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Essay on Mesoscopic and Quantum Brain Date 2004-7-6 16:51 |
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Essay on Mesoscopic and Quantum Brain
_____________________________________
Haret C. Rosu
Instituto de Fisica de la Universidad de Guanajuato,
Apdo Postal E-143, Leon, Gto, Mexico
Institute of Gravitation and Space Sciences,
Bucharest, Romania
rosu@ifug.ugto.mx
(received: February 7, 1997)
The fox knows many things, Brooks has used the subsumption
But the hedgehog knows one big thing architecture to build insect
Archilochus -like robots. But insect minds
... what about the grasshopper? are not very interesting.
We are now exploring the space
between the insect and the
adult human.
D.C. Dennett, Phil. Trans. R. Soc. Lond.
A349, 146 (1994)
Abstract
________
In the pure essay style (no mathematical formulas), I present a number
of speculative reflections and suggestions on possible applications of
mesoscopic methods and of quantum mechanical concepts to as such a complex
system as the human brain. As an initial guide for this essay I used "The
Emperor's New Mind" of Roger Penrose.
I. Introduction
_______________
The almost one hundred years of historical development of quantum
theory are a manifest proof of its viability and successfulness, despite a
number of persisting conceptual and/or philosophical difficulties, e.g.,
measurement, quantum-Zeno, and EPR paradoxes, that may be considered
ever-lasting open problems. Due to their versatility the quantum methods can
be applied in principle to any space-time scale, when amended with
corresponding innovations, usually by generalizing certain delicate
interpretational aspects. For example, one may encounter ambitious programs
such as describing the whole universe in quantum mechanical terms, a case in
which the usual Copenhagen interpretation, apparently sufficient at
microscales, have to be replaced by more general schemes, as for example, the
"sum over histories" interpretation [1], a modern variant of Everett's
"relative state" (1957) [2], or of the slightly different language of "many
worlds" [3]. For a recent `map' of the various interpretations and other
issues of quantum mechanics, I recommend the paper of Sonego [4].
Unfortunately, what happens when one is trying to extend too much the usual
domain of a theory, even if it is of the rank of quantum mechanics, which is
*superb and useful* in Penrose's classification, is to turn it into a purely
formal and almost unuseful scheme.
Since a common way of scientific reasoning in physics is that
phenomena at normal macroscopic scales are to be explained in terms of
concepts built up of quantities formally existing at microscopic scales, many
people believe that quantum theory is a universal theory [5]. Therefore
quantum theory/mechanics should have something to say regarding one of the
most sophisticated systems, and actually for the time being, the most
sophisticated we know about, which undeniably is the *human brain*. This
"porridge-like" biological assemble is the command unit of the human body and
of extreme importance to all of us for any need, including the scientific one.
One can think of it at three spatial scales: the microscopic, the mesoscopic,
and the macroscopic ones. By microscopic scales I would like to mean quantum
length scales, i.e., 10^-10 - 10^-9 m, the mesoscopic scales, where
according to Feynman [6] "there's plenty of room...", are those between
10^-9 - 10^-7 m, while beyond that one can say that we passed into the
macroscopic realm, which in fact for the brain reduces to the centimeter
scale. This division is of course not sharp and there are no well-established
criteria for the relative separation. Most of the brain activity proceeds at
the mesoscopic and macroscopic scales and it seems a priori unuseful to think
of quantum features and quantum mechanics for such a complex
self-organization. But for a physicist this is not so, and as a matter of
fact, he/she should attempt at finding arguments for making relevant the
quantum features of the human brain. Moreover, some of the quantum methods and
ideas can find interesting applications in this field even at scales which are
not properly quantum ones. The spatial scales mentioned above are standard
ones in physics, i.e., they are the scales with which most of the physicists
are dealing. Since human brain is a complex physical, biological, and
information-processing system, one will expect multiple spatial and temporal
scales to be mixed up, with interactions taking place at multiple hierarchical
levels. Therefore the structural division of the brain activity usually
considered by neuroscientists might look more natural, i.e., the microscopic
scales are those of synaptic-neuronal interactions, the mesoscopic ones belong
to minicolumns and macrocolumns of neurons, and the macroscopic scales are
characterized by the regional activity over centimeters of neocortex (see [7]
and the next section). The columns are defined as filamentary cluster
structures of neurons in the (neo)cortex.
