Realization of a concept as a set of space-time surfaces

The space-time surfaces defined as roots of g_º ...g_º f, where f is a prime polynomial and g(0,0)=(0,0) (here f is an analytic map H=M⁴×CP₂→ C² and g an analytic map C² → C²) form a kind of ensemble of disjoint space-time surfaces. Abstraction means formation of concepts and classically concept is the set of its different instances. Could this union of disjoint space-time surfaces as roots represent a concept classically?

What comes to mind are biological systems consisting of cells: do they represent a concept of a cell? What about a population of organisms? What about an ensemble of elementary particles: could it represent the concept of, say, electrons?

1. Holography= holomorphy principle would be essential for the realization of the geometric correlate of collective quantum coherence. Only initial 3-surfaces defining holographic data matter in holography. The 4-D tangent spaces defining the counterparts for initial velocities cannot be chosen freely. This would force a coherent synchronous motion. Also classical non-determinism would be present. Could it correspond to piecewise constant Hamilton-Jacobi structure with different structure assigned to regions of the space-time surface.
2. The Hamilton Jacobi structure of all members of the ensemble from by the roots of g_º ...g_º f is the same so that they can be said to behave synchronously like a single quantum coherent system. Could the loss of quantum coherence mean splitting: p^k roots forming a coherent structure would decompose to p^k₁ sets with different H-J structures containing p^k-k1 roots. Cognitive ensemble, as a representation of a concept, would decompose to ensembles representing p^k₁ different concepts. Is continual splitting and fusion taking place? Could this conceptualization make possible conceptualized memory: the image of the house would be represented by an ensemble of images of houses as kind of artworks.

I have often enjoyed looking at a crop field in a mild summer wind. To me, the behaviour suggests quantum coherence.

1. Crop field in the wind seems to behave like a single entity. Could the crop field correspond to an abstraction of the notion of crop as a set of its instances, realized as a set of space-time surfaces realized as roots of for g_º...._º f. Also more general composites (g_1)º (g₂)...(g_n)_º f, g_i(0,0)=(0,0), are possible. The roots could also represent the notion of a crop field in wind as a collection of crops, each moving in wind as a particular motion of air around it.
2. Do I create this abstraction as a conceptualization, a kind of thought bubble, or does the real crop field represent this abstraction? Could f correspond to the primary sensory perception and does cognition generate this set (not "in my head" but at my field body) as a hierarchy of iterations and an even more general set of g-composites? Different observers experience crop fields very differently, which would suggest that this is a realistic view.
3. If this set represents the real crop field, there should also be a space-time surface representing the environment and the wind. Could wormhole contacts connect these surfaces representing the concept and the environment to a single coherent whole.

   The usual thinking is that crops from uncorrelated systems and wind as a motion of air causes the crops to move. The coherent motion would correspond to a collective mode in which crops move in unisono and synchronously. What creates this coherent motion? Could macroscopic quantum coherence at the level of the field body be the underlying reason in the TGD Universe?

4. How to describe the wind if one accepts the crop field in wind itself represents the notion of crop in wind? Usually wind is seen as an external force. Coherent motion correlates with the wind locally. What does this mean? How could one include the wind as a part of the system? Wind should affect the crops as roots of g_º...g_º f. Each root should correspond to a specific crop affected locally by the wind. Or should one accept that the concept of crop field in the wind is realized only at the level of cognition rather than at the level of reality?

See the article Classical non-determinism in relation to holography, memory and the realization of intentional action in the TGD Universe or the chapter Quartz crystals as a life form and ordinary computers as an interface between quartz life and ordinary life?

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.