Please note that as of today Sept 22 registration is closed - up to today we allowed stragglers from their summer holidays in. All registrants have been supplied with a password for the course material at http://universityofireland.com/course-neuroscience-and-experience/
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 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 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.
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 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.
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 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.
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.
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, 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.
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