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<div class="moz-forward-container">(sorry, the problems continue,
seemingly, and I have to re-enter the messages--Pedro)<br>
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<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Dear Jerry,</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Thanks for
the intriguing questions!</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">I thank our guest,
Pedro Marijuan, for giving us the
opportunity to talk with such high-ranked scientists. </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span
style="font-size:10.5pt;font-family:'Arial',sans-serif;mso-fareast-font-family:'Times
New Roman';mso-ansi-language:EN-US"> Let’s start!</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><i><span
style="font-size:10.5pt;font-family:'Arial',sans-serif;mso-fareast-font-family:'Times
New Roman';mso-ansi-language:EN-US">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.</span></i><span
style="font-size:10.5pt;font-family:'Arial',sans-serif;mso-fareast-font-family:
'Times New Roman';mso-ansi-language:EN-US"></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Are we
really sure that this proposition is true?
</span><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;letter-spacing:.1pt;background:#FCFCFC;mso-ansi-language:EN-US">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.</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US"></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">For further
details, see: </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://link.springer.com/article/10.1007/s11571-015-9337-1"
target="_blank">http://link.springer.com/article/10.1007/s11571-015-9337-1</a></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><i><span
style="font-size:10.5pt;font-family:'Arial',sans-serif;mso-fareast-font-family:'Times
New Roman';mso-ansi-language:EN-US"> 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. </span></i></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">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. </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">The best
example is the following, that shows how a novel approach
might lead to
unpredictable testable results: </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;letter-spacing:.1pt;background:#FCFCFC;mso-ansi-language:EN-US">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.</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">For further
details, see: </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://link.springer.com/article/10.1007%2Fs11571-016-9379-z"
target="_blank"><span style="color:windowtext">http://link.springer.com/article/10.1007%2Fs11571-016-9379-z</span></a></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">We puzzled
the neuroscientific community, giving rise to a hot debate:
</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://blogs.discovermagazine.com/neuroskeptic/2016/06/11/the-four-dimensional-brain/#.WDvjihrhCUm"
target="_blank"><span style="color:windowtext">http://blogs.discovermagazine.com/neuroskeptic/2016/06/11/the-four-dimensional-brain/#.WDvjihrhCUm</span></a></span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"> </span>
</p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Until we
found the smoking gun: </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size: 10pt;font-family: 'Times New
Roman', serif;background-image: initial;background-position:
initial;background-size: initial;background-repeat:
initial;background-attachment: initial;background-origin:
initial;background-clip: initial;">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.</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">For further
details, see (this manuscript is not yet published, but it
is in advanced
review): </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://biorxiv.org/content/early/2016/08/30/072397"
target="_blank">http://biorxiv.org/content/early/2016/08/30/072397</a></span></p>
<p
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-align:justify;line-height:normal"><b><i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US">Concernig your answers
to our
questions, I may summarize our response in this way: </span></i></b></p>
<p
style="mso-margin-top-alt:auto;mso-margin-bottom-alt:auto;text-align:justify;line-height:normal"><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US;mso-bidi-font-weight:bold">A</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US">s 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 </span><span
style="font-size: 10pt;font-family: 'Times New Roman',
serif;background-image: initial;background-position:
initial;background-size: initial;background-repeat:
initial;background-attachment: initial;background-origin:
initial;background-clip: initial;">assess cortical activity
in terms of McKean-Vlasov
equations, derived from the classical Vlasov equations for
plasma</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US">: </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://vixra.org/abs/1610.0014" target="_blank">http://vixra.org/abs/1610.0014</a></span></p>
<span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"> </span>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">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. </span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"><a
href="http://www.tandfonline.com/doi/abs/10.1080/09515080903238948"
target="_blank"><span style="color:windowtext">http://www.tandfonline.com/doi/abs/10.1080/09515080903238948</span></a></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Becthel
states that </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-US">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.</span> This means that, when
looking down is combined with looking around and up,
mechanistic research
results in an integrated, multi-level perspective. </p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><i><span style="font-size:10.0pt;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">But the main question here
is: </span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">w</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-GB" lang="EN-GB">hat does
a topologic reformulation add in the </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">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. </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-GB" lang="EN-GB">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 (<a
href="http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002400"
target="_blank">http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1002400</a>).
The </span><span style="font-size:10.0pt;font-family:'Times
New Roman',serif;mso-ansi-language:EN-US">real, measurable
nervous activity can be described in terms of paths
occurring on n-spheres. </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-GB" lang="EN-GB">It leads
</span><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-US">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 </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">could be useful in
neuroimaging data optimization. BUT
and its </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">ingredients
can be modified in different guises, in order to assess a
wide range of </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US">nervous functions. Although
this field is nearly novel and still
in progress, with several unpublished findings, we may
provide some examples</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">. 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 (<a
href="http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract"
target="_blank">http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract</a>).