In the following, the reader will find several incipient and quite
provisional opinions on the problem of the human brain at the mesoscopic and
quantum level that I started to gather together mainly in the summer of 1992,
when I began this essay while spending some really good time browsing in the
ICTP-SISSA libraries and looking more carefully into "The Emperor's New Mind".
Being an essay, I escape any mathematical rigor, thus allowing me to utter,
even though in a cursory manner, what might be some interesting and hopefully
useful ideas for future analyses.
Previously to start reading this essay, I recommend the reader to take
a look in Chapters 9 and 10, at least, in the aforementioned book of Penrose
[8] for world-wide known opinions on the brain, to which I will frequently
refer in the following. Philosopher Owen Flanagan has recently classified many
of the scientists not belonging to the mainstream neuroscience as "the new
mysterians". These are supposed to be people whose more or less declared
beliefs are that topics such as *consciousness* and *free will* are too
profound for scientific studies. Therefore what "the new mysterians" do is to
mistify (consciously or unconsciously) those concepts, usually by relating
them to other mysteries (of quantum mechanics in the case of Roger Penrose;
recall that Chapter 6 in "Emperor's" has the title: "Quantum magic and quantum
mystery"). I am negative to such an opinion, and I found in expressing my
disagreement another motivation for the present essay. I think that scientists
have the right to speculate. It is only a question of time for some small
amount of their speculations to convert into scientific and even technologic
truths. These were the main underlying arguments for writing the present
essay.
II. What is the human brain?
____________________________
The brain is by itself a complex, i.e., self-organized
quantum-meso-macro-scopic system/state of biological material which is more
than a logical machine (composite-computer), showing some ability to react at
phase correlations. J.J. Hopfield [9] remarked that the question "How does it
work?" is one of the best motivations for many scientists. In the case of the
brain, an efficient answer is "it is doing computations", and this in its
particular "biological" way. The powerful paradigm here is to view the brain
composite-computers as input-output devices performing transformations on the
input signals to generate the output ones. However, this in-out mapping is
extremely complicated in the case of biological computers. It is also the main
subject for the artificial intelligence projects. Apparently, the paradigm of
computing is at odd only with the concept of consciousness of the human brain.
If a measure or a parametrization of the consciousness will be found, for
human brains as well as for all biological computers, then this will make the
difference between biological computers and electronic ones.
One defines a central nervous system to be a network of `N'
interconnected neurons. The total number of neurons is approximately 10^10,
each of which connects to a so called signal target `S T' made of a cluster
of some 10^3 - 10^4 neurons. The nearest neighbour connections are called
synapses (Sy), by which neurons are sending electrical and chemical signals to
their `S T' cluster. It is supposed that any `Sy' is in one of the two
possible states: firing and non-firing. As such, a certain analogy with spin
systems, the well-known Little-Hopfield model [9], has been developed for
simulating the associative memory of neural networks [10] and constructing
learning algorithms for artificial intelligence. I would like to suggest
possible connections of the activity of neural networks with some of the
self-organized criticality models, that clearly one can envision, especially
with the forest-fire (FF) class of models [11]. By appropriately generalizing
the automaton rules of the FF models one can put them in correspondence with
the quasi-stable patterns (memory) of neuronal firing activity. On the other
hand, the Hopfield model is based on a quasispin representation of the
physical states of firing and nonfiring [12]: memories to be stored are
just patterns of binary sequences of quasispin variables S_i = +/- 1 where the
index _i is running over the whole number `N' of neurons in the network. Such
a sequence may be regarded as an `N'-component vector, characterizing the
patterns, which are stored if they are turned into attractors of the spin-flip
dynamics. This dynamics is governed by the signs of the exchange sums, where
the coupling constants are considered to be the synaptic strengths. One can
turn given patterns into attractors by the Hebb's mechanism [13], i.e., by
appropriate modifications of the synaptic strengths, known as learning
algorithms. Major difficulties were surpassed by bounding the synaptic
strengths (learning within bounds), and at the present time the "Ising-like"
models with all the apparatus of spin-glass theory [14] are by far the most
powerful paradigm of physics for studying the brain activity considered as
sets of computations. These are, in a few words only, the basic facts required
in order to proceed in a constructive-computing manner towards further
understanding of the higher functions of human brain and/or the
interconnections among its subsystems (visual cortex, somatosensory cortex,
motor cortex, thalamus, peripheral cortex).
Hopfield's paradigm is fine and quite efficient for artificial
intelligence purposes. Nevertheless there is one really difficult question for
it and this is the title of the first chapter in "Emperor's": "Can a computer
have a mind?" In other words, what is the fact providing the distinction
between a biological computer and an electronic one? Is a biological computer
just a more complicated electronic one or is there a fundamental difference?
