(sorry, the problems continue, seemingly, and I have to re-enter the
messages--Pedro)
---------------------------------------------------------------------------------------------------------------------------
Dear Jerry,
Thanks for the intriguing questions!
I thank our guest, Pedro Marijuan, for giving us the opportunity to talk
with such high-ranked scientists.
Let’s start!
/The questions raised in this post are highly provocative. From the
perspective of physical phenomenology, it is necessary to identify
corresponding illations between the electric fields of brain dynamics
(such as EEG patterns) and the mathematics of electric fields /
electro-magnetism. It goes without saying that such correspondences
must associate the measured quantities with the theoretical quantities.
In other words, the units of measurements of “brain activity" should
be associated with Maxwell’s equations./
Are we really sure that this proposition is true? How does central
nervous system process information? Current theories are based on two
tenets: (a) information is transmitted by action potentials, the
language by which neurons communicate with each other—and (b)
homogeneous neuronal assemblies of cortical circuits operate on these
neuronal messages where the operations are characterized by the
intrinsic connectivity among neuronal populations. In this view, the
size and time course of any spike is stereotypic and the information is
restricted to the temporal sequence of the spikes; namely, the “neural
code”. However, an increasing amount of novel data point towards an
alternative hypothesis: (a) the role of neural code in information
processing is overemphasized. Instead of simply passing messages, action
potentials play a role in dynamic coordination at multiple spatial and
temporal scales, establishing network interactions across several levels
of a hierarchical modular architecture, modulating and regulating the
propagation of neuronal messages. (b) Information is processed at all
levels of neuronal infrastructure from macromolecules to population
dynamics. For example, intra-neuronal (changes in protein conformation,
concentration and synthesis) and extra-neuronal factors (extracellular
proteolysis, substrate patterning, myelin plasticity, microbes,
metabolic status) can have a profound effect on neuronal computations.
This means molecular message passing may have cognitive connotations.
This essay introduces the concept of “supramolecular chemistry”,
involving the storage of information at the molecular level and its
retrieval, transfer and processing at the supramolecular level, through
transitory non-covalent molecular processes that are self-organized,
self-assembled and dynamic. Finally, we note that the cortex comprises
extremely heterogeneous cells, with distinct regional variations,
macromolecular assembly, receptor repertoire and intrinsic
microcircuitry. This suggests that every neuron (or group of neurons)
embodies different molecular information that hands an operational
effect on neuronal computation.
For further details, see:
http://link.springer.com/article/10.1007/s11571-015-9337-1
/ In the philosophy of science, this is the basic distinction between
traditional mathematical narratives as pure abstractions and APPLIED
mathematical theories of explanations of scientific facts. /
Pursuing Quine’s naturalized epistemology, we are aware that we need to
make testable previsions, in order to “link” mathematical theories with
explanations of scientific facts. This is exactly what we (try to) do.
The best example is the following, that shows how a novel approach might
lead to unpredictable testable results:
Current advances in neurosciences deal with the functional architecture
of the central nervous system, paving the way for general theories that
improve our understanding of brain activity. From topology, a strong
concept comes into play in understanding brain functions, namely, the 4D
space of a “hypersphere’s torus”, undetectable by observers living in a
3D world. The torus may be compared with a video game with biplanes in
aerial combat: when a biplane flies off one edge of gaming display, it
does not crash but rather it comes back from the opposite edge of the
screen. Our thoughts exhibit similar behaviour, i.e. the unique ability
to connect past, present and future events in a single, coherent picture
as if we were allowed to watch the three screens of past-present-future
“glued” together in a mental kaleidoscope. Here we hypothesize that
brain functions are embedded in a imperceptible fourth spatial dimension
and propose a method to empirically assess its presence. Neuroimaging
fMRI series can be evaluated, looking for the topological hallmark of
the presence of a fourth dimension. Indeed, there is a typical feature
which reveal the existence of a functional hypersphere: the simultaneous
activation of areas opposite each other on the 3D cortical surface. Our
suggestion—substantiated by recent findings—that brain activity takes
place on a closed, donut-like trajectory helps to solve long-standing
mysteries concerning our psychological activities, such as
mind-wandering, memory retrieval, consciousness and dreaming state.