</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Further, BUT
has been proved useful in the evaluation of cortical
histological images previoulsy
treated with Voronoi tessellation (<a
href="http://www.sciencedirect.com/science/article/pii/S0304394016301999"
target="_blank">http://www.sciencedirect.com/science/article/pii/S0304394016301999</a>).</span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">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 </span><span
style="font-size:10.0pt;line-height: 107%;font-family:'Times
New Roman',serif;mso-ansi-language:EN-GB" lang="EN-GB">nervous
</span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-ansi-language:EN-US">nonlinearity</span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US"> and </span><span
style="font-size: 10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-ansi-language: EN-US">Hopf bifurcations
in terms of algebraic topology. </span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-US">Hopf bifurcation </span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">transformations
(the antipodal points) </span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">can be described as paths or
trajectories on abstract
spheres embedded in n-spheres where n stands for </span><span
style="font-size: 10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-ansi-language: EN-US">the Feigenbaum
constant’s irrational number</span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">.</span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-ansi-language:EN-US"> Although the
paper takes into account just </span><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Hopf
bifurcations among the brain nonlinear dynamics, this is
however a starting
point towards the “linearization” of other nonlinear
dynamics in the
brain. </span><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">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. </span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">BUT and its variants
are not just a <i>methodological</i>
approach, but also display a <i>physical</i>,
quantifiable counterpart. To make an
example, although anatomical and functional relationships
among cortical
structures are fruitfully studied, <i>e.g.</i>,
in terms of dynamic causal modelling, pairwise entropies and
temporal-matching
oscillations, nevertheless <i>proximity</i>
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).</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-US">BUT allows the
evaluation of energetic nervous requirements
too. </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family: 'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">There exists a
physical link between
the </span><span style="font-size:10.0pt;font-family:'Times
New Roman',serif;mso-ansi-language:EN-US">two spheres <i>S<sup>n</sup></i>
and <i>S<sup>n-1 </sup></i></span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">and </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">their energetic
features. When </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">two
antipodal functions </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-US">a</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB"> n-sphere </span><i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">S<sup>n</sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">, standing for
symmetries,</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US" lang="EN-GB"> </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">project to a
<i>n</i>-Euclidean manifold (where </span><i><span
style="font-size:10.0pt;font-family: 'Times New
Roman',serif;mso-ansi-language:EN-US">S<sup>n-1</sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB"> 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 </span><i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">S<sup>n-1 </sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">displays energy
parameters lower than the sum of two
corresponding antipodal functions on </span><i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">S<sup>n</sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">. Therefore,
in
the system </span><i><span style="font-size:
10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language:EN-US">S<sup>n</sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB"> and </span><i><span
style="font-size:10.0pt;font-family: 'Times New
Roman',serif;mso-ansi-language:EN-US">S<sup>n-1</sup></span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">, 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 </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">detection of Bayesian
Kullback-Leibler divergence </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">during unsure
perception </span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-GB" lang="EN-GB">(Tozzi and
Peters, 2016, see above)</span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">. Therefore,
paraphrasing what you
stated, t</span><i><span style="font-size:
10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">he meaning specified by
the mathematical symbol IS the
meaning specified by a physical symbol, </span></i><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">at least in our BUT case.</span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">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: </span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US"><a
href="http://journal.frontiersin.org/article/10.3389/fnsys.2016.00079/full"
target="_blank"><span style="color:windowtext">http://journal.frontiersin.org/article/10.3389/fnsys.2016.00079/full</span></a></span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">The paper says: “<span
style="background-image: initial;background-position:
initial;background-size: initial;background-repeat:
initial;background-attachment: initial;background-origin:
initial;background-clip: initial;">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.<span>”</span></span> </span></p>
<p style="text-align:justify"><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US">In such a context, a
phrase of yours is very important: “</span><i><span
style="font-size:10.0pt;line-height:
107%;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Perhaps this premise rests
on the a priori Kantian
notions of space and time rather than the systematic
categories of Aristotelian
causality”. </span></i><span
style="font-size:10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">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. </span><span style="font-size:
10.0pt;line-height:107%;font-family:'Times New
Roman',serif;mso-ansi-language: EN-US"></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Another
example:<i> “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”. </i></span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">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 (<a
href="http://link.springer.com/article/10.1007/s10773-016-2998-7"
target="_blank"><span style="color:windowtext">http://link.springer.com/article/10.1007/s10773-016-2998-7</span></a>),
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… </span></p>
<span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"></span><span
style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US"> </span>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Thanks a
lot!</span></p>
<p style="margin-bottom:0cm;margin-bottom:.0001pt;line-height:
normal"><span style="font-size:10.0pt;font-family:'Times New
Roman',serif;mso-fareast-font-family:'Times New
Roman';mso-ansi-language:EN-US">Ciao!</span></p>
<p
style="margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span
style="font-size: 10.0pt;line-height:107%;font-family:'Times
New Roman',serif;mso-ansi-language: EN-US"> </span><span
style="font-size: 14px;line-height: normal;text-align:
start;"><font face="courier new, monospace"><b>Arturo Tozzi</b></font></span></p>
<p
style="margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span
style="line-height: 115%;"><font face="courier new,
monospace">AA Professor Physics, University North Texas</font></span></p>
<p
style="margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span
style="font-size: 14px;line-height: normal;text-align:
start;"><font face="courier new, monospace">Pediatrician ASL
Na2Nord, Italy</font></span></p>
<p
style="margin-top:12.0pt;margin-right:0cm;margin-bottom:12.0pt;margin-left:0cm;mso-add-space:auto;text-align:justify;line-height:115%;mso-layout-grid-align:none;text-autospace:none"><span
style="font-size: 14px;line-height: normal;text-align:
start;"><font face="courier new, monospace">Comput Intell
Lab, University Manitoba</font></span></p>
<font face="courier new, monospace"><a
href="http://arturotozzi.webnode.it/" style="font-size:
14px;color: rgb(5, 68, 126);line-height: normal;text-align:
start;" target="_blank">http://arturotozzi.webnode.it/</a><span
style="font-size: 14px;line-height: normal;text-align:
start;"> <br>
</span></font></div>
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