, subthreshold oscillations, and stochastic resonance in the nervous system. In this paper, we first offer a radically different computational model of neural functioning, in which integrate and fire behaviour is seen as a special case of the more encompassing resonate and fire processes. After commenting on the explanatory vista opened up by this model, we speculate on its utility for signal processing.

KEYWORDS: Subthreshold oscillations; neural resonance; signal processing; resonate and fire.

1. Introduction

While neural resonance can exist without subthreshold oscillations, a vast literature connects the two. For Wu et al (2001), the oscillations emerge from membrane resonance. The resonant current is steady-state potassium current, amplified by a sodium current. Izhikevich (2002) most explicitly drew consequences from the fact that the Hodgkin-Huxley model is a resonator. His point that a neuron's firing may depend on the timing of its afferent impulses is one that we believe to be well-taken. We have been careful to ensure that our model caters to all the possible scenarios (in-phase doublets, and so on) that he envisages. Like Wu et al (op. cit.) he interrelates subthreshold oscillations and bursts, coming to the conclusion that the intervals in bursts may be significant for communication. This is one line of reasoning that emerges, transformed and extended, in our work.

System level phenomena are also increasingly beginning to attract attention. Wu et al (ibid.) comment that a single excitatory stimulus to a mesencephalic V neuron can result in high-frequency spiking in a whole network under certain circumstances. Even more interestingly, the phenomenon of stochastic resonance (SR) has come into focus in neuroscience. SR is essentially a non-linear systems phenomenon through which, apparently paradoxically, a noisy environment can be exploited to amplify a weak signal. Reinker et al (2004) integrate the two resonance phenomena by asserting that subthreshold neural resonance manifests itself when thalamocortical neurons are stimulated with sine waves of varying frequency, and stochastic resonance emerges when noise is added to these stimuli.

The possibility that these phenomena have computational utility has not been lost on these and other researchers. However, we believe that ours is the first work credibly to interrelate the signal-processing task faced millisecond to millisecond by the brain with the phenomena in question. In their review article, Hutcheon et al (2000) comment that resonance and oscillation may have a role in such phenomena as gamma waves. Rudolph et al (2001) venture a more specific conjecture; responsiveness of neo-cortical pyramidal neurons to subthreshold stimuli can indeed be enhanced by SR, and under certain conditions the statistics of this background activity, as distinct from its intensity, could become salient. Obviously, such forms could have computational consequences.

For Freeman et al (2003), the conversion of sensory data into meaning is mediated by those gamma wave processes. The distinction between ours and Freeman's approach, which we are admirers of, is that we are looking for the resonant frequencies at the microscopic level in single neurons using novel solutions to the 4th order Hodgkin-Huxley equation, whereas Freeman finds them at the mesoscopic level in the characteristic frequencies of populations. Nevertheless, the thrust of the two approaches, and the critique of the integrate-an-fire model, is similar.

Yet the integrate -and-fire (INF) neuron has emerged largely intact, even if supplemented with resonant abilities (Reinker et al, op cit.). In this paper, our first goal is to call the integrity of the INF paradigm into question in a novel way. In particular , we wish to show that INF behaviour can be viewed as a specific phase in the cycle of a different neural model, the resonate-and-fire model (RNF). Our model caters to all the bursting situations-doublet, triplet etc -identified by Izhikevich (2002). However, our background as computer scientists impels us on another previously unexplored path at this stage. What actually are the sensory data that the brain is operating on? Intriguingly, a decomposition of such stimuli into their constituent power spectra affords a vista in which each resonating neuron may accomplish a part of a Fourier transform. These digital analog signalling processing (DASP) concerns form the next part of the paper. We recognise that, since the frequencies involved are changing, a more complex function approximation method like the Hilbert transform may be closer to neuroscientific reality; however, the ethos whereby individual neurons or groups thereof have the roles proposed remains the same.

Yet the way ahead may be more fascinating still. While quantum computing, as distinct from quantum cryptography, may still be a generation away, computational tasks such as data base search have already been achieved by exploiting the phenomenon of classical wave interference. In the most speculative part of the paper, we propose that dendro-dendritic connections may be complicit in this. Particularly in neocortex the dendrodendritic connections have only recently been recognized, since they are comparatively uncommon, in contrast to the axosynaptic connections among pyramidal cells, accounting for maybe 85 Finally, we allude to further work that we have done in which the RNF paradigm is applied to some classical problems with artificial neural nets (ANNS).

2. The Resonate and Fire Model

The Hodgkin-Huxley system exhibits a stable low amplitude oscillation which can be considered in isolation to the production of action potentials. Izhikevich has done preliminary work on the possibility that neurons may exhibit either integrative or resonance properties. He posits that the neuron experiences a bifurcation of the rest state and depending on the outcome subsequently behaves as either an integrator or a resonator.

If the rest state disappears via fold or saddle-node on invariant circle bifurcations, then the neuron acts as an integrator; the higher the frequency of the input, the sooner it fires. If the rest state disappears via an Andronov-Hopf bifurcation, then the neuron acts as a resonator; it prefers a certain (resonant) frequency of the input spike train that is equal to a low-order multiple of its eigenfrequency. Increasing the frequency of the input may delay or even terminate its response.

Integrators have a well-defined threshold manifold, while resonators usually do not. Integrators distinguish between weak excitatory and inhibitory inputs, while resonators do not, since an inhibitory pulse can make a resonator fire.

Izhikevich points out that the Hodgkin-Huxley model exhibits behaviors which are a superset of the standard IFN model. The low amplitude oscillation of the membrane potential can be sustained for long periods without the need for an action potential to result. Only when the amplitude of oscillation reaches a threshold value does depolarisation and action potential generation ensue. The resonance phase of the process is non-trivial. Complex waveforms are permissible, and would suggest that this phase of neuronal behaviour is of some importance to the behaviour of the cognitive apparatus. The oscillations are directly related to the action potential, since the same parameter, membrane potential, is central to both phases. Since the action potential is of undoubted importance to the activity of the brain, it would appear that an intimately related phenomenon should be given thorough consideration. The IFN model is the result of a view of the neuron which only considers a brief period prior to the generation of the action potential. As such, we will show that the resonate and fire model is a superset of the IFN, that it is capable of capturing all of the properties of the IFN in addition to new and interesting capabilities with strong evidence supporting the idea that such properties are critical to the transduction of sensory data.

The physical basis for the resonate and fire model lies in the fact that every object has a frequency or a set of frequencies at which they naturally vibrate when struck, strummed or somehow distorted. Each of the natural frequencies at which an object vibrates is associated with a standing wave pattern. Standing waves are formed when oscillations are confined to a volume, and the incident waveform from the source interferes with the reflected waveform in such a way that certain points along the medium appear to be standing still. Such patterns of interference are produced in a medium only at specific frequencies referred to as harmonics. At frequencies other than the set of harmonic frequencies, the pattern of oscillation is irregular and non-repeating. While there are an infinite number of ways in which an object can oscillate, objects prefer only a specific set of modes of vibration. These preferred modes are those which result in the highest amplitude of vibration with the least input energy. Objects are most easily forced into these modes of vibration when disturbed at frequencies associated with their natural frequencies.

The model described here seeks to compromise between plausibility in the biological domain, and efficiency in the computational domain. The level of granularity of the model is an essential factor in this compromise. In order to model systems with many interacting neurons, it was necessary to avoid the computational overhead of compartmental models. The current model provides no spatial extent for its neurons. The mathematical physics governing the harmonic oscillator is used as a basis for the development of the resonate and fire model. The entity that actually oscillates is the membrane potential. The driving forces are the input spikes received on the neuron's dendritic field. The neuron's oscillations are lightly damped under normal conditions. For a brief period after firing, the oscillation is heavily damped, reflecting the quiescence period found in biological neurons, typically referred to as the absolute refractory period. The fundamental frequency of the neuron is a tunable parameter, in our consideration; the details which would determine this quantity in the biological instance are omitted. We treat it simply as a single parameter that may be set arbitrarily.

The oscillation of the membrane potential can alternatively be viewed as the oscillation of the threshold at which the action potential is generated. The arrival of an excitatory pulse to a dendrite will result in the summation of the current membrane potential with the new input. If the current membrane potential is high, smaller input will result in the threshold being reached and an action potential being generated. Similarly, if the current potential is low, a larger input will be required to force the resultant potential across the threshold. From this viewpoint, the resonate and fire model can be seen to be a superset of the IFN model. The behaviour of the IFN model can be simulated with a resonate and fire neuron with a low resonant frequency (long period). Input spikes are then summed in the usual manner with negligible influence from the oscillation of the membrane potential.

The IFN model, in which two neurons that innervate a third node with excitatory connection are always considered to cooperate, does not apply here. Such an event sequence also illustrates the other side of selective innervation, when the post-synaptic neuron is not selected by the pre-synaptic neuron, by virtue of the fact that its resonant frequency means that the interspike delay is not an integral multiple of the period of oscillation.

Such properties have obvious applications, one can envision an array of neurons forming a ``spectrographic map''; each neuron in the array is attuned to a different resonant frequency. Two input neurons innervate every neuron in the map, so that when the two input neurons fire, the time between their firing (inter-spike delay) will cause a single neuron in the map to react most positively. The neuron that reacts with an action potential is the neuron whose resonant period (the inverse of the frequency) most closely matches the inter-spike delay. Such an arrangement can be generalized to implement a pseudo-Fourier transform of an input channel. Each neuron in the spectrographic map will ``own'' a particular narrow frequency band. The input channel is a signal containing multiple frequencies superimposed upon one another. The input innervates all neurons in the map, which produce action potentials if their particular resonant frequency is present in the original signal.