Is this difference provided by quantum mechanics? I shall try to formulate
some arguments based on quantum ideas in Section IV below. Here I shall list
other general properties of the brain that one can notice when is passing at
the level of the higher brain functions:
(i) The higher functions are in general delocalized, display some degree of
stochasticity, and are intercorrelated in parallel computing manner. There are
many unresolved questions concerning the integration of cortical activity and
the `higher' integrative areas [15]
(ii) The neurons have the capacity of working out several inputs and are
selecting the output signal and its frequency, the cooperative result of such
a processing being a kind of generalized holographic recording of the outside
world.
An interesting columnar self-organization of the neocortex is well-known:
"minicolumns " of about 110 neurons (about 220 in the visual cortex) comprise
modular units vertically oriented relative to the warped and convoluted
neocortical surface through almost all the regions of the neocortex. The
short-ranged fiber interactions (both excitatory and inhibitory) between
neurons take place within about 1 mm, which is the extent of a "macrocolumn"
comprising about one thousand minicolumns, whereas the long-ranged
cortico-cortical excitatory fibers (the white matter) have an averaged length
of several centimeters. This structural organization supports the idea of
computing-oriented activity of the brain.
Shelepin, whom I cite in Section IV below, has suggested the theory of complex
Markov chains as a sufficiently general mathematical description of the higher
functions of the brain, which include quantum mechanics as a particular case,
but in any case, one has to be aware of the impressive panoply of disciplines
contributing to their understanding: neurobiology, computer science,
biochemistry, artificial intelligence, molecular biology, mathematics,
psychology, physics, and philosophy.
III. Consciousness and mesoscopia
_________________________________
Perhaps the most fundamental notion in neuropshycology is the global
attribute of the brain known as consciousness. In general terms, what we
usually call awareness or consciousness or "unique personality" might be
considered a problem of spatio-temporal synchronization between the two
cerebral hemispheres. This interpretation comes out from an interesting
neuro-disease, which manifests itself by the so-called "multiple
personalities'' cases to be found for example in the book of Gazzaniga and
LeDoux [17]. This neuro-disease is the result of the therapeutic operations
(severing of the corpus callosum) for some forms of epilepsy, and more
generally can be considered as split-brain experiments. Such cases have the
exterior data mapped only on one cerebral hemisphere without the other
hemisphere being aware of them. Thus, one can think simply of a
deshyncronization of the two hemispheres at the level of their neuronal
signals. This alone explains the attention paid to the synchronized
oscillations in the cerebral cortex [18]. "Emperors's" p. 385 mentions also
the interesting `P.S.' split-brain case revealed by neurophysiologists,
showing a transient phase in which only one hemisphere could speak, but both
hemispheres could comprehend speech. For the cases with removed portions of
visual cortex and comments on the phenomenon of *blindsight* as related to
consciousness, see "Emperor's" pp. 386-387.
Clearly, it is extremely difficult to accept a definite physical base
for such an esoteric concept as consciousness dealing mainly with the
subjective activity of the brain. It may be called a sense for which the
receptive organs are directly the neurons, in which all the other sense
stimuli can be more or less included on a subjective base, that is with
degrees of importance varying from one brain to another. The neuronal global
response to such a brain activity is the personal representation of the
exterior and interior world altogether and may be called consciousness. It is
also a parameter of the evolution in time of an individual brain, obviously
connected with both short-term and long-term memory. It is a direct neuronal
"pshycological", and sometimes almost physiological sense that occurs as an
outcome of all the mental functions of an individual brain working in
*synergis*, and probably, from this standpoint, one can interpret it as an
informational measure of the coupling between the `subjectivity' and the
`objectivity' of a brain.
