[Fis] R: further analysing: A TOPOLOGICAL/ECOLOGICAL APPROACH TO PERCEPTION

Mon Nov 28 08:29:48 CET 2016

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" <markov at foibg.com>

Data: 27/11/2016 23.58

A: <tozziarturo at libero.it>, "FIS"<fis at 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: tozziarturo at 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 markov at 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: tozziarturo at 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: 
    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

      _______________________________________________ 
Fis mailing list 

wlmailhtml:/compose?To=Fis at listas.unizar.es 

http://listas.unizar.es/cgi-bin/mailman/listinfo/fis 

    _______________________________________________ 
Fis mailing list 
wlmailhtml:/compose?To=Fis at listas.unizar.es 

http://listas.unizar.es/cgi-bin/mailman/listinfo/fis 

  _______________________________________________ 
Fis mailing list 
wlmailhtml:/compose?To=Fis at listas.unizar.es 

http://listas.unizar.es/cgi-bin/mailman/listinfo/fis 

  _______________________________________________ 
Fis mailing list 

wlmailhtml:/compose?To=Fis at listas.unizar.es 

http://listas.unizar.es/cgi-bin/mailman/listinfo/fis 

_______________________________________________
Fis mailing 
list
Fis at listas.unizar.es
http://listas.unizar.es/cgi-bin/mailman/listinfo/fis

-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://listas.unizar.es/pipermail/fis/attachments/20161128/7e8b09c3/attachment.html>