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<div>Dear Arturo, James, and FIS Colleagues,<br>
<br>
Thanks for the intriguing presentation. Maybe it is difficult to
make sense in depth of these curious topological views applied to
nervous systems function. In an offline exchange with the authors
I was arguing that the countless mappings among cerebral areas,
both cortical and subcortical, are almost universally described as
"topographical" and that the information related to deformations,
twisting, gradients, inversions, bifurcating "duplications", etc.
is not considered much valuable for the explanatory schemes.
However, just watching any of those traditional "homunculus"
described for both motor and somatosensory mappings, the extent of
deformations and irregularities becomes an eloquent warning that
something else is at play beyond the strictly topographic
arrangement. <br>
<br>
Now, what we are being proposed --in my understanding-- is sort of
an extra-ordinary cognitive role for crucial parts of the whole
topological scheme. Somehow, the projection of brain "metastable
dynamics" (Fingelkurts) to higher dimensionalities could provide
new integrative possibilities for information processing. And that
marriage between topology and dynamics would also pave the way to
new evolutionary discussions on the emergence of the "imagined
present" of our minds. Our bi-hemispheric cortex so densely
interconnected could also be an exceedingly fine topological
playground with respect to the previous organizational rudiments
in the midbrain (in non-mammalian brains). Therefore, couldn't we
somehow relate emergent topological-dynamic properties and
consciousness characteristics?... <br>
<br>
In what follows am trying to respond the initial questions posed:<br>
<p style="text-align:justify;mso-list:l0 level1 lfo1">1)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>Could we use projections and mappings, in order to
describe brain activity?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">**Yes, quite
a bit; in my opinion, they are an essential ingredient of
complex brains.<br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">2)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>Is such a topological approach linked with previous
claims of old “epistemologists” of recent “neuro-philosophers”?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** At the
time being I am not aware of similar directions, except a few
isolated papers and a remarkable maverick working in late 1980s
(Kenneth Paul Collins), with whom I could cooperate a little (with
his help, I prepared a booklet in Spanish) .<br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">3)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>Is such a topological approach linked with current
neuroscientific models?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** I think
Collins was a (doomed, ill-fated) precursor of both the
topological ideas and the quest for dynamic optimization
principles, somehow reminding contemporary ideas, eg, the great
work of Alexander and Andrew Fingelkurts, who are also inscribed
in the list for this discussion. <br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">4)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>The BUT and its variants display four ingredients, e.g.,
a continuous function, antipodal points, changes of dimensions
and the possibility of types of dimensions other than the
spatial ones. Is it feasible to assess brain function in terms
of BUT and its variants?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** I think
it should be explored. Future directions to investigate this
aspect could also contemplate the evolutionary changes in
central nervous system structures and behavioral/cognitive
performances.<br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">5)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>How to operationalize the procedures?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** Today's research
in connectomics can help. Some very new neurotechnologies about
cell-to-cell visualization of neuronal activity and gene
expression could also help for future operationalization
advancements. <br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">6)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>Is it possible to build a general topological theory of
the brain?</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** Topology,
Dynamics, Neuroinformation and also elements of Systems Biology
and Signaling Science should go hand-with-hand for that crazy
purpose. <br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">7)<span
style="font-variant-numeric: normal;font-stretch:
normal;line-height: normal;font-family: 'Times New Roman';">
</span>Our “from afar” approach takes into account the dictates
of far-flung branches, from mathematics to physics, from
algebraic topology, to neuroscience. Do you think that such
broad multidisciplinary tactics could be the key able to unlock
the mysteries of the brain, or do you think that more specific
and “on focus” approaches could give us more chances? <br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">** In my
view, both the disciplinary specific and the multidisciplinary
synthetic have to contribute. Great syntheses performed upon
great analyses--and which should be updated after every new
epoch or new significant advancements. One of the founding
fathers of neuroscience, Ramón y Cajal, made a great
neuro-anatomical (and functional) synthesis with the elements of
his time at the beginning of the past century. It was called the
"doctrine of the neuron" and marked the birth of modern
neuroscience...<br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">Finally, before
saying goodbye, half dozen new Chinese parties from the recent
conference in Chengdu have joined the list; they have ample
expertise in neuroscientific fields and in theoretical science
domains. At their convenience, it would be quite nice hearing
from them in this discussion.</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">Greetings to
all, and thanks again to Arturo and James for their valiant
work,<br>
</p>
<p style="text-align:justify;mso-list:l0 level1 lfo1">--Pedro </p>
</div>
<pre class="moz-signature" cols="72">-------------------------------------------------
Pedro C. Marijuán
Grupo de Bioinformación / Bioinformation Group
Instituto Aragonés de Ciencias de la Salud
Centro de Investigación Biomédica de Aragón (CIBA)
Avda. San Juan Bosco, 13, planta 0
50009 Zaragoza, Spain
Tfno. +34 976 71 3526 (& 6818)
<a class="moz-txt-link-abbreviated" href="mailto:pcmarijuan.iacs@aragon.es">pcmarijuan.iacs@aragon.es</a>
<a class="moz-txt-link-freetext" href="http://sites.google.com/site/pedrocmarijuan/">http://sites.google.com/site/pedrocmarijuan/</a>
------------------------------------------------- </pre>
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