There are at least two physical phenomena contributing to
consciousness in its objective form. One is the synchrony of the neurons. When
synchrony is between the neurons of the two hemispheres it provides the
`unique personality' character of the brain. The other mechanism is the
stationarity of the 40 Hz collective oscillations of the neurons as shown by
experiments on animals. Synchrony and the 40 Hz oscillations together are
related to the so-called `binding problem' in neuroscience which is
essentially the making of a unified perception. But what makes neurons to
oscillate collectivelly at roughly 40 Hz. Is this a reflection of the
nonlinear dynamics of the neuronal network as a result of functions such as
memory and attention or it has to do with the microtubule architecture of the
neuron skeletons? Again cummulative effects can be invoked. The microtubules,
which are long (350-750 microns in the axons), and rigid polymers made of a
globular protein called tubulin, were suggested to generate quantum effects of
importance for consciousness by Penrose [16]. I would like to come here with
an argument of interest for microtubules taken from the mesoscopic phenomena
recently put into evidence in the realm of carbon nanotubes (for their history
see [19]). Carbon nanotubes are thread-like structures forming in carbon
deposition stimulated by an electron beam, and are pretty well observed in
scanning transmission electron microscopy [20], and, as a matter of fact,
they are amongst the few laboratory-produced structures covering the crossover
from microscopic to the mesoscopic regime. In an interesting experiment,
Kasumov, Kislov and Khodos [21] observed displacements of the free ends of
threads of amorphous hydrocarbons of 200-500 Anstroms in width and 0.2-2.0 um
in length relative to a fixed reference point on the screen of a transmission
electron microscope. The minimal displacements were of about 5 Anstroms, and
the observations were made in a stationary regime of the threads, i.e., very
low density of the beam current (0.1 pA/cm^2). They observed random jumps of
the free ends of the carbon threads of 10-30 Anstroms in length with a
frequency of 1 Hz. All the possible reasons of induced vibrations were taken
into account by the authors with the conclusion that no classical external
force can explain the jumps and finally they attributed the oscillations to
jumping effects related to spontaneous localization ideas of Ghirardi, Rimini,
and Weber [22]. In our opinion, the jumps in length of the carbon nanotubes
can result from a mesoscopic Brownian motion in which there is a competition
between some dynamical instability and damping, being different from the
microscopic Brownian jumps which never damp out. If such jumps will be
confirmed by other experiments, and their origin identified, there will be
important consequences for neuronal microtubules too. For instance, one can
associate the 40 Hz oscillations either with the frequency of the jumps of the
network of neuronal microtubules due to a mesoscopic Brownian motion as
mentioned above or with spontaneous localization ideas [22] as applied to
microtubules. Actually, microtubules are already an active experimental and
theoretical research field [23]. Their interesting growth properties have
been recently under focus [24], and also non-linear energy-transfer
mechanisms in microtubules have been proposed [25] making the field more
physical. They may play an important role in the brain plasticity ("Emperor's"
pp. 396-398). At the same time, it is quite obvious that graphene tubules can
reveal many phenomena of worth for biological microtubules as well.
IV. Hints for quantum approaches to the human brain
____________________________________________________
I shall start this section by recalling Penrose's rather strong
speculation on the existence of single-quantum sensitive neurons ("Emperor's"
pp 400-401). Yet independently of this speculation, there are various other
ideas concerning possible quantum treatments of the brain.
I would like to present shortly some facts from superfluorescence (SF)
that might be of importance for Hopfield's paradigm as I already mentioned at
the end of Section II. Perhaps the simplest and probably useful way to think
of quantum effects within human brain is to consider it as a kind of
generalized Dicke superfluorescent (superradiant) system. This has been
suggested by Shelepin [26] as an analogy for the two-position switch of
axons. Four decades ago, Dicke has pointed out that `N' atomic oscillators
interacting with a common radiation field are not independent and live in a
correlated state [27] that, under certain conditions, can display a
collective radiative deexcitation, with all `N' oscillators acting like a
single rigid dipole. In the original treatment, the matter-radiation system is
described by a Hamiltonian of three terms corresponding to a collection of
two-level atoms, a one-mode field, and a one-photon Dicke interaction (a
simple coupling between the transition operators and the absorption/emission
operators of the photon). On these lines, particularly interesting would be to
reveal counterpropagating correlations of the type recently put into evidence
and discussed in solid-state superfluorescence [28] [29] with
quasi-one-dimensional active volumes (pencil-shaped excitation volume) of
length much longer than the emitted wavelength. Let me point out that even of
more relevance to the problem of superradiant neurons is the observation of
*hyperradiance* (HR) from phase-locked soliton oscillators in the setup of
*long* Josephson junctions [30], because neurons are closer to soliton
oscillators than to atomic ones. In any case, the *hyperradiance* phenomenon
must be investigated in detail in the newly fabricated superconducting neural
circuits [31]. To pass to neurons, one can simply assume that SF brain
phenomena are induced by certain particular neurons acting similarly to the SF
centres in crystals, whereas one can invoke some magnetic coupling between the
synapses when the analogy with the Josephson junctions is pursued. In the
first case for example, one is allowed to consider distributed-feedback
structures due to density fluctuations of the SF neurons as the origin of the
correlations.
