[Fis] Fwd: Response to Jerry LR Chandler (From Arturo Tozzi)

[Pedro C. Marijuan]

(sorry, the problems continue, seemingly, and I have to re-enter the 
messages--Pedro)
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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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