Dear Krassimir, the main problem with our theory is that it is... too young!Indeed, I met James Peters for the first time on August 2015.By then, we published quite a lot papers together, but the most of them are still under review.Therefore, the (published) general picture is still incomplete. Our starting point is the recently published Springer-book by Peters:http://www.springer.com/in/book/9783319302607This book illustrates the concepts of topological proximity and closeness, that are the mathematical fundations of our ideas. The common features you are talking about are the "proximities" among parts lying on a manifold. We transferred such concepts in the realm of biology and physics. Being aware of their abstract mathematical nouance, we always tried to make empirically testable previsions. While Newton said: "hypotesis non fingo" (even if he did exaclty that, to be honest...), we cleary state: "hypothesis fingo"!However, the pure theory and mathematics, in our framework, is never left in a pure speculative sky: we always try to chain our ideas with the ground! The novel variants of BUT have been partially published. See, for example, the one that I consider our best one: http://onlinelibrary.wiley.com/doi/10.1002/jnr.23720/abstract Other variants can be found here: https://arxiv.org/abs/1606.04031https://arxiv.org/abs/1605.02987 Thanks a lot for your attention!
Arturo TozziAA Professor Physics, University North TexasPediatrician ASL Na2Nord, ItalyComput Intell Lab, University Manitobahttp://arturotozzi.webnode.it/ ----Messaggio originale---- Da: "Krassimir Markov" <mar...@foibg.com> Data: 27/11/2016 23.58 A: <tozziart...@libero.it>, "FIS"<fis@listas.unizar.es> Ogg: [Fis] further analysing: A TOPOLOGICAL/ECOLOGICAL APPROACH TO PERCEPTION Dear Arturo, 1. In your letter you wrote: BUT does not describe just POINTS with matching description, but COUNTLESS other types of matching descriptions! I have read your paper again. I looked for proofs of the NOVEL VARIANTS of BUT you have pointed. Sorry, but I could not find any. Please, be so kind to give me links to publications which contain (preferably - mathematical) proofs of these Novel variants of BUT. 2. In your letter you pointed the class “Single descriptions”. >From the examples you have given, I conclude that this class contains many quite different sub-classes – from “points” up to “signals” and “strings”. I could not find any common features which define this class. Only what I can imagine is that all subclasses maybe are “mental structures”, it it true? If yes, than is this class is the same as “gestalt” (see http://www.users.totalise.co.uk/~kbroom/Lectures/gestalt.htm) or as “reflection” (see http://marxistphilosophy.org/pavlov.htm)? Friendly regards Krassimir From: tozziart...@libero.it Sent: Sunday, November 27, 2016 12:49 AM To: fis Subject: Re: [Fis] Let analyse: A TOPOLOGICAL/ECOLOGICAL APPROACH TO PERCEPTION Dear Krassimir, first of all, thanks for reading all the paragraphs of our most difficult paper! We are grateful to you! Concerning the BUT (AND ITS NOVEL VARIANTS!) let's recapitulate: Every feature is embedded in a structure. The structure displays n-dimensions. We call this feature: single description. Single descriptions are points, or lines. Single descriptions are perimeters, or areas. Single descriptions are single points. Single descriptions are functions, or vectors, or tensors. Single descriptions are algorithms, or parameters. Single descriptions are spatial patterns, or images. An illumined surface is a single description. Single descriptions are groups, or range of data. Single descriptions are symbols, or signs. Single descriptions are temporal patterns, or movements. Single descriptions are particle trajectories, or paths. Single descriptions are syntactic, or semantic, constructions. Single descriptions are thermodynamic parameters, or signals. A region is single description. Single descriptions are strings. Single descriptions project onto a n+1 structure. Single descriptions stand for two descriptions with matching features on the n+1 structure. I call the two above matching features: matching description. What does it mean? This means that the BUT does not describe just POINTS with matching description, but COUNTLESS other types of matching descriptions! Therefore, it also describes a visual and an auditory inputs, if they come from the same environmental source (e.g., in the case of multisensory integration): this occurs for a MATHEMATICAL concept (not a qualitative, nor inaccurate, nor a metaphysical concept) coming from computational proximity, which is a branch of algebraic topology. -- Inviato da Libero Mail per Androidsabato, 26 novembre 2016, 10:12PM +01:00 da Krassimir Markov mar...@foibg.com: 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 Androidsabato, 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. 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