Dear Arturo, Gordana, Joseph, and FIS Colleagues, The key to our current discussion I found in the newest work of Arturo (I have read it before last letter of Arturo ):
A TOPOLOGICAL/ECOLOGICAL APPROACH TO PERCEPTION http://biorxiv.org/content/biorxiv/early/2016/11/11/086827.full.pdf or https://www.researchgate.net/profile/Arturo_Tozzi/publication/310006296_A_TOPOLOGICALECOLOGICAL_APPROACH_TO_PERCEPTION/links/5827617808ae254c50832922.pdf?origin=publication_list What is important is that there exist a non correct using of the topological theory (concretely the BUT). It is taken as an idea to explain the perception when different stimulus create the same meaning in the consciousness. See the example with ambulance of Figure 5a (visual and sound stimulus) which is connected to the same meaning on Figure 5b (single point). But !!! BUT explicitly proof that (citation from the Arturo’s paper): BUT states that, if a single point on a circumference projects to a higher spatial dimension, it gives rise to two antipodal points with matching description on a sphere, and vice versa (Figure 1A) (Borsuk, 1933; Marsaglia, 1972; Matoušek, 2003; Beyer, 2004). This means that the two antipodal points are assessed at one level of observation in terms of description, while a single point is assessed at a lower level (Tozzi 2016b), i.e., point location vs. point description. Points on a sphere are “antipodal”, provided they are diametrically opposite (Henderson, 1996). Examples of antipodal points are the poles of a sphere. This means, e.g., that there exist on the earth surface at least two antipodal points with the same temperature and pressure. BUT looks like a translucent glass sphere between a light source and our eyes: we watch two lights on the sphere surface instead of one. But the two lights are not just images, they are also real with observable properties, such as intensity and diameter. i.e. the antipodal points have the same characteristics !!! This is not valid for the sound and vision with the same meaning! Nevertheless, Arturo wrote very important conclusion (citation): Gibson’s work strengthens and brings to the front the primary question of “what” is perceived, before questions of mechanisms and material implementation are introduced (Rao et al., 1997). Finally, I like the conclusion. My remark is to be more precise when we use mathematical theoretical results. Friendly regards Krassimir From: Joseph Brenner Sent: Saturday, November 26, 2016 10:05 PM To: tozziart...@libero.it ; fis Subject: 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: tozziart...@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 mar...@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 _______________________________________________ Fis mailing list wlmailhtml:/compose?To=Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis ------------------------------------------------------------------------------ _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis -------------------------------------------------------------------------------- _______________________________________________ Fis mailing list Fis@listas.unizar.es http://listas.unizar.es/cgi-bin/mailman/listinfo/fis
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