Charles R Paez Monzon - 2020 - aNatureTechnologies

                      - " There are only things and sentients in the world in an horizont
                          in which their relations that are passing over " - Julian Barbour
  1. 7.1. aFootball aPLandscape is a Shape-Space Architecture
    1. 7.1.1. Shape Space and Shape Space of Shape Spaces in aFootball
  2. 7.2 Wisdom of the Homological Mirror Symmetry between Real and Ideal aFootball on aPLandscape
    1. 7.1.2. Change as Difference of Shape of Ball-Trajectories

7.1. aFootball aPLandscape is a Shape-Space Architecture

7.1.1. Shape Space and Shape Space of Shape Spaces in aFootball

Our aFootball Universe is a close geometric-dinamical system. The Universe has only inside and a perimeter -the bounded landscape - but no outside. We decided to analyse all possible geometric dynamic in the inside of a patched aPLandscape. Therefore, it only contains things sentients - now, only Gon - and order in it is the separation of the entities. The key entity is the ball and its motion. So, the minimal shape of a g-motion is the shortest path from an start alpha- point to a final omega-point that it is a vector; but in general the fundamental shape creates a trajectory or a multivector.

In summary, the aPLandscape constitutes mainly a shape space [Barboum].

Now, I would like to examine the possibility of existence of some sort of invisible framework of reference in which every action, event or relation between entities that Gon can divise inside the closed Universe unfolds on it. And, we see a thing - the ball - and sentient monads - Gon now and, 22 players later on - moving relative to each other. And in every event that happen we just capture a relational view of the state of the patched landscape of aFootball. Now we would like to focus to ball-events data, later .the insterest would be centered on tracking data

My proposal is a theory that can explain all possible genuine relationships between genuine things - the ball, the perimeter, the lines demarking special areas, and the goals - in the game, genuine relationships between thing and the sentient monads and, genuine relationships bewteen sentient monads and the genuine things. This is the Weltangshuung, my closed cosmology as explanation of aFootball shape-space dynamics in the shape-space of shape-spaces where the orbit of all possible trajectories could happen.

Therefore, I would like to present this fabric of relational-shape space as un unfolding structure of all possible events that can be assimilated as an invisible, but understood framework of reference of the aFootball game. Moreover, it will be the conection between our Academia Emeritense’s talents, profesional players and head coaches views with those views of proper data science sport analytics.

7.2 Wisdom of the Homological Mirror Symmetry between Real and Ideal aFootball on aPLandscape

At the fronteir of physical science we have reach a sacred knowledge that is present since antiquity wisdom:

  • There is a homological mirror symetry between the real and the ideal world[Frank Wilzcek].

Applied to football in the mindset of a patched landscape and the fluid performance it can be summarized as:

  • The shape-space-of-relations of the patched landscape tells to the players of a team _how to move
    • yin:

      “move the football in the same direction the longest you can”

    Executing it, the football can reach the original point where the it started the movement and it is called periodicity of the symmetry in 1D real-line direction, where all numbers are positive if they are squared x2 >= 0. The outcome is that the shape-space over the horizon of ball-events fibrates with the direction of the ball and all the framed patched landscape is a field of fibration lines.

    Additionaly, the set of relevant affordances of the patched landscapeh invites Gon to change the direction of movement or break the symmetry.

  • The fluid performance or distribution and movements of Gon and the rest of the players with respect of the ball tells to the shape-space-over-the horizon-of-relations in the framed aPLandscape how to curve or in which new direction the football can move on.

    • yang:

      “go to an empty space (choose the relevant affordance, an island of order and certainty) in the aPLandscape rounded by closed spaces of uncertainty (to minimize surprise)”

    The new direction is a symmetry break.

    There is a hierarchy of fundamental breaks. i-direction is perpendicular to the 1D-real horizontal direction and mirrors the framed landscape using the midgoals lines as reference.Therefore, any point (x1,y1) or coordinate of a point in the framed landscape is a kind of *complex number x1 + y1i and the square of i or i2 is -1 < 0. The final point (x2,y2) is other complex number x2 + y2i or vector of the symmetry break.

    The shape space of shape-spaces over an all possible ball-event horizon in football is a multidimensional hyperspace holding all possibles chains of symmetry breaks or trajectories of a complex system and only need information about the position (x1,y1) where the ball is and the momenta or tangent vector directed to (x2,y2) in a system with N degrees of freedom.

7.1.2. Change as Difference of Shape of Ball-Trajectories

The reality in aFootball is the shape of ball-trajectories using the centroid of each patch as ideal reference of any point in the patch.

The difference of shape is a fundamental concept of change that distinguish events based on observable perception and cognition from inside of the closed Universe. A metrics for change or difference of shape will be by best matching. It is the variational principle that can be used to handle the evolution of the shape law that encodes as initial information the view of the relational state of any alpha point in phase space any where when Gon goes to on-ball control state - a break possession symmetry - and he - and his team mates - execute a possession phase whose task is build-up, develop and end-up into an omega point in any point near by the opponent goal to create an effective Levy flight or try to score a goal whose outcome will be 1-out-of-m possibilities, where m:{score, miss it up, miss it left|right, kept possession, break-possession} and viceversa. If Gon - and its team mates - lost the ball and the breaks possession symmetry set up him - and them - in off-ball relational state where his|their effort is oriented to re-gain possession and save the possibility of a conceded goal.

4 0 The sequence of patch centroids of the Levy flight: [6, 13, 4, 6, 6, 6, 12, 12, 1, 7, 8, 0, 0, 6, 1, 7, 7, 9] is shown in Figure 7.2; but most important is that it can be sintactically represented as a word of gamma-motions or a sequence of interactions coded as: [‘2_73_0613’, ‘5_5_1304’, ‘3_30_0406’, ‘0_6_0606’, ‘0_6_0606’, ‘4_28_0612’, ‘0_12_1212’, ‘4_27_1201’, ‘2_39_0107’, ‘1_35_0708’, ‘2_44_0800’, ‘0_0_0000’, ‘2_30_0006’, ‘1_23_0601’, ‘2_39_0107’, ‘0_7_0707’, ‘3_44_0709’]. Therefore, all possible aFootball that happened in a match can be represented as a sequences of words of gamma-motion interaction codes.