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 Android
sabato, 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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