The implementation details of the resonate and fire model are straightforward. We consider an idealized harmonic oscillator, similar to a mass on a spring. There is a single point of equilibrium in such a system, where the position of the mass is at the point where the spring is neither compressed nor stretched. The mass is assumed to be floating in free space outside the influence of the gravitational force, while the other end of the spring is bound to an idealized fixed point. The mass is displaced from the equilibrium point by the arrival of an impulse (push) of negligible duration. The displacement of the mass then oscillates back and forth past the equilibrium position. The spring exerts a ``return force'' proportional to the magnitude of the displacement. The frequency of oscillation is determined by both the size of the mass and the magnitude of the return force exerted by the spring. In the real world, all such oscillations gradually die off (though remain at the same frequency), due to the damping effects of friction.

A more familiar analogy would be that of a playground swing. Here the equilibrium position of the swing seat is directly below the supporting bar, i.e. hanging straight down. When we push the swing, it begins to swing to and fro (oscillate) past the equilibrium point. If we want to make the swings ``higher'' (increase the amplitude of oscillation) we must push the swing ``in phase'' with the basic oscillation. This simply means that we must push it as it is at the top of the back swing, or heading away from us. If we push it as it is coming toward us, we are pushing ``out of phase'' with the basic oscillation, and the amplitude thereby is decreased.

The mathematical details of the model follow directly from the math used to describe harmonic oscillation in bodies such as the mass on a spring, pendulums and playground swings. The task here is to translate the basic ideas into a form applicable to the resonate and fire neuron. Additionally we must formulate this in a manner that is amenable to computational implementation.

The starting point for analysis is to consider the mass on a spring arrangement. Here we have a mass that is displaced from the equilibrium point by

at any given moment; this displacement may be positive or negative. Due to the physical form of the spring, the mass always experiences a return force in the opposite direction to the current displacement:

where

is a positive constant referred to as the spring constant. This equation captures the fact that the return force is proportional to the current displacement. This is a key fact in that such systems are characterized among Harmonic Oscillators. The basic behaviour of Harmonic Oscillators is captured by the differential equation:

By Newton's second law, we can relate the mass, return force and acceleration thus:

Substituting we arrive at

The above equation is simply shorthand for that which we know intuitively. It states that the current acceleration is proportional to the current displacement, and in the opposite direction. For the purposes of simulation, we rewrite the equation in its more common form, replacing

and

with the term

, defined below.

The term

is defined as

This result allows us to re-express the acceleration term in terms of

A particular example of an equation which represents a solution to the general differential relation described above is written

where

is any constant length and

is any constant angle. The parameters which give an oscillator its unique properties are

and

. The value of

determines the amplitude of oscillation, that is how far the maximum displacement from equilibrium will be. The

term determines the strength of the returning force. This in turn determines how quickly the mass returns to the equilibrium point (and indeed the velocity at which the equilibrium is passed). This equates to the more familiar concept of the frequency of oscillation. The frequency of oscillation is the number of complete cycles performed per second, and is the inverse of the period, the length of time required to complete a single cycle.

The period of oscillation of such a system is denoted

and related to the other terms as follows:

In a fashion similar to the delta functions used to describe the IFN, we now demonstrate the operation of the resonate and fire model in mathematical terms. First, we must define some variables unique to the model:

where

is the resonant frequency of node

, and

is the frequency of the global clock. The global clock frequency determines the granularity of simulation and may be set to any value, the default used to produce the graphs discussed previously is 1000. The term

is referred to as the counter multiplier for node

. This term is introduced since it may be calculated once the resonant frequency is specified, and thus does not need to be calculated in subsequently.

The rate of change of the membrane potential

of neuron

, or its velocity, is denoted by

. The change in the velocity for the current time step is calculated first. The contribution from input pulses from all pre-synaptic neurons is calculated by the sum of products term

, where

is the weight of the connection from neuron

to neuron

, and

is the current (axonal) output of neuron

. The current axonal output is always either a

or a

, since action potentials are all or none events. The return force's contribution to the velocity calculation is expressed as

, which is the expression we arrived at for

previously, divided by

. We divide by

because we are performing a time slice calculation; in each step of the calculation we are simulating a period of time that is the inverse of the global clock frequency. The final term is the damping factor. The damping constant,

ranges from

, and is typically assigned a value of around

. The effect of this parameter is to cause the oscillation to gradually die off, slowly reducing the amplitude, as seen previously in the graphs.

The calculation of the new membrane potential,

, is straightforward once we have calculated the new velocity. In a single period of the global clock,

will change by the product of the current velocity and the time that we are simulating. Since period is the inverse of the frequency, this sum can be expressed as shown above. At this point we have calculated the new membrane potential. All that remains is to handle the production of action potentials.

The above equation is the mathematical characterization of the model's method for deciding the output of neuron

, denoted

. The result is simply that if

is greater than

, which denotes the threshold, then

is set to

, otherwise it is set to

. There are a number of actual mathematical functions that provide suitable implementations of

, however in the computational implementation a single ``if'' statement suffices.

The mathematical structures described thus far handle axonal inputs from pre-synaptic neurons. Another major feature of the model is direct dendro-dendritic connections. This aspect is accommodated through a simple extension to the delta rule.

The new sum of products term

is the sum across all neurons providing dendritic inputs to neuron

, of the products of the current membrane potential of neuron

, minus the current membrane potential of neuron

and the weight of the dendritic connection from neuron

to neuron

, denoted

. This factor is the key element in the creation of the dendritic field, through which waveforms may propagate. The difference between the axonal inputs and the dendritic connections in this model is that axonal inputs permit the transmission of single impulses,

. The term

is non-zero only when neuron

has generated an action potential, while the term

is almost always non-zero, hence the difference between the two sum-of-product terms. The dendritic connections transmit electrical ``pressures'' which cause recipient neurons' membrane potentials to become closer to their own.

It is easy to extend this model to provide for propagation delays. Each neuron is modeled as a set of parameters, including the current value of

and

. We extend this to provide a history of the values of these parameters. As each time step of the simulation passes, the new value calculated for

and

becomes the ``current'' value, while the old current value is stored in the history record. Axonal and dendritic connections are then augmented to specify which element of the history array they refer to, so that instead of using the current value of

in the delta rule, we may use the value as it was

time steps ago. For convenience of implementation, the current value is stored in the history array as element

, element

is the value as it was during the last time slice, and so on. The terms

and

which represent the parameters of the connection, are augmented to account for this, with a superscript,

indicating the element of the history array that they refer to. This additional parameter is a fundamental property of the network topology of a resonate and fire network. So the final delta rule, which encapsulates resonance, axonal inputs, the dendritic field, and propagation delays, becomes

The model described above has been implemented using the C programming language.

3. Signal processing and RNF.

Sherrington (1906) first suggested the concept of the integrate-and-fire neuron. Under this scheme, the higher the frequency of the input spike trains, the larger the input activity is considered to be. The neuron is then assumed to respond with a firing rate that is a function of the input firing rates. McCulloch and Pitts (1943) formalised the model and showed how to encode any logical proposition in a network of their neurons. Similarly, any network could be shown to encode a logical proposition.

Eccles (1957) used spinal cord recordings to correlate the spike frequency with the intensity of the applied stimulus as well as the intensity of the perceived sensation. Under the frequency-coding scheme, neurons encode information by frequency modulation of action potentials output on the axon. Increased firing rates in the presence of certain stimuli were taken to indicate that the neuron under observation was reacting directly to the presence of the feature which it was tuned to react to.

An alternate view of neuronal signaling which uses frequency coding as its basic component is that of ``population coding'' (Georgopoulos et al., 1982). Under this scheme, the intensity or salience of the content is conveyed using frequency modulation, but the content itself is represented by a distributed combination of spike trains across a population of neurons.

In terms of visual processing, the assumption of feature detection follows an Euclidean geometry hierarchy. First, there are point and line detectors. These feed into edge and boundary detectors, and so on up the scale. Barlow (1972) suggested the possibility of such hierarchies when he made the claim that aspects of perceptual awareness are related to the activity of specific neurons. The ``grandmother'' cell hypothesis follows logically from this sequence. This concludes that there can be a single cell in the brain which is best attuned for a single recognition task, such as the recognition of a single human face (Grandma's). There has been some experimental evidence for such ``fine tuning'' of individual neurons, such as the demonstration of Tanaka (1993) of ``grandmother'' style cells in monkeys which respond to moderately complex figures.

There are numerous problems with such specific specialization of function at the cellular level. From a redundancy viewpoint, it is simply bad design to have a single point of failure of the recognition process as would be the case were a single cell assigned to a single pattern. A key feature distinguishing neural networks from other computational devices is the property of graceful degradation - meaning that a large part of the system can be destroyed without completely annihilating the behaviour of the system.

Hubel and Weisel's work on the receptive fields of individual neurons in the cat's striate cortex was taken by many as proof positive that visual perception followed the Euclidean hierarchy of points, lines and contours, shapes and forms (1959). Each stage was seen to be built on the previous. The basic assumption underlying this scheme is that the visual processing operation begins with a two dimensional retinal image formed by the eye. As observes, the situation is much more complex than that. The optical image is a flow in at least three dimensions, the retinal image is curved, not flat, and the perceptual system has evolved to operate under conditions where the subject is moving. As experiments (Rock, 1983) show, the primitives of perception are ``relations between changes in oculocentric and egocentric direction. Lines and edges are not the primitives that configure the perceptual process; lines and edges result from the perceptual process, they do not determine it.'' .