Perhaps it is worthwile to note that the strong correlations between
counterpropagating one-dimensional pulses are absent in the gas phase. One
might have in this way more than a naive answer to the naive question of why
the brain is in a solid-state phase and not in a gas one. Clearly, it would be
extremely interesting to look for counterpropagating correlations between the
two cerebral hemispheres and to see the implications for brain
synchronization. Their similarity with the EPR quantum correlations [32]
should be investigated in order to get insight and provide good answers to the
question: "Does quantum mechanics/quantum-like effects make us intelligent?"
It is worth mentioning at this point that some time ago, Vinduska [33]
elaborated on the impossibility of creating quantum correlations with
electronic computers. It might well be that a biological computer makes use of
EPR-type correlations, thus promoting itself to a superior level of existence.
What one should keep clear in his mind is that superfluorescence is a
cooperative phenomenon, i.e., the output is proportional to the squared number
of neurons involved, and it is due to some type of emission process and not to
an amplification of an input signal. This implies a "laser"-like action of
some brain activity.
On the other hand, there are many mathematical aspects involved in
treating the human brain as a macroscopic quantum state. The first problem is
to define rigorously the macroscopic brain quantum state. In this respect, we
draw attention to the paper of Duffield, Roos, and Werner [34], who defined
some notions of mean field limit for nets of states converging to a
macroscopic limit state.
Of much relevance to the field of neuropshycology might be the
experimental findings of Kelso *et al* [35] who put into evidence, by means
of SQUID detectors, spontaneous transitions in the neuromagnetic field
patterns. They claimed that such transitions are to be associated with the
switching of the non-equilibrium patterns formed by the brain during the
transition between coherent states, and so from one behavior to another one.
One might guess that various types of coherent and squeezed states [36], when
appropriately generalized, and within information-theoretic pictures [37],
will have important applications in this field.
V. Quantum effects in human receptors
_____________________________________
We are interested in the human receptory organs since they are the
places where manifestations of quantum effects from the standpoint of their
sensitivity and response have been reported so far. At the cell scale, human
brain has quantum (molecular) receptors of the outside fields. These receptors
absorb electromagnetic radiation at the level of tens to thousands of quanta
per mode as well as phonons in the same amount. More powerful fluxes are
already damaging.
A. Visual or electromagnetic reception
______________________________________
Perhaps, the best sensory system in which one may have hopes for
studying quantum correlation phenomena to be associated with the human brain
is the visual system (from the eye up to the visual cortex). In fact, in this
case one encounters experimental results on the rod sensitivity to single
photons. Actually, biological photoreception has mesoscopic scale, and as
such, is just at the transition point from quantum reception to classical one.
For a good introduction to quantum fluctuations in the human vision we refer
to the review paper of M.A. Bouman *et al* [38]. For the absorption of a
single photon by a rhodopsin pigment and its amplification ending up into a
neural response see Lewis and Del Priore [39], and for the responses of the
retinal rods of toads to single photons see Baylor, Lamb, and Yau [40].
Penrose is also citing Hecht, Shlaer, and Pirenne [41], who established in
a famous experiment that an input signal of seven photons is required by
humans for conscient perception.
I now address the relationship between the electromagnetic vacuum
fluctuations and the possibility of four-dimensional and more-dimensional
vision. My point is that the electromagnetic zero-point fluctuations are not
very sensitive to the spatial dimensions of the macroscopic world. In other
words, the number of spatial dimensions is a quite free parameter at the level
of vacuum fluctuations [42]. Of course, the conversion of two-dimensional
images into three-dimensional ones is well explained in the optics of the eye
as a stereoscopic effect and it is for this reason that we need two eyes, but
here I am referring to more-than-three spatial dimensions. In my opinion, the
Regge calculus approach [43] to the more-dimensional manifolds, in its
strict geometrical meaning, will be quite useful for the problem of producing
vision in more dimensions, especially when the quantization of 4D Regge links
will be properly understood [44]. The detailed features of the Regge quantum
links will be essential in proceeding toward a biological more-than-three
dimensional vision. Moreover, one should be aware of the experimental
discovery of Hubel and Wiesel [45] who first observed that endstopped
hypercomplex cells (that is, selective to moving-bar stimuli of specific
lengths) in the visual cortex could respond to curved stimuli and sugessted
they might be involved in the detection of curvature. More recently, Dobbins,
Zucker and Cynader [46] provided both a mathematical model relating
endstopping to curvature and physiological evidence that endstopped cells in
area 17 of the cat visual cortex are selective for curvature.
