[Fis] R: Re: Who may prove that consciousness is an Euclidean n-space ???

Sat Nov 26 21:57:43 CET 2016

Dear Joseph, thanks a lot for the support!  I appreciate it very much, now that I'm under fire!
I agree with you, with a sole difference, when you say "within the same high overall energy level".  Indeed, our approach predicts different energetic levels in different brain functional dimensions.  A BUT topological approach, which states that mappings among every brain
signal and energetic information have the potential to be operationalized in fMRI and EEG studies.  We will provide a proof-of
concept example, in order to demonstrate the feasibility of a BUT topological approach and its aptitude of providing very accurate testable
previsions.  We have two mental states,
one standing for a symmetry, and another for a broken symmetry. Imagine that
the brain at rest displays a preserved symmetry, while the brain during a
visual task displays a broken symmetry. Our model sharply predicts the energetic
values for both the cases, either in EEG and fMRI series. Indeed, according to BUT, a single microarea with
symmetry breaking (e.g., a primary visual area), necessarily
projects to TWO areas with preserved symmetry (e.g., a default mode network's  area). The single area in lower dimensions and the two areas with matching description
need to display the same values of entropy. This allows us to recognize which
zones of the brain are correlated during symmetry breaks, e.g., during the
projective steps from higher to lower level of complexity, and vice versa.
Therefore, our framework is able to
predict the following hypothetical results: if we find, during a visual task,
say, three microareas with an entropy 1.08, we expect to find, during rest, six
or more microareas with entropy=1.08.  In
sum, by knowing just the entropy values for each BOLD-activated or EEG brain subarea,
we are allowed to correlate two different brain states, e.g., a
lower-dimensional state with symmetry breaking 
and a higher-dimensional state with preserved symmetries. 

 You can find further details in our manuscript (under review): http://arturotozzi.webnode.it/products/a-topological-approach-assesses-brain-enthalpy-fre-energy-and-entropy/

Ciao, and thanks again!
Arturo TozziAA Professor Physics, University North TexasPediatrician ASL Na2Nord, ItalyComput Intell Lab, University Manitobahttp://arturotozzi.webnode.it/ 

----Messaggio originale----

Da: "Joseph Brenner" <joe.brenner at bluewin.ch>

Data: 26/11/2016 21.05

A: <tozziarturo at libero.it>, "fis"<fis at listas.unizar.es>

Ogg: Re: [Fis] Who may prove that consciousness is an Euclidean n-space	???

Dear FISers,

At the risk of attracting the anger of all the 
mathematicians in the group, I will agree with Arturo, contra 
Krassimir. For a non-mathematician like me, a description of complex 
dynamic processes such as consciousness and information can be partly 
mathematical but need not involve proofs and their reduced logic.

The question I have is whether the field 
description is itself necessary and sufficient and if incomplete, what is 
missing. Perhaps it is my intuition that consciousness is both continuous and 
discontinuous, and so is its opposite, unconsciousness, which still 
involves high-level nervous functions. In my picture, antipodal points are 
of little relevance compared to the 
non-Euclidean multi-dimensionality of this dynamic opposition, 
moving between identity and diversity, presence 
and absence, clarity and vagueness, symmetry and dissymetry, within the same 
high overall energy level. In any case, perhaps we can agree that everything 
that is moving here is information!

Thank you and best wishes,

Joseph

  ----- Original Message ----- 
  From: 
  tozziarturo at libero.it 
  To: fis 
  Sent: Saturday, November 26, 2016 7:06 
  PM
  Subject: Re: [Fis] Who may prove that 
  consciousness is an Euclidean n-space ???

  Dear Krassimir, 
Thanks a lot for your 
  question, now the discussion will become hotter!
  First of all, we never stated that consciousness lies either on a 
  n-sphere or on an Euclidean n-space.
Indeed, in our framework, 
  consciousness IS the continuous function. 
Such function stands for a gauge 
  field that restores the brain symmetries, broken by sensations. 
Concerning 
  brain and gauge fields, see my PLOS biology paper: 

http://journals.plos.org/plosbiology/article?id=10.1371%2Fjournal.pbio.1002400
  When consciousness lacks, the inter-dimensional projections are 
  broken, and the nervous higher functions temporarily disappear.  
  Concerning the question about which are the manifolds where brain 
  functions lie, it does not matter whether they are spheres, or circles, or 
  concave, or flat structures: we demonstrated that the BUT is valid not just 
  for convex manifolds, but for all the kinds of manifolds.  
See our: 

http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract?userIsAuthenticated=false&deniedAccessCustomisedMessage=

  Therefore, even if you think that brain and biological functions 
  are trajectories moving on concave structures towards lesser energetic levels, 
  as suggested by, e.g., Fokker-Planck equations, it does not matter: you may 
  always find the antipodal points with matching description predicted by 
  BUT.  
  Ciao!

  --
Inviato da Libero Mail per Androidsabato, 26 
  novembre 2016, 06:23PM +01:00 da Krassimir Markov markov at foibg.com:

Dear FIS colleagues,

I think, it is needed to put 
    discussion on mathematical foundation. Let me remember that:

The Borsuk–Ulam theorem 
    (BUT), states that every continuous function from an 
    n-sphere into Euclidean n-space maps some 
    pair of antipodal points to the same point. 

Here, two points on a sphere are 
    called antipodal if they are in exactly opposite directions from the 
    sphere's center.

Formally: if 
    f : S n → R 
    n  is 
    continuous then there exists an x ∈ S n  such that: f ( − x ) = f ( x ).

[ https://en.wikipedia.org/wiki/Borsuk%E2%80%93Ulam_theorem ] 

Who may proof that 
    consciousness is a  continuous function from 
    reflected reality ???

Who may proof that 
    consciousness is an Euclidean n-space 
    ???

After proving these statements we may 
    think further.

Yes, discussion is interesting but, I 
    am afraid, it is not so scientific.

Friendly regards

Krassimir

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