This is not to say that the whole paradigm of viewing neural perceptual stages as feature extraction exercises is wrong. Rather that it is time to examine carefully the assumptions underlying the choice of features that we think are being extracted. Ultimately, sensory data come in the form of a power spectrum, a continuous stream of intensity values. The fact that hair cells in the ear are tuned to specific frequencies, and the existence of neurons in the inferior colliculus specifically oriented to pitch extraction is now commonplace in the literature (see, for example, Braun 2000). We make the following suggestions:

The stimulus for processing of sensory data is ultimately a power spectrum
Conventional neural net systems have great difficulty in handling phenomena like rotational invariance, scaling, and so on
These problems can be avoided by considering the action of RNF neurons that own a part of the frequency spectrum

We now wish to open out the discussion to talk about the specific role of dendro-dendritic connections, and the possibility that the well-examined phenomenon of stochastic resonance may point to a general process, ubiquitous in the brain, of computing with wave interference.

4. Computing with wave interference; the role of dendro-dendritic connections.

While quantum computing has become bogged down by the decoherence phenomenon, Ian Walmsley and his associates, inter alia, have demonstrated the possibility of computing by wave interference alone. Their celebrated demonstration is effectively an interference-based optical computer. Our work described above exemplifies the possibility of neurons implementing Fourier transforms by stealth, as it were, by a single neuron "owning" a particular bandwidth. In this brief section, we wish to suggest the possibility that the structure of dendro-dendritic connections affords a more flexible and potentially computationally powerful means of signal processing. In general, we are suggesting, such mechanisms perform the work of computation in the brain; INF effectively handles computation.

Pribram sees the dendritic microprocess as a central location of computational activity in the brain. Spike trains, action potentials are seen more as communicative devices than as the essence of the computational process. Izhikevich's resonate and fire neuron and the neural model described later place greater emphasis on the dendritic microprocess than conventional neural network models.

An important departure in Pribram's (1991) work is the emphasis on the role of dendro-dendritic connections. Such connections are similar to normal axonal-dendritic synaptic connections; however, the entity being transmitted is not an action potential, instead it is the current internal state of the neuron. In this way, Pribram proposes that computations can occur which involve multiple neurons, but which do not utilise axonal action potentials. This is not to say that action potentials are relegated to insignificance in the model; rather dendritic processes have been promoted to a level on a par with action potentials and conventional axonal transmission.

Recent evidence from experimental studies have confirmed that subthreshold dendritic dynamics are complex and would appear to have an important role to play in the computational activity of the brain. Particularly, calcium channels (Schutter ,1993) react strongly to subthreshold inputs. Callewaert , Eilers and Konnerth (1996) express the case for the dendritic process thus:

Recent results obtained by using high resolution imaging techniques provide clear evidence for new forms of neuronal signal integration. In contrast to the quickly spreading electrical potentials, slower intracellular signals were found that are restricted to defined dendritic compartments. Of special significance seem to be highly-localized, short-lasting changes in calcium concentration within fine branches of the neuronal dendritic tree. These calcium signals are evoked by synaptic excitation and provide the basis for a dendritic form of signal integration that is independent of the conventional electrical summation in the soma. There is experimental evidence that dendritic integration is critically involved in synaptic plasticity.

The general feature whereby neurons can ``tune in'' to a particular frequency component of the aggregate oscillation in the dendritic field provides an important computational asset to the model as a whole. It is also a phenomenon predicted to exist in biological neurons by Llinas (1988). The fact that the dendritic field supports such interference effects has deep ramifications; the modes by which the brain performs computation may be very different to the current action-potential centric paradigm.

Readers familiar with Young's slit experiment may find the analogy useful. In this case, the light source is the input neuron, while the slits correspond to the two output neurons. The screen on which the interference pattern appears is the entire set of possible values of the delay constants; for a particular pair of values we are measuring the interference at a single point on the screen. So, for each experimental simulation of the network, we select a value of the delay constants. As for Young's slit experiment, if the distance from the slits to the point on the screen is exactly the same, then waves from each slit arrive in-phase and constructively interfere. If, however the distance differs by exactly half a wavelength, then destructive interference occurs and the waves cancel each other out. In addition to standard inputs coming from the axons of presynaptic neurons, the RFN model implements inputs from the dendrites of other neurons, transmitting the current activation of the pre-synaptic node. This feature is directly inspired by Pribram (1991), who emphasizes the role of such channels in the computational process in the brain.

Here we have modeled the feature in a manner similar to the standard axonal input -- the sum of the products of connection weight and pre-synaptic output is augmented with the sum of product of dendritic connection weight and the current activation of the pre-synaptic neuron. Therefore, the only difference is that the current activation is used instead of the current output.

On its own, this mechanism would not be very useful. The contribution from dendro-dendritic connections to a post-synaptic neuron's activation would simply be the linear sum of the current activations of its pre-synaptic neurons. This situation is corrected by the addition of the delay mechanism discussed previously. Each dendro-dendritic connection has an associated weight, and delay. The delay corresponds to a propagation delay in the biological case. As the diagrams illustrate this mechanism permits an innervated neuron to position itself in any position in the interference field of a set of neurons, by tuning the delay parameters of its dendritic connections.

We have also implemented a neural net architecture using this basic idea. Neurons are to learn which frequencies to respond to.

5. Conclusions

This paper makes a set of claims ranging in strength from categorical to extremely tentative. The fact that after a century of modern neuroscience we have yet to establish the neural basis for a single symbolic cognitive act must surely give pause. Elsewhere (O Nualláin, (2003) ) we speculate that entirely different formalisms like Lie groups may be appropriate for analysis of brain function in addition to the Hilbert and other transforms hinted at here. It is uncontroversial at this stage to contend that old-fashioned INF needs greatly to be augmented. We contend that RNF may offer a superset formalism. We go on to posit that dendro-denritic connections may yield a fundamental set of new insights, which we look forward to pursuing.

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Wu, M, C-F Hsiao, and S.C. Chandler (2001) "Membrane reonance and subthreshold membrane oscillations in Mesencephalic V Neurons: Participants in Burst Generation The Journal of Neuroscience, June 1, 2001, 21(11):3729-3739

Lecture 2

This relatively technical beginning will prove essential by the end of the course. It is my view that the phenomenology of consciousness - including our remarkable ability to feel "in tune" with the cosmos as we rationally explore it with tools like mathematics - points to the plausibility of a quantum explanation. It is only in the past decade that quantum effects in biology have been demonstrated.

Briefly, what we're trying to establish is a situation wherein quantum states can be communicated by the mechanical resonator which we use to describe the neuron; and, of course vice versa. Please take a look at

http://www.nature.com/nature/journal/v471/n7337/full/nature09800.html

which is mechanical states being transmitted by a quantum state.

So here the effect persists over the tens of micrometers; we are on track for a quantum story to complement the classical on. The converse story, of entangled/quantum states being transmitted by classical mechanics, can be found at;

http://prb.aps.org/abstract/PRB/v72/i19/e195411

So what we're saying is that our model of the neuron affords a perspective in which quantum states can occur and can realistically be transmitted

I add my 2013 paper on this subject which can be found at http://www.jcer.com/index.php/jcj/article/view/311

Neural oscillations and consciousness; attention as a litmus test for the quantum mind hypothesis

Seán O Nualláin Ph.D. University of Ireland, Ca, USA

president@UniversityofIreland.com

Abstract

The “quantum mind” hypothesis, the notion that quantum phenomena are causal and perhaps even essential in mentation and particularly consciousness, has met with fierce resistance. This has been particularly the case over the past 20 years, and the first task of this paper is to show that while there are indeed strong - mainly empirical - arguments against the thesis, the ‘in principle arguments published to date evince premature closure.

The burgeoning field of “Quantum cognition” has established that quantum models are appropriate for decision-making, and that of “Quantum biology” has now made the notion of quantum effects at physiological temperatures plausible. If quantum effects are relevant to consciousness, they are likely to be seen in the contrast between attended to and not attended to streams of information. An exciting confirmation of this theme is the fact that attended to streams involve a decorrelation of the informational fluctuations in streams not so attended to. This gives rise to the idea that perhaps what enters our consciousness is the result of such a decorrelation from a superposed state.

Decorrelation for the purposes of sparsification is prevalent in the brain; what may enter consciousness in the schema proposed here is mental processes with a duration greater than the sampling rate of consciousness (about 80ms) the wave function of which is undergoing state-vector reduction in a manner described by the Quantum Zeno effect. This allows also for truly voluntary action in the manner Von Neumann suggested. This is distinct from the situation with binocular resolution dichoptic stimuli which is a mixture, and is an example of what Fodor calls a “vertical” module with its operation mandatory. There is nothing to be gained by making binocular synthesis subject to voluntary choice. Likewise, it is realistic to propose that attention in lower animals with their less complex brains involves a much simpler mechanism than human consciousness.

A model of the individual neuron as a harmonic oscillator is outlined, with a causal role for ion channels in the generation of the oscillations; it is clear that ion channels are critical for attention. Moreover, at a mesoscopic level, it is demonstrated that the brain enters a quiet “shutter” mode several times a second in which quantum effects may be appropriately amplified. If quantum effects exist in the brain, it is likely that this complex of phenomena will be central to them. The de Barros and Suppes models, in addition to the similar formalism due to Henry Stapp, are also briefly described.