There seems possible the implementation of multi-dimensional image
construction as well as multi-dimensional photoreceptors at the mesoscopic
level, either by using new types of "depth" effects or holographic methods.
Also, more should be known on the connection between the internal
representations of rigid transformations and cortical activity paths as
suggested by Carlton [47].
Let me remark on another important feature of living creatures. While
within the sonic world, the living creatures possess as a rule both receptory
and emitting organs, this is not so in the electromagnetic world, where, in
overwhelming majority, only receptors are present, and there is no
electromagnetic `mouth'. Moreover, if this is to exist, it should be a kind of
biological laser [48], in order to be used for communication purposes.
Although in the animal world there are certain species of fishes possessing
organs recepting and emitting electrical pulses [49], it appears that the
electric activity of the human brain, which is chemical in essence, is too
weak to sustain a lasing activity of the brain, at least of the
electromagnetic type. This looks frustrating, but we have to accept that it is
much easier to build up mechanical organs than laser ones using biological
materials.
Finally, we recall that according to Chomski [50], the fisiology of
the eye-brain system is essential in interpreting the various trajectories we
are observing in our visual field. Such an argument is put forth as a
consequence of the so-called "rigidity principle" in human vision, that is the
interpretation of the visual scene in terms of rigid objects in motion. On the
other hand, the animal visual systems are projected to react to other types of
movements.
B. Hearing or sonic reception
_____________________________
Quantum detection can be looked for in other sensory systems, in particular in
the hearing system, where by quantum one should mean the phonon, although one
can immediately estimate that the thermal environment actually forbids single
phonon detection for humans [51]. In this subsection I would like to draw
attention to an ethnological claiming I heard about in Trieste. Some time ago,
the ethnomusicologist Mantle Hood wrote an essay on a ... quantum theory of
music [52]. He advocates the idea that a manifestation of Bohr complementarity
principle is to be encountered in this discipline of arts as "the continuity
of the first partial of a tone sounded and the discontinuity of constantly
shifting energies in the distribution of upper partials". These ethno-concepts
are not clear to the present author who is merely quoting the paper as a
curiosity. According to Hood, *Musics*, as a form of cognitive learning, is
based on physiological responses to aural stimuli transcending any mechanical
differences in construction between the musical instruments. I remember that,
during my stay in Trieste, I participated in Prof. Hood's ethno-experiment,
which meant just hearing successively as diverse instruments as: Scotish
bagpipe, flute, tambura, mridangam, Tibet funeral horns, Korean kayagam,
Japanese gagaku, Irish tin whistle, and so on, in order to test his
assumption, but frankly I was not capable of saying anything interesting about
my aural stimuli.
As for the mesoscopic musical scales to which some technologies are
already knocking the door, one can foresee the numerous applications of
wavelets in processing musical sounds [53]. The wavelet approach [54] looks
already essential for studying the hearing system of the brain, as well as the
visual system and other brain phenomena, at the mesoscopic scale.
C. Uncertainty principles
_________________________
The usage of wavelet principles is not at all new for psychophysical
experiments, especially in models of vision. The old Gabor functions (harmonic
oscillations within Gaussian envelopes) [55] are in fact wavelets, and have
been introduced by applying arguments from quantum mechanics. Gabor
demonstrated that this class of "modulated probability pulses" is optimal in
the sense that it possesses the smallest product of effective duration (or
alternatively spatial extent) by effective frequency width. In the eighties,
Daugman extended Gabor's work to two dimensional filters [56]. For linear
filters there is an "uncertainty relation" which limits the resolution
simultaneously attainable in space and frequency. In the past decade 2D Gabor
functions have been applied to receptive fields of neurons in the striate
cortex by many authors. They concluded that this filters provide a good
description for the receptive field structure of simple cells in the cat
striate cortex. In the words of Daugman "... the visual system is concerned
with extracting information jointly in the 2D space domain and in the 2D
frequency domain, and because of the incompatibility of these two demands, has
evolved towards the optimal solution via 2D channels that roughly approximate
2D Gabor filters." The problem of `energetic' uncertainty principles in human
visual perception has recently been tackled by Trifonov and Ugolev [57].
Moreover, in their paper there is a good historical account of the problem.
The main idea is that since the human eye responds to the emitted
luminescence, one may be endowed to look for an uncertainty principle
involving the luminescence threshold and the spatial resolution.