For further details, see:
http://link.springer.com/article/10.1007%2Fs11571-016-9379-z
We puzzled the neuroscientific community, giving rise to a hot debate:
http://blogs.discovermagazine.com/neuroskeptic/2016/06/11/the-four-dimensional-brain/#.WDvjihrhCUm
Until we found the smoking gun:
We introduce a novel method for the measurement of information in fMRI
neuroimages, i.e., nucleus clustering's Renyi entropy derived from
strong proximities in feature-based Voronoi tessellations, e.g., maximal
nucleus clustering (MNC). We show how MNC is a novel, fast and
inexpensive image-analysis technique, independent from the standard
blood-oxygen-level dependent signals, which facilitates the objective
detection of hidden temporal patterns of entropy/information in zones of
fMRI images generally not taken into account by the subjective
standpoint of the observer. In order to evaluate the potential
applications of MNC, we looked for the presence of a fourth dimension's
distinctive hallmarks in a temporal sequence of 2D images taken during
spontaneous brain activity. Indeed, recent findings suggest that several
brain activities, such as mind-wandering and memory retrieval, might
take place in the functional space of a four dimensional hypersphere,
which is a double donut-like structure undetectable in the usual three
dimensions. We found that the Renyi entropy is higher in MNC areas than
in the surrounding ones, and that these temporal patterns closely
resemble the trajectories predicted by the possible presence of a
hypersphere in the brain.
For further details, see (this manuscript is not yet published, but it
is in advanced review):
http://biorxiv.org/content/early/2016/08/30/072397
*/Concernig your answers to our questions, I may summarize our response
in this way: /*
As we stated above, the bipolarity of electrical particles is just one
one the countless functional phenomena occurring in the brain. See, for
example, our still unpublished manuscript, where we assess cortical
activity in terms of McKean-Vlasov equations, derived from the classical
Vlasov equations for plasma:
http://vixra.org/abs/1610.0014
From a philosophical point of view, we pursue the William Bechtel’s
approach of a mechanistic explanation in psychology, that goes from
reduction back to higher levels.
http://www.tandfonline.com/doi/abs/10.1080/09515080903238948
Becthel states that the components of a mechanism interact in complex
ways involving positive and negative feedback and that the organization
often exhibits highly interactive local networks linked by a few
long-range connections (small-worlds organization) and power law
distributions of connections. This means that, when looking down is
combined with looking around and up, mechanistic research results in an
integrated, multi-level perspective.
/But the main question here is: /what does a topologic reformulation add
in the evaluation of the nervous processes? BUT and its extensions
provide a methodological approach which makes it possible for us to
study experience in terms of projections from real to abstract phase
spaces. The importance of projections between environmental spaces,
where objects lie, and brain phase spaces, where mental operations take
place, is also suggested by a recent paper, which provides a rigorous
way of measuring distance on concave neural manifolds
(http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002400).
The real, measurable nervous activity can be described in terms of paths
occurring on n-spheres. It leads to a consideration of affinities among
nervous signals, characterized as antipodal points on multi-dimensional
spheres embedded in abstract spaces. To provide an example, embedding
brain activities in n-spheres allows the quantification of geometric
parameters, such as angles, lengths, and so on, that could be useful in
neuroimaging data optimization. BUT and its ingredients can be modified
in different guises, in order to assess a wide range of nervous
functions. Although this field is nearly novel and still in progress,
with several unpublished findings, we may provide some examples. Such a
methodological approach has been proved useful in the evaluation of
brain symmetries, which allow us to perform coarse- or fine-grained
evaluation of fMRI images and to assess the relationships, affinities,
shape-deformations and closeness among BOLD activated areas
(http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract).
Further, BUT has been proved useful in the evaluation of cortical
histological images previoulsy treated with Voronoi tessellation
(http://www.sciencedirect.com/science/article/pii/S0304394016301999).
A wide range of brain dynamics, ranging from neuronal membrane activity
to spikes, from seizures to spreading depression, lie along a continuum
of the repertoire of the neuronal nonlinear activities which may be of
substantial importance in enabling our understanding of central nervous
system function and in the control of pathological neurological states.