Keywords

Quantum mind, harmonic oscillator, attention, phase synchrony

1. Introduction

The “quantum mind” hypothesis, the notion that quantum phenomena are causal in mentation, is one of the truly exciting ideas of the past century. Until recently, it also seemed very unlikely. If true, it gives us a language to describe our thought in the context of the emanation of the cosmos, and – on what is relatively a prosaic level – to assert human free will, soul, and mental capacity greater than Turing machines. This article begins its analysis below by considering one of this theory’s main proponents, Henry Stapp

In previous work (2012) this author has indicated how the non-classical probability regime that epitomized the quantum vacuum prior to the creation of the inflaton and the big bang may be recapitulated in the brain through consciousness. Many leaps of faith are required, and this article proposes the evidence that will be necessary from a variety of disciplines to make this hypothesis plausible. Alternatively put, the subject/object relationship in QM is the most bare in nature; my 2008 paper describes the various other types of epistemological relations that hold a, for example, we move around the world, or map a domain in terms of the formal symbols used in language.

In the first place, we need some regime in which quantum effects can be causal in biological systems. We then need some evidence that the artillery of Hilbert spaces is relevant for cognition as for quantum mechanics. As it happens, neither hypothesis – unthinkable even a generation ago – is in the slightest currently implausible, and we will simply refer to prior art.

For example, Hu et al (2010) give a list of various theories that have emerged, and the empirical evidence on which they are based. That article features work analyzing the evidence for non-locality in neural phenomena which is not the focus here; rather, a targeted analysis of attention and how it might be subject to quantum effects is going to be the core of this paper. Ball (2011) authoritatively announces the field of “quantum biology”. While skeptical about the “quantum mind” hypothesis, de Barros and Suppes (2009) point to the existence of quantum cognition, and presage their later work of how neural oscillator structures may give rise to these phenomena, echoing the work described later in this paper.

The second step after quantum biology is the justification of the “quantum mind” hypothesis, the notion that there is some real quantum process causally affecting the mind. The Penrose/Hameroff model has argued that human cognition cannot otherwise be described; rather less well known is the painstaking investigation of Berkeley’s Henry Stapp into the consequences of Von Neumann’s analysis of the system and the observer. That shall constitute our next port of call. If Stapp is right, then Penrose/Hameroff may similarly be correct in their insistence that, through quantum effects, the mind transcends the chugging of the Turing machine, and both models assert human free will as a consequence.

Should this model be valid, it is reasonable to expect the neural data to reflect it. In particular, it should be possible to see phenomena in attention that resemble state-vector reduction. Remarkably, here our model holds up well in the face of the thorough research into attention by Jude Mitchell, inter alia.

A complicating factor is the lack of metatheory in neuroscience, it is fair to say that we must emphasise how time is increasingly being agreed on as the lingua franca of the brain. It may be asserted with some confidence that information is conveyed by markings on the phase of neural oscillations like gamma – or indeed the individual neurons that we study below. In particular, phase synchrony seems to be essential for cognition in general, and for both consciousness and meditation in particular. In fact, even if the quantum model is wrong, the fact that it has focused attention of waves and their effect in neural function may in itself have justified the area, if not the extravagant claims. The data with which I end this paper are valid whether “quantum mind” is right, or another beautiful, well-motivated and failed theory.

According to Tegmark (2000) the theory is indeed a failed one. With some patience, he explains neural impulses/firing, and demonstrated that decoherence would occur far too quickly for any conceivable “condensate’ to last long enough to support a conscious experience. However, he fails completely to reference gap junctions, which allow almost instantaneous transmission of signals and do not need the conventional “action potentials” that Tegmark describes. (Shepherd et al, 2010). In fact, Tegmark is in many ways the George W Bush of this area; faced with what only he considered an existential threat, he attacked the wrong enemy.

In like vein, Reimers et al (2009) point out that the then favoured location of coherent states for the Hameroff/Penrose model – Froehlich condensates – is impossible in principle. While this may indeed be right, it also, like Tegmark misses the target. In fact, it belongs to a near-phrenological obsession with locating the “faculties’ of the mind in specific cerebral locations, a bizarre recapitulation of a Victorian thread that we will consider in the last section below.

There is, on the contrary, an emerging and indeed burgeoning consensus that the attested fact that the brain can support stable patterns of oscillatory circuits, particularly through dendro-dendritic connections (Shepherd et al, 2010) is critical for 21^st century neuroscience. The remainder of this paper will examine several such models and their background.

2. The work of Henry Stapp

In the famous “quantum zeno” effect (Stapp 2009; forthcoming, 2013), the QM event selects the code to be used in the next Energetic cycle. This results in a situation where the tiny time-scales involved in Qm can have macroscopic effects. Much of my published experimental neuroscience work (2008, 2009; with Tom Doris, 2009, 2011) has shown how individual neurons, correctly described as harmonic oscillators, can have their oscillations entrained by large-scale and synchronized gamma to recruit them to produce states more congenial for quantum effects.

Stapp (2009) is allowed speak for himself about the details of his model. Tegmark(2000) glosses Stapp as proposing that “interaction with the environment is probably small enough to be unimportant for certain neural processes” which is rather like saying that “certain Iraqis may object to our presence”.. In fact, Stapp (2009) is extremely aware of the problem of environmental decoherence. He suggests, correctly, that the existence of harmonic oscillators is not in doubt and proposes what are trivial extensions to give them quantum traction. He then argues that the “quantum zeno” effect allows Von Neumann’ process 1, the putting of a question to nature and apprehending the result, ensures that conscious choice is neurally as plausible as it clearly is physically plausible, embedded as it is in the structure of Von Neumann’s classical approach to QM. Note that one can also allow that state-vector reduction occurs absent any observers, be that mechanism spontaneous localization or whatever.

Likewise for bistable stimuli, those that change from one perception to another in th manner of the Necker cube and the rabbit/duck fluctuation. In this case, there is work indicating that a single perception can be maintained for 3 seconds, giving a zeno moment of perhaps 30 ms, compatible with gamma waves. (Atmanspacher et al, 2008)

So without violating any real neuroscience, Stapp (forthcoming) puts it we can say that we are “ psychophysical agents that can freely instigate probing actions of our own mental choosing ". All that we need is a very limited but relatively free capacity to choose the object of our attention – as I wrote before (2012), we do not have absolute free will to change long-entrenched habits but we do have the capacity to change our focus and thus begin to work on ourselves. Thereafter as it is possible to demonstrate, attention becomes biased in the direction of the free choice previously made., as Sheng He and his colleagues have demonstrated (Jiang et al, 2006). My own work on the subject can be found in my 2010 paper.

Similarly, in visual attention work, as it turns out from He et al,, stereoscopic fusion does NOT happen without attention. Instead, in the absence of attention, a fused/patchwork image gets relayed. so there is a role for attention with perhaps QM implications ; however, it looks as though what obtains in binocular vision more resembles a mixture. (Zhang et al, 2011) than a superposition.

As Stapp (forthcoming) puts it “Each observing ego is empowered to pose probing questions about the facts of the world in which it finds itself. “. That is all we need for at least a limited notion of free will ; we can look on will (self-mastery) as something that can vary from person to person, and involves familiarity with the thousands of years of human culture in which we're immersed, the fact that we're highly social primates used to living in groups, and other factors which shape us; nevertheless, there is a “free” core. As Stapp (forthcoming) puts it about development;

“The ego of the infant begins in the womb to inquire about the structure of its world, and by virtue of its intrinsic conceptual capacities begins, by trial and error, to acquire a conception of the world in which it finds. This conception is a construction in terms the validated feeling about it.”

This can usefully be expanded by looking at the work of Jean Piaget , whose constructivism has survived the attack of his experiments (see my 2003 book)

It is worthwhile thinking of the analogy of the cinema, with 28 frames per second being necessary to fill. Once a stream is the object of attention, it reaches a threshold (perhaps 10 frames/sec) and gets promoted to conscious awareness. Once in consciousness, it can “broadcast” to the rest of the processes in the brain in the manner of an actor on stage. This broadcast is achieved, at least partially, by modulating the fast gamma oscillations in the brain. In consciousness, these oscillations become more synchronized. In reality, consciousness involves perhaps 12 frames per second; 80 ms seems the minimum time we need to recognize objects. (Again, please see my 2010 paper)

A fundamental point that presents itself ais the status of “elements of reality” in Qm. Indeed here Bohr and Von Neumann are greatly at odds. In particular, Bohr is committed to an epistemological interpretation in Born's view – “the electron IS FOUND at x” – whereas Von Neumann is willing to say “the electron IS at x”. There are profound reasons for this distinction, arising from Mach who also corrupted Einstein– albeit in such a way that Bohr and Einstein felt themselves in disagreement.

As Stapp (ibid.) expresses it “ the empirical validity of certain predictions of quantum mechanics entails that some supposedly mere practical tools for the calculation of predictions, namely the actualized quantum mechanical states, are real essences “

This is the core of the issue and what we're doing is trying to cash it out in terms of present knowledge; “Thus quantum mechanics becomes, in von Neumann’s orthodox formulation, directly and explicitly, a theory of the mind-brain connection.” (ibid). However, it is this author’s view, further developed below, that the notion of what “elements of reality” may never be resolved in terms of cognition, or indeed in terms of classical epistemology; QM, accurate beyond our wildest dreams, may forever remain inscrutable.

