[Fis] NEW DISCUSSION SESSION--TOPOLOGICAL BRAIN

[Pedro C. Marijuan]

Dear Arturo, James, and FIS Colleagues,

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.

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?...

In what follows am trying to respond the initial questions posed:

1)Could we use projections and mappings, in order to describe brain 
activity?

**Yes, quite a bit; in my opinion, they are an essential ingredient of 
complex brains.

2)Is such a topological approach linked with previous claims of old 
“epistemologists” of recent “neuro-philosophers”?

** 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) .

3)Is such a topological approach linked with current neuroscientific models?

** 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.

4)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?

**  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.

5)How to operationalize the procedures?

** 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.

6)Is it possible to build a general topological theory of the brain?

** Topology, Dynamics, Neuroinformation and also elements of Systems 
Biology and Signaling Science should go hand-with-hand for that crazy 
purpose.

7)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?

** 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...

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.

Greetings to all, and thanks again to Arturo and James for their valiant 
work,

--Pedro

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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)
pcmarijuan.iacs at aragon.es
http://sites.google.com/site/pedrocmarijuan/
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