One can foresee that more complicated families of wavelets and
wavelet-based representations of the signals will be involved in reproducing
the signal processing of more complicated visual and auditory receptive fields
of neurons. In this case, the detailed study of new types of uncertainty
relations will be of great importance. The interested reader is referred to
the literature [58].
D. Quantal synaptic transmission?
_________________________________
There is considerable debate in neurophysiology on the problem of
quantal synaptic transmission. This is a dominant hypothesis concerning the
chemical transmission, which is the principal means of neuronal communication
in the central nervous system. The debate centers around statistical analyses
of recorded histograms of excitatory postsynaptic currents, whose quantal
nature means demonstration of successive peaks, ideally evenly spaced, which
are thought to be of biological and not of statistical origin [59]. My
opinion is that whenever one is facing statistical treatment of data one
should proceed with extreme care since there may occur unexpected statistical
artefacts. I agree more with the demonstration provided by Clements [60]
that regularly spaced peaks in a synaptic amplitude histogram can arise from
sampling error than with the answer of Larkman, Stratford, and Jack [61].
VI. Limitations of the human brain to the quantum knowledge
___________________________________________________________
Recently, James D. Edmonds Jr. [62] examined the human brain
limitations to quantum knowledge, citing Bohr's opinion that the task of
physics is to reveal what we can say about Nature and not what is Nature [63].
According to this conjecture, which seems quite reasonable, "we only do brain-
limited physics !". Hence, our theories are only strategies, i.e., decision
making in the face of uncertainties. However, the crucial assumption which
determines the structure of a strategy is due to dynamics and not to
probabilities and is based on microscopic reversibility. This fundamental
assumption gives rise to the equation of detailed balance, which is, as a
matter of fact, Bayes's postulate in probability theory, i.e., the common
way of conditioning for macroscopic probabilistic thinking. It is well-known
that microscopic reversibility does not imply necessarily time reversal
invariance [64]. On the other hand, the main components of logical reason
are cause-effect relationships. By their very nature cause-effect correlations
involve dynamics with a prefered direction of time. It would be therefore
interesting to develop non-Bayesian strategies, since they might find a
direct experimental field in the mesoscopic world. Such strategies will be
applicable whenever one will take into account violations of microscopic
reversibility and the activity related to some mesoscopic agent working like
a Maxwell demon [65]. An interesting discussion of the breakdown of
microscopic reversibility in enantiomorphous systems in the context of
chemical evolution and origins of life has been provided by L. D. Barron [66],
who introduced the concept of enantiomeric detailed balancing, that can be
of interest to neuronal networks too.
The common logic of human thinking seems to be in difficulty whenever
probabilistic reasoning is coming into play. It is not at all an easy matter
to elaborate languages and appropriate terminology for generalized probability
judgements [67]. Indeed, Arthur Miller attributed to Heisenberg the
following remarkable recollection of the years 1926-1927: "we couldn't doubt
that quantum mechanics was the correct scheme but even then we didn't know how
to talk about it, and the discussions left us in a state of almost complete
despair". As a matter of fact we are at this point very close to the theories
of language formation, which predict a period of chaotic dynamics both in
groups of cerebral neurons and in the thalamocortical pacemaker [68].
According to Damasio & Damasio [69]: "A large set of neural structures
serves to represent concepts; a smaller set forms words and sentences. Between
the two lies a crucial layer of mediation..." and I would say of "meditation".
It is this layer of mediation that one can associate with the period of
chaotic dynamics.
At a more physical level, let's touch upon Zipf's principle of
minimal effort in speaking [70] or, equivalently, Mandelbrot's condition of
minimal cost of information transmission [71]. Such variational principles or
conditions can be associated with 1/f noise in speaking and writing as a
manifestation of information transmission in normal human communication. For a
recent derivation of a universal 1/f noise from an extremized physical
information see Frieden and Hughes [72]. Recall now that a 1/f noise is only
one of the two requirements of the self organized criticality (SOC) paradigm.
The second one is a fractal or multifractal spatial structure of the region
producing the 1/f noise, i.e., for speech, Broca's area, and for understanding
languages, Wernicke's area. What we suggest here is self organized critical
states of these brain areas as possible non-equilibrium dynamical brain states
for normal verbal communication. Passing to an electromagnetic (nonverbal)
communication, and accepting the idea of an electromagnetic lasing organ as
alluded above, the information transmission would be through the vortex
patterns in the transverse plane of the laser beam [73], but again taking
into account the result of Frieden and Hughes [72], one can claim that a SOC
paradigm will still be at work, however at much superior levels of information
rates.