Moreover, the following (ibid) needs to be explicated in view of what we now know about attention;

“The mind, or “abstract ego”, has a battery of efforts E each of which corresponds to an act of putting to Nature a particular question about the world inhabited by that ego. According to the quantum precepts, Nature immediately responds by either returning a feeling F that is tied to the effort, F=F(E), or by failing to return immediately a response. “

In fact, it resembles nothing so much as the “self-conscious mind” that John Eccles eventually saw incarnated in a “probability cloud” due to his (mis?) reading of Margenau, described in my 2003 book We do not need this in any case to support the idea that there is a core capacity for voluntary action in humans, and it is hard to uphold in the face of the relevant neuroscience and psychology evidence.

It is better to start from here;

“The key to such an understanding is an understanding of the way that a mind is connected to its brain; for that connection is that mind’s bridge to the future.” (Stapp, ibid)

In my 2012 paper I suggest, in this context, that it is possible to achieve a regime of non-classical probability in the brain and indeed Suppes et al (2012) com to precisely the same conclusion in the quantum cognition field, providing a mechanism in terms of neural oscillators similar to the one about to be outlined.

There is no need to assume that all our choices are absolutely “free”; indeed, it would be hard to function. In fact, it may be the case that, even granted a core of free will, and as described in my 2010 paper, nature and culture have gifted us to ability to confabulate, incorrectly to attribute agency to ourselves, the better truly to act freely at times in complex environments.

3.Superposition and the brain

There is a growing consensus that aspects of human decision-making and concept formation can best be described using models from QM (Aerts, 2009, .de Barros, J.A. & Suppes, P. 2009, Suppes et al, 2012). What we are now going to explore is whether the same can be said for attentional mechanisms.

There are arguments on the micro level related to the Quantum Zeno effect –“ watched phone never rings”. There are facts on the macro level related to attention – but these seem paradoxical in nature, allowing the speculation that attention actually ENDS superposition - eg the work at He's lab showing that non-attended visual data never get binocular synthesis, (Zhang et al, 2011) . However, the stream not attended to is best viewed as a mixture rather than a superposition .

Bressler et al’s work (2010, 2013) is also of interest here. It is not in doubt at this stage; attention ups the neural activity of the attendee-to stream, while suppressing response variability. It also suppresses the threads not attended to (ibid). In fact, it arguably turns the attended-to thread into von Neumann’s process 1, posing a yes/no question to nature.

That there is a link between neural attention and QM is apparent in these quotes from Dirac and Zhang et al;

Dirac; "The intermediate character of the state formed by superposition thus expresses itself through the probability of a particular result for an observation being intermediate between the corresponding probabilities for the original states, not through the result itself being intermediate between the corresponding results for the original states"

Or, as Zhang (2011) et al put it;

"Thus attention is necessary for dichoptic images to be engaged in sustained rivalry, and may be generally required for resolving conflicting, potentially ambiguous input, and giving a single interpretation access to consciousness."

4. Attention and Consciousness

I indicate below how a position that accepts at least a limited form of free will can be fleshed out wrt neuroscience and indeed developmental cognitive psychology. Here, then, is my view of the position that can be defended in the face of the QM and neuroscience. Human consciousness consists of the ability to take a stream of processing – for example, an action-perception cycle with feedback present – and to submit it to a regime of superposition and state-vector reduction. This stream must last in the order of tenths of seconds at least as the minimum conscious “moment” is about 80 ms. . Human consciousness is a superset of and distinct from lower animal “attention”, the ability to confer salience on a processing stream and up the gain of that stream.

Human consciousness is limited in that our ability to concentrate is limited, with 3 seconds being not a bad estimate (Atmaspaher et al, 2008). It uses mechanisms of decorrelation of an informational stream pervasive in the cortex, but does so in a voluntary way, one subject to will and featuring an immanent sense of self. In that, of course, it is consistent with the Von Neumann formulation of quantum mechanics. Its mechanism of a physiological level can perhaps be found in quantum coherent states related to ion channels, which seem related to the informational gain in attention. Our work will show how these ion channels establish the oscillation period for neurons considered as harmonic oscillators, and how the gamma oscillations synchronized through the cortex associated with consciousness help provide the entropically “quiet” environment in which quantum coherent states might occur.

Like it or not, materialists have to accept that that the Von Neumann formulation is consistent and can be interpreted as supportive of a form of dualism, more nuanced than the crude mind/body version. Like it or not, dualists have to accept that there are plausible neuroscientific accounts of a good deal of our perceptual experience, at least limited computer simulations of how symbols can be produced – though indications are that symbolic behavior at a higher level needs consciousness - and psychological evidence (a la Libet) that many of our choices are less free than we believe them to be. In fact, we confabulate a lot, not least to ourselves

The following any objections coming from the Libet et al (1983) work which argued that “conscious” intent was, follwing Hume, a “wont’ rather than a will, distinct from Von Neumann’s Proocss 1. Of course preafference will occur, whereby the brain lines up hypotheses for likely perceptual experience, and prepares responses. It is precisely the assimilation of such processes to an informational stream, and the use of a superposition and state-vector reduction on that stream, that constitutes human consciousness. That in turn introduces quantum indeterminacy into human decision making, and Aerts (2009) and many others have demonstrated the pervasiveness of quantum cognition in the human case, even be that cognition less than useful for particular decision-making tasks.

It also leads to the hypothesis that animals may forever be better at some attentional tasks than humans, as the mechanism used is simpler and does not involve free will; there is some evidence supporting the viewpoint that the types of process involved are different (Zangenehpour et al, 2008). This is of course aside from the obvious perceptual adaptations that attune animals to different parts of the electromagnetic spectrum to us, or better reflexes in cats, to take one example.

My guess is that the Quantum mind hypothesis is testable under this regime;

1. Does human consciousness involve superpositions? If not, it is game over and there are no quantum effects.
2. If yes, and this superposition is indeed to be seen in the suppression of response variability in attention, even in macaques, is it the case that humans can modulate their attention to create new superpositions in their execution of complex plans?

The fact that Tversky and Kahneman's results are interpretable as "quantum cognition" rather than straightforward application of Bayes or some other regime now comes into play. What this writer finds really interesting about Mitchell's work (2009) is that attention DECORRELATES information so it is irreversible - pretty much what we want for state-vector reduction. In fact, it's beginning to look as plausible that our stream of consciousness is serial not parallel as a result of exploitation of quantum effects.

The critical issue then is that attention decorrelates information fluctuations. If this looks more like state-vector reduction than anything classical, the QM approach to mind is vindicated. Therefore, the Libet et al (1983)work actually supports the Quantum mind hypothesis as only one course of action was being "prepared". There exists also the possibility that Libet's instruments were not sensitive enough to detect alternative actions. Where such measurements have taken place (Bressler et al, 2010, 2013) it is clear that streams not being attended to, while retaining thir physiological integrity, have their activity suppressed in the service of keeping one stream, the focus of attention, enriched.

So what we defend is a notion that, as W James put it, the mind seizes on one of many streams of activity in the brain which then becomes the focus of attention. This stream is then characterized by differential informational statistics, as Mitchell et al (2009) have demonstrated, and this confirms a refutable hypothesis. In particular, we now have a “deus ex machina” - attention- preparing an observation in a way that shows purely “mental” effects on the “physical” world of the brain. It is indeed possible that this process may become assimilated to neural activity afterward; nevertheless the capacity is there for voluntary action.

The immediately above goes for bistable perception in general. There is also compelling evidence that the statistics of attended -to streams are different from those not so attended (Mitchell et al, 2009), and that response variability is less in attended-to streams (Cohen et al, 2009). Finally, He's lab has also demonstrated that attention is initially assigned unconsciously but in a way consistent with the disposition and formation of the observer (Jiang et al, 2006).

5. Neural models ; mesoscopic and microscopic , and the relation with gamma waves.

There are models attested by ECOG data that invite speculation that the brain enters “limit cycles” a few times per second (Freeman et al 2008). These limit cycles correspond to synchronized gamma, meditation and consciousness as my various papers on the subject (2009, 2012) and those with Doris (2011) attest. The 2009 paper is consistent with the researchers who have proposed that the signature of the meditative state is the phase synchrony of the relatively fast gamma waves (40 Hz approx). The general approach of the Freeman work in summarized in my own 2008 paper.

The existence of phase coherence in gamma waves in the brain, and the relation of this phenomenon to consciousness, is a point of much consensus. It has been further argued that the entropically minimal state resulting from this phase coherence might yield an environment conducive to quantum coherence.