Nonlinear dynamics are frequently studied through logistic maps equipped
with Hopf bifurcations, where intervals are dictated by Feigenbaum
constants. Tozzi and Peters (2016, quoted above) introduced an approach
that offers an explanation of nervous nonlinearityand Hopf bifurcations
in terms of algebraic topology. Hopf bifurcation transformations (the
antipodal points) can be described as paths or trajectories on abstract
spheres embedded in n-spheres where n stands for the Feigenbaum
constant’s irrational number.Although the paper takes into account just
Hopf bifurcations among the brain nonlinear dynamics, this is however a
starting point towards the “linearization” of other nonlinear dynamics
in the brain. In sum, BUT makes it possible for us to evaluate nonlinear
brain dynamics, which occur during knowledge acquisition and processing,
through much simpler linear techniques.
BUT and its variants are not just a /methodological/ approach, but also
display a /physical/, quantifiable counterpart. To make an example,
although anatomical and functional relationships among cortical
structures are fruitfully studied, /e.g./, in terms of dynamic causal
modelling, pairwise entropies and temporal-matching oscillations,
nevertheless /proximity/ among brain signals adds information that has
the potential to be operationalized. For example, based on the
ubiquitous presence of antipodal cortical zones with co-occuring BOLD
activation, it has been recently suggested that spontaneous brain
activity might display donut-like trajectories (Tozzi and Peters 2016,
see above).
BUT allows the evaluation of energetic nervous requirements too. There
exists a physical link between the two spheres /S^n / and /S^n-1 /and
their energetic features. When two antipodal functions an-sphere /S^n
/, standing for symmetries,project to a /n/-Euclidean manifold (where
/S^n-1 /lies), a single function is achieved and a symmetry break occurs
(Tozzi and Peters 2016, see above). It is known that a decrease in
symmetry goes together with a decrease in entropy. It means that the
single mapping function on /S^n-1 /displays energy parameters lower than
the sum of two corresponding antipodal functions on /S^n /. Therefore,
in the system /S^n /and /S^n-1 /, a decrease in dimensions gives rise to
a decrease in energy. We achieve a system in which the energetic
changes do not depend anymore on thermodynamic parameters, but rather on
affine connections, homotopies and continuous functions. A preliminary
example is provided by a recent paper, where BUT allows the detection of
Bayesian Kullback-Leibler divergence during unsure perception (Tozzi and
Peters, 2016, see above). Therefore, paraphrasing what you stated, t/he
meaning specified by the mathematical symbol IS the meaning specified by
a physical symbol, /at least in our BUT case.
Concerning the a priori Kantian notions (not just of space and time!),
the most successful current neuroscientific approaches are framed
exactly on… Kantian a priori! See:
http://journal.frontiersin.org/article/10.3389/fnsys.2016.00079/full
The paper says: “Predictive processing (PP) is a paradigm in
computational and cognitive neuroscience that has recently attracted
significant attention across domains, including psychology, robotics,
artificial intelligence and philosophy. It is often regarded as a fresh
and possibly revolutionary paradigm shift, yet a handful of authors have
remarked that aspects of PP seem reminiscent of the work of 18th century
philosopher Immanuel Kant.”
In such a context, a phrase of yours is very important: “/Perhaps this
premise rests on the a priori Kantian notions of space and time rather
than the systematic categories of Aristotelian causality”. /Therefore,
your premise (e.g., the systematic categories of Aristotelian
causality) is as questionable as a Kantian approach, or every other… All
of us are just playing Wittgenstein’s linguistic jokes.
Another example:/“Given the theory of quantum mechanics and the critical
role that angular momenta play in the organization of brain dynamics, I
would conjecture that it is conceivable that electro-dynamic equations
akin to Feynman diagrams are needed to quantify brain phenomenon”. /
This is another linguistic joke. Nobody ever demonstrated that the
brain works with quantum mechanics and that angular momenta play a role
in the organization of brain dynamics! To be honest, we published on
BUT and quantum mechanics
(http://link.springer.com/article/10.1007/s10773-016-2998-7), therefore
we were tempted to use such kind approaches for our brain models.
However, in this case, a quantistic brain it is not a falsifiable
theory at all. And despite Lakatos’ disruption of Popper’s
falsifiability, I still think, in another linguistic joke, that a theory
needs to be falsifiable…
Thanks a lot!
Ciao!
*Arturo Tozzi*
AA Professor Physics, University North Texas
Pediatrician ASL Na2Nord, Italy
Comput Intell Lab, University Manitoba
http://arturotozzi.webnode.it/
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