Dear “germane” Pedro,
Thanks a lot for your comments.
Entia non sunt multiplicanda. It’s the Occam razor:
it’s better to use the simplest explanation, rather than more complicated
descriptions of facts and events.
You talked about metabolic cellular networks, cellular life cycle, abstract
processing of neural
information, human behavior, learning biases, emotional reactions, and so on.
Despite I hate the Occam razor, rejected by the most basic physical assumptions
(see quantum entanglement and the vacuum that is able to produce matter and to
display virtual particles), nevertheless it is very useful for the description
of the brain function and biological systems. Why is the Occam razor useful,
in such cases? Because, I think, they are "desperate" cases: despite two
centuries of true, galileian science, we do not know very much either of living
beings or the brain function. To maxe an example, we are not even sure whether
emotions are completely splitted from higher "cognitive" activities, or are
not.
Therefore, in such case, I think that our only hope to try to assess such still
elusive phenomena is to use an approach from "above" and from "afar". In
touch with you claims, brain activity can be assessed either at
anatomical/functional micro-, meso- and macro- spatiotemporal scales of
observation, or at intertwined levels with mutual interactions. Every
neuro-technique is an observational domain of the whole neuro-scientific
discipline, each one evaluating an anatomical or functional scale different
from the others.
Dimensional scales, as well as multilevel brain activity, can be assessed in
terms of algebraic topology, a general framework that holds for all the
experimental approaches (and "specific" functions) to the central nervous
system, independent of their
peculiar features, resolution, magnitude and boundaries. The Borsuk-Ulam
theorem tells us that a single feature at a lower level can be mapped to two
features with matching description at an higher level, and vice versa.
Therefore, brain activities with matching descriptions embedded in higher
anatomical or functional nervous levels map to single activities in lower
scales.This means that activities described in higher observational levels
necessarily display a counterpart in the lower ones, and vice versa. Next,
consider Brouwer’s fixed point theorem: no matter how you continuously slosh
the coffee around in a coffee cup, some point is always in the same position
that it was before the sloshing began. And if you move this point out of its
original position in the sloshing coffee, you will eventually move some other
points back into their original position.In neurobiological terms, not only we
can always find a brain region containing an activity, but also every activity
comes together with another.
This leads to a novel scenario, where different scales of brain activity are
able to scatter, collide and combine, merging together in an assessable way.
Therefore, different neuro-techniques and brain functions are dual under
topological transformation. The term dual refers to a situation where two
seemingly different physical systems turn out to be equivalent. If two
techniques or phenomena are related by a duality, one can be transformed into
the other, so that the one ends up looking just like the other. A topological
investigation reveals that brain activities always have some element in common:
they do not exist in isolation, rather they are part of a large interconnected
whole, with which they interact.The distinction among different coarse-grained
levels of nervous activity does not count anymore, because nervous function at
small, medium and large scales of neural observation turn out to be
topologically equivalent and fully interchangeable. Topological paths elucidate
how the tight coupling among different neural activities gives rise to brains
that are in charge of receiving and interpreting signals from other cortical
zones, in closely intertwined relationships at every spatio-temporal level.
Summarizing, whether you experience pain or pleasure, or chomp on an apple, or
compute a mathematical expression, or quote a proverb, or remember your
childhood, or read Heidegger's Being and Time, it does not matter: the large
repertoire of your brain functions can be described in the same
topological fashion.
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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