While we believe that the work of Walter Freeman indeed is indicative of entropically minimal states in the brain occurring several times a second, we also believe that the EEG/ECOG signal is too coarse to indicate synchrony. Indeed, we can adduce findings from PCA , among other methods, indicating that a 64-electrode grid produces at most two signals with any dgree of magnitude. In fact, there are data to indicate that much of the statistical inferences in classical EEE/ECOG evince premature closure, and that this approach is certainly not ready – pace, the ORCH OR proponents – for the non-classical world. So the gamma hypothesis, though beautiful, is “not proven’. The PCA work can be found in my 2011 paper with Doris which also finally gives the lie to the notion that epileptic seizure is a minimally entropic state.
As for phase coherence, the stated electronic specifications of the equipment used in ECOG and EEG expressly prohibit any such inference, as the error range of the equipment is too large. This argument may become ever more salient over the years to come, as it does appear to be the case that one of the critical mechanisms used by the brain to convey information is frequency modulation of a carrier wave (like FM radio). In particular, phase information may indeed turn out to be critical once we learn how to measure it accurately.
This is a fortiori the case as simulations give a lot of support to the “zero power” gamma hypothesis for consciousness. If we simulate groups of 10,000 neurons - the “mesoscopic” level – and consider their firing as a random process with a mean frequency of 200 times/second, then we can graph how the power consumption of the brain is affected by gamma. The graph below indicates that it enters a brief period of “zero power” – of minimal consumption of energy – between 2 and 12 times per second. If this is done in synchrony throughout the brain, we indeed can speculate about health effects of meditation as the brain frees up energy to be used by the rest of the organism. In the diagram below, we have time of the x axis and energy consumption on the y axis;

These same models can be extended with models of individual neurons that explain how the attended- to stream of processing maximizes its gain in the broadcast system of the cortex (O Nualláin, Seán and T. Doris 2010). We consider each neuron as a harmonic oscillator, and consider how the oscillation of the membrane potential is altered in synaptic and dendro-dendritic connections. It is the latter that would seem to be more susceptible to quantum effects. Following are the details of the model, as presented in our 2010 paper.(IFN = the “standard” integrate and fire model; our model claims that this is a subset of the more general resonate and fire (RFN) behaviour in this discussion)

Ours (2004) was the first work to show how single neurons could realistically perform processing of sensory data expressed simply as spectral such data. This work has since been corroborated by, for example, Tiago et al. (2010). Essentially, we argued that subthreshold oscillations of the neuron allowed groups of neurons to “own” part of the spectrum. That can be conceived of using only classical physics. As mentioned, we have data to indicate that much of the statistical inferences in classical EEE/ECOG evince premature closure, and that this approach is certainly not ready – pace, the ORCH OR proponents – for the non-classical world.

We therefore speculate that gap junctions might allow a quantum superposition of states of the membrane potential of each neuron to be communicated to thousands of others. This will lead to entanglement of a scale that would allow the Fourier decomposition we envisage for the classical case to be extended to a quantum description. This is the only currently physiologically plausible story about Quantum effects in the brain that we can currently envisage as having quantum effects.

Our model (O Nualláin, and Doris 2010) shows how ion channels' activity interacts with the frequency of subthreshold oscillations in a neuron. This is on the one hand causative of different patterns of firing and on the other hand of phase changes in the quantum state and we propose this in conjunction with the current Reynolds work as a possible interrelation of attention and neural processing (Reynolds et al, 2009). It also is consistent with the Suppes et al work (2012) which, while in favour of the harmonic oscillator paradigm, arges that the allegedly quantum effects are in fact artefacts of the structure of neural oscillators.

We will take some time to look at the structure of our model;

The basic behaviour of Harmonic Oscillators is captured by the differential equation:

The parameters which give an oscillator its unique properties are

and

. The value of

determines the amplitude of oscillation, that is how far the maximum displacement from equilibrium will be. The

The period of oscillation of such a system is denoted

and related to the other terms as follows:

In a fashion similar to the delta functions used to describe the intergate and fire neuron (IFN) – for Tegamrk (2000) the only type of neural mechanism - , we now demonstrate the operation of the resonate and fire model in mathematical terms. First, we must define some variables unique to the model:

where

is the resonant frequency of node

, and

is referred to as the counter multiplier for node

. This term is introduced since it may be calculated once the resonant frequency is specified, and thus does not need to be calculated in subsequently.

The rate of change of the membrane potential

of neuron

, or its velocity, is denoted by

. The change in the velocity for the current time step is calculated first. The contribution from input pulses from all pre-synaptic neurons is calculated by the sum of products term

, where

is the weight of the connection from neuron

to neuron

, and

is the current (axonal) output of neuron

. The current axonal output is always either a

or a

, since action potentials are all or none events. The return force's contribution to the velocity calculation is expressed as

, which is the expression we arrived at for

previously, divided by

. We divide by

because we are performing a time slice calculation; in each step of the calculation we are simulating a period of time that is the inverse of the global clock frequency. The final term is the damping factor. The damping constant,

ranges from

, and is typically assigned a value of around

. The effect of this parameter is to cause the oscillation to gradually die off, slowly reducing the amplitude, as seen previously in the graphs.

The calculation of the new membrane potential,

, is straightforward once we have calculated the new velocity. In a single period of the global clock,

Finally, the early caveat that quantum effects cannot exist at physiological temperatures in biological organisms no longer applies in the face of what we know about photosynthesis, and perhaps avian navigation; this work just cited provides the possibility that quantum coherent states could be maintained in an otherwise noisy brain.

7. Quantum mind and the sciences

There is a fundamental question prior to how “God’ or “spiritual’ entities in general, if such exist, can be cognitively apprehended. This question relates to the structure of knowledge itself, in a context in which - perhaps unfortunately - distinctions between the physical, biological, and psychological have been elided to the point that methodologically all are considered fair game for such approaches as the rather grotesquely-named “big data”. Indeed, there does not seem to any attested and principled way of distinguishing the physical and social sciences, and - absent a view of self as object - it is difficult indeed to see how we can create a narrative in which the ebb and flow of spiritual experience, an immediate sense of the noumenal that is physical, emotional and intellectual at the same time, can be encompassed. The “thinglessness”, the ineffability suggested by quantum mechanics affords an entrée.

This project is an initial foray into this vast question. As argued below, it seeks to reinstate a notion of the ontological to distinguish between the various “physical” sciences, starting with physics and biology. Indeed, we will produce better science – even in the short term – if, eschewing statistical extravagances, we begin to honour ontological distinctions. It argues that the “cognitive” is best thought of in terms of the principles of cognitive science, rather than as “psychologism”, the attempt to describe objective (or at least consensually attested ) entities solely in terms of the metaphors or other psychological operations that underpin their presentation to consciousness.

It further contends that the main problem underlying construal of the “spiritual’ is the same as that which has destroyed the normative aspect of political experience in favor of an over-used “rights-based” approach. To wit, this is skepticism about the existence of an algorithmically compact level of description, the noetic level, which gives the correct entrée into an area of discourse. Once we have such an entrée, and with it the confidence that we are construing the area veridically, we can be more sure of our spiritual insights, our political calls to arms, and our scientific intuitions.

The noetic stance refers to how a discipline - be it a conventional academic discipline, spiritual perspective, a political call to arms, or a technical skill – should be apprehended. It is distinguishable from the cognitive description, which is a post hoc attempt to map onto the structures of cognitive science including recursion, schemes and so on. The noetic description is more algorithmically compact than the cognitive such. Finally, this summary can be perhaps read as the appropriate interrelation of the cognitive and the noetic stance,

For example, folk psychology – explanation of behaviour in terms of motives, desires and so on – is a noetic description and is psychologically prior to the eschatological hope of eliminative materialism that we can dispense with all these terms through neuroscience. Similarly, as exemplified in the famous break-up scene with Sheldon and Amy in the “Big bang theory”, the noetic description of the physical domain is couched in the language of mathematical physics and no description in terms of neurobiology will be more elliptical or veridical – a point Sheldon , the “genius physicist” ,fails to make in this hilarious scene.

Yet even physics requires a causal notion of information; not only can addition of a bit change the area of a black hole, as demonstrated inter alia by Susskind, but the observer can cause state-vector reduction. The noetic level of physics must acknowledge this by including, suitably nuanced, the idea that “a bit gives it”. Similarly, the noetic level of biology includes the fact that syntax IS indeed intrinsic to the biology, if (as Searle, following Kripke argued) not the Physics) and the $billions that have gone into projects like the HGP that ignore this fact have largely been wasted. Indeed, one result has been the absurdity of a genome with over 99% thereof, while preserved for millions of years by evolution, somehow seen as “non-coding”. Once we accept the existence of different ontological layers in nature – so far the physical and biological - our science gets a lot better.

We come now to the cognitive level – as mentioned the structures of cognitive science including recursion, schemes and so on. This area must also explain the structures of our physical and biological theory, and by the mid explain the mind. Yet it is constrained by the structures of these theories in ways that have not really been made clear. If Einstein could use a fourth-order tensor to produce general relativity, then clearly fmri with its scalars (0 order tensors) is not an appropriate formalism.

Indeed, cognitive science has spawned the area of consciousness studies. This can best be seen as an attempt to extend the objectivist, third-person explanation pattern in science to primitive aspects of subjective experience like visual illusions and sensorimotor experience. Consciousness studies, as exemplified by the work of the late Jim Newman and John Taylor (see our 1997 collection) can be interpreted as providing support for the notion that the phenomena of attention on which we have based so much of the argument of this paper may not hold out any promise for quantum mind. It is indeed the case that attention results in a simple yes/no question, a la maniere de Von Neumann being put to nature; but, argues Taylor, that is simply because the nuclei reticularis thalami gate every access to attention, and will allow only one item in at a time.

Now we come to the punch line of this final argument. If Taylor is correct about the gating mechanism’s existence, that may buttress the quantum mind idea in an unexpected way. It may just as well be argued that the structure of the mammalian brain has conformed to the requirement, implicit from Von Neumann, that there be a single yes/no question imminent from whatever process has grabbed the resources of attention. Luckily, this single serial stream of consciousness is what’s needed also for dealing with the classical, macroscopic world, and control of action therein.