An interesting debate concerns the non-verbality of thought
("Emperor's" pp 423-425). There is the remarkable phrase of Henry Adams in his
"Education": "No one means all he says, and yet very few say all they mean,
for words are slippery and thought is viscous." Many artists certainly don't
think their masterpieces in words, at least during the creative instants, and
also a number of eminent scientists were completely against words and insisted
on their drawback and even damaging effect with respect to thoughts (for
examples, see "Emperor's" pp 423-425). However, as Penrose mentions, there are
persons managing to process a rapid and efficient transcription of their
thoughts into words such as philosophers, and this certainly with no less
merits. Admittedly, there are ways of thinking, like artistic and/or
scientific ones, for which words are not so much useful. So what are thoughts
really? Can they be associated with various transport phenomena of nerve
signals, like various types of solitons and other non-linear wave structures
in neuronal nets? For example, one can work out a simple non-linear
Schrodinger equation, either discrete or continuous, for the propagation of
thought interpreted as an envelope soliton and discuss "collapse"-like and/or
"blow-up"-like phenomena corresponding to various phases of the creativity
processes. Moreover, non-linear extensions of the quantum mechanics, not
fulfilling the second law of thermodynamics [74], may well be at their home
inside the human brain, which being a living system does not obey the usual
formulation of the second law of thermodynamics.
Penrose's discussion of the nerve signals ("Emperor's" pp 389-392) is
very short. Hodgkin-Huxley oscillator model and the FitzHugh-Nagumo one are
two well-established nonlinear models for this phenomenon. To fully be aware
of the importance of non-linear partial differential equations for pulselike
voltage waves carrying information along a nerve fiber I refer the reader to
the review paper of Scott [75].
I also quote as being very close to Bohr's conjecture, Wolfram's point
of view [76] who, in a cellular automaton context, claimed that physical
processes are only computations, whence the difficulty of answering physical
questions is directly connected to the difficulty of performing the
computations. At the quantum level of the human brain, it will be of interest
to obtain further insight into its "quantum computer" aspects [77], taking
into account the recent claims of improved efficiency for certain algorithms
[78], and also for reasons implied by quantum logic theories [79].
VII. Conclusions
________________
In this essay, I expressed a range of speculative ideas that resulted
from the notes I used to make during my first reading of "The Emperor's New
Mind" and my simultaneous random jumping from shelf to shelf in the ICTP-SISSA
libraries. One warning for the reader is that none of those ideas may be truly
of worth, although my feeling is that human brain can support phenomena
described by generalized quantum methods, other than the usual Ising-like
transcription of memory patterns in neural networks. Particularly interesting
would be a generalized brain superradiance. Also direct vision (not by
projections) in more than three dimensions is another interesting issue.
Quantum mechanics *per se* seems to be a weak theory and not a proper
scientific language when confronting it with the complexity of the brain
activity, and also when compared with other methods put forth in tackling this
highly interdisciplinary research field. However, the progress in our
technologies and the advancement of our understanding of the functioning of
the human brain at quantum and mesoscopic levels may well have important
consequences in the future. It is somewhat amasing yet not surprising, that
while the most advanced tomographic techniques of visualising the brain
activity are based on quantum mechanical phenomena, we have so little to say
about the quantum-mechanical brain. For the time being, the main doctrine that
brain activity is entirely computation is dominating the field despite a few
metaphysical objections related for example to the consciousness issue, and I
am afraid that even the microtubules and their infrastructure can be included
in a computational scheme (according to the principle that digital computing
can be used to model and/or to describe most physical systems). Indeed, M.P.
Barnett [80] has already suggested that microtubules are processing channels
along which strings of bits are propagating from one place to another, and
they may well be the material base for the *ultimate computing* [81] in the
molecular framework. Microtubule networks may turn into a major research field
in the near future. For example, they are predicted to possess piezoelectric
properties allowing a possible application of recently proposed experimental
techniques called two-photon diffraction and holography [82].
Finally, whether or not the quantum features of the human brain will
prove difficult to reveal, this does not mean at all that a quantum brain
cannot be fabricated.
_________________________________
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_______________
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_______________
Consciousness, Microtubules, Robot, Thought,
____________________________________________
Quantum Mechanics, Perception
_____________________________
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Laser-type phenomena
____________________
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Encephalograms
______________
N. Pradhan and P.K. Sadasivan, "elevance of surrogate-data testing in
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