The reference for the following is;
Ó Nualláin Seán (2013)“Neural Oscillations &
Consciousness: Attention as a Litmus Test for the Quantum Mind Hypothesis” Journal of Consciousness Exploration & Research| July 2013 | Volume
4 | Issue 7 | pp. 697-713
and this journal offers open-source access which is the main reason I submitted there rather than a more "prestigious" closed venue. the following will probably not print properly so go to JCER's site to get the full version
Article
Neural
Oscillations & Consciousness: Attention as a
Litmus
Test for the Quantum Mind Hypothesis
Seán O'Nualláin*
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.
Key Words: 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 21st
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 result 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 is 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; and 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,
Branco 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.
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, 2012). 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 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 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.
, 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:
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 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.
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 to , 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.
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 to , 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 and endro-dendritic interactions.
, 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 and endro-dendritic interactions.
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.
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, it 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 modeled 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.
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