We can go further. This yes/no question will inevitably change the superposition manifest in the processing stream by removing information, precisely as in state-vector reduction. Given a similarly superimposed object – and such may occur in visual processing in particular – that too will change, as we know occurs in photosynthesis. A bit gives it; information is causal, and the mind has capacities that we will only slowly discover.

8. Summary

The health of the quantum mind hypothesis, even subjected to a robust devil’s advocate as here in this paper, is surprisingly robust. We find that it is compatible with best practice in experimental and computational neuroscience, and the classical Von Neumann QM approach. That is not to say that it is proved.

This leads to a surprising hypothesis – that it is those streams of cortical processing that are attended to are those to which the quantum description in terms of superposition, and the Quantum Zeno effect apply . Once a stream is attended to, it will be broadcast to the entire nervous system through a mechanism in which the fast gamma oscillations are modulated – in the manner of FM radio – to convey information to the rest of the nervous system, and this is susceptible to classical description. It makes evolutionary sense that superposition should be reserved for only some processes , the better to exploit the kind of processing now being modelled in quantum computation while yet maintaining the single serial stream of consciousness that we need to engage the world when the wave-function collapses.

The model thus suggests that the brain s hybrid quantum-classical in its assignment of attentional resources. Superposition occurs in a manner that indeed allows the possibility of conscious processing in a manner redolent of quantum computation, and indeed it is not controversial to suggest that many of the finest results in mathematics ( a la Poincaré's famous discovery as he got on a bus) seem to arise in consciousness almost effortlessly. Only decohered streams of thought can so appear; once there, they may be broadcast to the rest of the nervous system through the mechanism of consciousness. Our work (Freeman et al, 2008) indicates that this mechanism in discontinuous and has perhaps 10 events per second and in this is consistent with the findings that the conscious moment is around 80 to 100 ms.

Streams of processing that have decohered compete for conscious resources, and the total of 10 events per second are each also a chance for another stream to get on stage and broadcast to the nervous system. It is also uncontroversial to suggest that meditation, where an attempt is made to enthrone one innocuous stream on stage for some time at the expense of more informational-rich streams, has health benefits and seems to allow the gamma oscillations to remain more coherent as the focus of awareness is changed less often.

The consequences for free will are consistent with common-sense intuitions, psychology, and Von Neumann's work in that our freedom may above all be the ability to regulate the focus of our attention, and thus action, over time. It is not claimed that every act is absolutely “free”; however, human beings are capable of modifying the objects that become foci of attention as what initially were acts of will become habits of the nervous system. The degree of this freedom will vary between individuals.

In summary, then a paradoxical situation obtains with respect to attention and superposition. On the one had, attention may be seen as turning a mixture into a superposition (Jiang et al 2009), The counter-argument may be made that this is an artificial situation, with dichoptic stimuli manipulated in a way that does not occur in nature. On the other hand, it seems to be the case that attention decoheres/decorrelates input streams, and this reduces response variability (Mitchell et al, 2009). Yet such processes occur even in dendrites in the hippocampus as a way of sparsifying signals.

The final situation, then is one on which quantum superposition is one of many mechanisms used by the brain. In some cases, it appears to be the case that attention works with only decohered signals as a way of decreasing response variability. Yet decorrelation is used elsewhere in the brain as a way of sparsifying signals, without any attention.

It is therefore plausible to suggest that attention causes some signals to decohere from a state that resembles a superposition, rather than a mixture. Moreover, this process can occur for areas like concept-formation and decision-making as for perception. Our inability to maintain focal consciousness on any particular item for very long may be the result of such consciousness as being dependent on state-vector reduction happening. Human voluntary action, as opposed to involuntary action that is the subject of attention, can be thought of as subject to the Quantum zeno effect and therefore of a different kind to animals' reactions to their environment

The existence of coherent quantum states at physiological temperatures in biological systems is no longer in doubt, which buttresses the position that it is plausible to suggest that attention works as one of many decohering processes in the brain.

Reynolds is currently working on a model in which voltage modulation in ion channels can produce a huge gain change in attention. This may be suitably sensitive to and/or causative of quantum effects in the manner of quantum effects in transistors; also the Ahranov-Bohm effect, inter alia, shows that the electrical field potential can change a quantum state.

In particular, only processing streams of sufficient duration in time to be susceptible of becoming the focus of consciousness seem candidates for superposition and state-vector reduction. Attention may be merely one of many mechanisms in the brain for state-vector reduction; alternatively, it may be the case that we can become aware only of sufficiently durable such processes.

References

Aerts, D. (2009). Quantum structure in cognition. Journal of Mathematical Psychology, 53, 314-348

Atmanspacher, H., Bach, M., Filk, T., Kornmeier, J., Römer H. (2008): “Cognitive time scales in a Necker-Zeno model for bistable perception”. Open Cybernetics and Systemics Journal 2, 234–251.

Ball (2011) “Physics of life: The dawn of quantum biology” Nature 474, 272-274 (2011) |doi:10.1038/474272a Published online 15 June 2011 News Feature

Bressler DW, Silver MA (2010) “Spatial attention improves reliability of fMRI retinotopic mapping signals in occipital and parietal cortex” Neuroimage. 2010 Nov 1;53(2):526-33. doi: 10.1016/j.neuroimage.2010.06.063. Epub 2010 Jul 1.

Bressler DW, Fortenbaugh FC, Robertson LC, Silver MA. (2013) “Visual spatial attention enhances the amplitude of positive and negative fMRI responses to visual stimulation in an eccentricity-dependent manner” Vision Res. 2013 Jun 7;85:104-12. doi: 10.1016/j.visres.2013.03.009. Epub 2013 Apr 3.

Cohen M & John H R Maunsell (2009) “Attention improves performance primarily by reducing interneuronal correlations” Nature Neuroscience 12, 1594 - 1600 (2009)

de Barros, J.A. & Suppes, P. (2009). Quantum mechanics, interference, and the brain. Journal of Mathematical Psychology, 53 (5), 306-313.

Hu, H &Wu, M. (2010) “Current Landscape and Future Direction of Theoretical & Experimental Quantum Brain/Mind/Consciousness Research” Journal of Consciousness Exploration & Research |November 2010 Vol. 1 Issue 8 pp. 888-897

Freeman, W., S. O'Nuallain and J Rodriguez(2008) "Simulating cortical background electrocortigram at rest with filtered noise" Journal of integrated neuroscience,7 (3 )Page: 337 - 344 Sept 2008

Hoyer et al, (2011) http://arxiv.org/pdf/1106.2911.pdf

Jiang Y, Patricia Costello ,Fang Fang ,Miner Huang , and Sheng He (2006) "A gender- and sexual orientation-dependent spatial attentional effect of invisible images" PNAS vol. 103 no. 45

17048–17052

B. Libet, C. A. Gleason, E. W. Wright, and D. K. Pearl, Time of Conscious Intension to Act, In Relation to Onset of Cerebral Activity (readiness Potential) (1983) Brain, 106, 623-642.

JF Mitchell, KA Sundberg, JH Reynolds (2009) “ Spatial attention decorrelates intrinsic activity fluctuations in macaque area V4 “ Neuron, 2009, 63. 879-888

O'Nuallain S "The Search for Mind" (Ablex, 1995; 2nd ed Intellect, 2002; Third edition
Intellect, 2003)

O Nualláin, Seán (1997)"Two Sciences of Mind" ( principal co-editor) (Benjamins)

O Nuallain, S CSLI, Stanford and T. Doris(2004) http://bcats.stanford.edu/previous_bcats/bcats04/html/nuallain.html

O Nualláin, Seán (2009) “Zero power and selflessness” Cognitive sciences 4(2)

O Nualláin, Seán (2012) “God’s unlikely comeback” Cosmos and History Vol 8, No 1 (2012) The Future of Philosophy Pp 339-382

O Nualláin, Seán (2008)“Subjects and Objects” Biosemiotics journal, Volume 2, Pp. 239-251

O Nualláin, Seán and T. Doris (2010) “What is neural resonance for?” Chaos and complexity letters 4(2). Reprinted in the collection “mondforce”

O Nualláin, Seán (2010) “Ask not what you can do for yourself:

Cartesian chaos, neural dynamics, and immunological cognition” Biosemiotics Vol 3 Issue 1, 2010 DOI 10.1007/s12304-009-9070-4

O Nualláin, Seán and T. Doris (2011) “Consciousness is cheap” Biosemiotics journal DOI: 10.1007/s12304-011-9136-y online; Hardcopy 2012 Biosemiotics journal 5(2) Pp 193-210

Reimers, Jeffrey R.; McKemmish, Laura K.; McKenzie, Ross H.; Mark, Alan E.; Hush, Noel S. (2009)."Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness". PNAS 106 (11): 4219–4224. doi:10.1073/pnas.0806273106.

Shepherd GM, Grillner S. 2010. Handbook of Brain Microcircuits. New York: Oxford University Press

Stapp H (forthcoming, 2013) “Quantum Theory of Mind” In Contemporary Dualism A Defense Edited by Andrea Lavazza, Howard Robinson

Routledge Studies in Contemporary Philosophy Series" November 2013

Stapp, H (2009 ) “A model of the Quantum-Classical and Mind-Brain Connections, and of the Role of the Quantum Zeno Effect in the Physical Implementation of Conscious Intent.” http://arXiv.org/abs/0803.1633 CH 14 in Minds Machines &QM 3rd edition 2009

P. Suppes, J. Acacio de Barros, and G. Oas (2012). Phase-oscillator computations as neural models of

stimulus–response conditioning and response selection. Journal of Mathematical Psychology, 56(2):

95–117, April 2012.

