<HTML><BODY><p style="margin-top: 0px;" dir="ltr">Dear “germane” Pedro, <br> Thanks a lot for your comments.<br> Entia non sunt multiplicanda. It’s the Occam razor: <br> it’s better to use the simplest explanation, rather than more complicated descriptions of facts and events. </p>
<p dir="ltr">You talked about metabolic cellular networks, cellular life cycle, abstract processing of neural <br> 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. </p>
<p dir="ltr">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. </p>
<p dir="ltr">Dimensional scales, as well as multilevel brain activity, can be assessed in terms of algebraic topology, a general framework that holds for all the <br> experimental approaches (and "specific" functions) to the central nervous system, independent of their <br> 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 <br> 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 <br> 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.</p>
<p dir="ltr">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.</p>
<p dir="ltr">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 <br> topological fashion.<br></p>
<p dir="ltr">Arturo Tozzi<br> AA Professor Physics, University North Texas<br> Pediatrician ASL Na2Nord, Italy<br> Comput Intell Lab, University Manitoba<br> http://arturotozzi.webnode.it/</p></BODY></HTML>