Tegmark, M. (2000). "Importance of quantum decoherence in brain processes". Physical Review E 61 (4): 4194–4206. arXiv:quant-ph/9907009

Tiago et al (2010) http://www.sciencemag.org/content/329/5999/1671

Zangenehpour S, Ghazanfar AA, Lewkowicz DJ, Zatorre RJ (2009) Heterochrony and Cross-Species Intersensory Matching by Infant Vervet Monkeys. PLoS ONE 4(1): e4302. doi:10.1371/journal.pone.0004302

Zhang, P Keith Jamison, Stephen Engel, Bin He, Sheng He (2011) "Binocular Rivalry Requires Visual Attention" Neuron, Volume 71, Issue 2, 362-369, 28 July 2011

Lectures 3-4

Here we are establishing how neurons can "resonate" with inputs coming at particular time intervals. These input impulses must synchronize with the subthreshold oscillations of the target neuron to cause it to fire. In other words, it's not simply the sum of all input impulses and their reaching a threshold that causes firing; they must be timed in a certain way. Otherwise, an input impulse can actually cause inhibition

We can put the networks of such "resonate and fire" neurons together as in this lecture.

Let's remember the big picture. We are looking at how in individual neurons can plausibly sustain a classical-quantum interface. En route, we find that - using classical wave interference like this lecture demonstrates – they can implement important perceptual tasks that integrate-and-fire has problems implementing. This is our last lecture at this level; we then move up to groups of neurons before starting next week at the cognitive level

Please remember the connection with meditation/consciousness and gamma waves. As lucidly described in Francisco Varela's conversation with the Dali Lama, what is happening in the brain in meditation/consciousness is that global gamma waves interact with the subthreshold oscillations of the neurons. Note that the action potential is of the order of millivolts, like gamma waves; EEG, a crude measure with electrodes on the skull, picks up only microvolts. Unlike Varela, we do not believe that phase synchrony has been established – though it is plausible.

Goleman (2000) “The brain's melody” In Goleman (ed) Measuring the immeasurable Boulder Co 2000 Pp 201-210

Lecture 5: Introduction to Neurodynamics

Neurodynamics uses the language of dynamical systems to describe brain function. So far in the course we have looked at the consequences of viewing single neurons through the prism supplied by harmonic oscillators. Now let’s look at what happens as we view groups of tens of thousands of neurons under the same rubric

Over the past half-century, the Freeman laboratory has accumulated a
large volume of data and a correspondingly extensive interpretive
framework centered around an alternative perspective on brain
function, that of dynamical systems. The contents of consciousness, by
contrast, are seen as an inevitably sparse sample of events in the
perception-action cycle. The paper proceeds to an attempt to elucidate
the contents of this sparse sample.

Freeman (2005a ) established that local dynamics in rabbit and human
neocortex are scale-free, and that every skilled action involves all
cortex and basal ganglia in varying degree. Self-similarity from the
microscopic to the macroscopic levels of the cortex allows the cortex
to change state very quickly. Freeman (2002) introduces the notion of
a wave packet, amplitude modulation of which constitutes the
expression of knowledge, which is stored in synaptic modifications and
expressed by phase transitions. Freeman (op.cit., 517) also makes
the radical contention that we do not need independent access to the
external world for communication to occur; it is sufficient that the
internal meanings in speaker and hearer come transiently into
harmony.

The felt experience of consciousness is constrained by the fact that
the cortex operates discontinuously, with “shutter” states
interspersed with the generation of wave packets (Freeman 2007).
Moreover, while eschewing the technical apparatus of decoherence,
recent work has adopted quantum field theory (Freeman et al, 2006c) to
explain the phenomenon of anomalous dispersion in the brain. Just as
the vibration induced by a blow will reach the other side of a solid
object at a different time to the sound thereof, wave packets show
properties of transmission independent of neural impulse itself. In
fact, the brain behaves in ways not dissimilar to a boson.

Freeman (2005b) introduces several other leitmotiven. 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.Briefly, once an action is lined up, the brain
prepares the system for the sensory consequences of this action in the
preafference process. The consequences for consciousness qua process
are enormous.

Essentially, Hume was right; there is no conscious will, but there
does exist a conscious “won't”. 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.

What is asserted, then, is that conscious states comprise a sparse
sample of the wave packets that embody motor commands, corollary
discharges, and pre-perceptions that we conceive as unconscious. 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.

A talk by Professor Walter Freeman of the University of California at Berkeley. Given to the Foundations of Mind seminar at UC Berkeley (http://FoundationsOfMind.org), organized by Sean O Nuallain. may be found at

https://archive.org/details/UC_Berkeley_FOM_2014_05_02_Walter_Freeman

Specifics of this paper

Walter states three precepts;

1.        The only evidence for consciousness other than introspective is the
existence of group behavious and goal-directed such, particularly when
both attributes are combined in hunting;
2.        Thus, it is speculated consciousness emerges around the Cambrian,
perhaps 500 million years ago;
3.        Neuropil, generically considered, is the organ for consciousness

He summaries his viewpoint thus;
“Consciousness is a biological process that is sustained by
coordination of activity in many parts of the brain of a subject who
is engaged in an action of searching for information that it needs to
cope with its environment………My hypothesis is that the summary action
is expressed in a global field of synchronized oscillation, which will
shape the next action. My conjecture is that we experience this wave
packet as consciousness”

What follows is a highlighting of some salient points from his
presentation to the FoM group on 2 May 2014. This description has been
endorsed by Walter;

In the first place, it is worth noting that Walter's is a thoroughly
neurobiological account. While much of his vocabulary draws on his
considerable math and engineering background, he eschews the
cognitive and symbolic lexicon. Thus, there is no reference to
Grammars, to Piagetian formal operations, to phenomena/conscious
experience or the like; the goal is consistent with Occam's razor.

Thus, we find references to perception-action cycles, to phase
transitions, to attractors, and to the propagation of entities in
state-space. Methodologies recommended include diffusion tensor
imaging, nonequilibrium thermodynamics and much else that may seem
quaint only in a world in which it is assumed that since we have
mapped psychological predicates onto locations in the brain,
neuroscience is basically over, is it not?

It is significant, therefore, that even such ascesis allows
abstraction and generalization; recall of memories; spatial
delocalization and readout by downsampling the delocalized amplitude
modifications. Chomsky may not be name-checked but Merleau-Ponty will
be referenced.

It is accepted, in the other hand, that the animals transform the
stimulus while processing it and the beta and gamma waves carry
amplitude modifications indicating the animal's memories of past
states aimed at future states of the evolving agent . These may be
read out with diffusion tensor imaging.

The entorhinal cortex sens out a sparse but global signal which is the
basis for the individual expectation of the next action. Clearly,
consciousness will have as a signature a sparsely sampled version of
this signal.

A critical innovation is that knowledge is to be distinguished from
merer information partly by the “condensed state of the global
cortical neuropil”. For our purposes, perhaps the critical notion is
that the neocortex is a single organ with no glial barriers. This
allows a phase transition in which the entire cortex is sustaining a
fluctuation and this is the basis for awareness

References

Freeman WJ [2000] Neurodynamics: An Exploration of Mesoscopic Brain
Dynamics, London UK: Springer
Freeman, W. (2002) “How and why brains create meaning from sensory
information” International journal of bifurcation and chaos, Vol 14,
No 2 (2004), 515-530
Freeman WJ [2005a] A field-theoretic approach to understanding scale-free
neocortical dynamics
        Biological Cybernetics 2005, 92/6: 350-359
Freeman WJ [2005b] William James on Consciousness, revisited. Chaos and
Complexity letters, 1 (1) : 17-43
Freeman WJ [2006a ] Origin, structure, and role of background EEG
activity. Part 4. Neural frame simulation. Clin. Neurophysiol. 117:
572-589.
Freeman WJ [2006b ] Scale-free neocortical dynamics. Encyc Comp Neurosci,
Izhikevich E [ed.].
http://www.scholarpedia.org/article/Scale-free_neocortical_dynamics
Freeman WJ [2007] Proposed cortical ‘shutter’ in cinematographic
perception. Ch. In: Neurodynamics of Cognition and Consciousness. Kozma R
and Perlovsky L [eds.]. New York: Soringer.
Freeman WJ, Vitiello G [2006c] Nonlinear brain dynamics as macroscopic
manifestation of underlying many-body field dynamics. Physics of Life
Reviews 3: 93-118.

Sean O Nuallain cinco de Maio 2014

Foundations of Mind

Tuesday, September 30, 2014

Lectures so far on "neuroscience and experience" course

Lecture 1: On single neurons

Lecture 2

Cohen M & John H R Maunsell (2009) “Attention improves performance primarily by reducing interneuronal correlations” Nature Neuroscience 12, 1594 - 1600 (2009)

Stapp H (forthcoming, 2013) “Quantum Theory of Mind” In Contemporary Dualism A Defense Edited by Andrea Lavazza, Howard Robinson

Zhang, P Keith Jamison, Stephen Engel, Bin He, Sheng He (2011) "Binocular Rivalry Requires Visual Attention" Neuron, Volume 71, Issue 2, 362-369, 28 July 2011

Lectures 3-4

Lecture 5: Introduction to Neurodynamics