"The mind is a compact, multiply connected thought mass with internal connections of the most intimate kind. It grows continuously as new thought masses enter it, and this is the means by which it continues to develop."

Bernhard Riemann On Psychology and Metaphysics ca. 1860

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Friday, June 02, 2006

Dreams: Biophysical, Aesthetical, and Topological Properties

Why sleep? When there is so much that humanity needs attending to? Perchance to dream. A glimpse at human activity from the standpoint of energetics. Which is to say a work function having the property of field potentiation. But, it is no ordinary such mathematical functional. In fact, it is only properly analyzed from the standpoint that Nicholas of Cusa pioneered in projective topology. His discussion of the non other is equivalent. That is, we cannot reduce this potential to neuronal synaptic bio-mechanical functioning.
Why not? Because human activity is qualitatively distinct from the substrate of animal activity. So, whereas dreams may be a mechanism for survival of mammals, which theta wave evidence supports, for humans survival is of a different sort entirely. This point, by the way, is the where Darwinism falls on its face.
What happens to make human activity distinct? The boundaries of what constitutes energy are constantly redefined (in a successful culture, that is) via advances in technology applied to humanity’s power to efficaciously reduce and reorganize the inorganic, biotic, and noetic domains. This process can only be preliminarily modeled adequately on a Riemannian multi sheeted topology. The reason for this is that older less advanced modes of production do not necessarily cease. They may be thought of as contiguous sheet on a multiply connected surface. It is the movement from one such sheet through a branch point of human invention that leads to a global topological reorganization. Such that the naïve impression of a multi sheeted surface on a globular projective plane must be cautioned against substituting for anything other than a heurism.
Therefore, the fact that researchers have noted that the sorting function in dreaming of sensory input is intimately tied in human dreaming to higher cognitive functions is crucial. This noetic work function that subsumes from a transfinite cardinal number higher ordering sense. (This is not Hausdorf rational numeric dimension, which only serves to create a fractal self similar geometry. Such self similarity is not the essence (it is only an artifact) of the higher dimension that is needed to be introduced. Only the Aleph series will perform this. The problem again, is that this is not quantitative in the usual sense of determination, but only in the higher analogical sense of a transfinite power series.)
Now this discussion must perforce move into the realm of aesthetics. Why? Because the nature of dreams cannot be modeled except from the vantage point of the compositional power of story qua aesthetics. This must be understood in the classical sense of Plato’s Symposium and not Aristotle’s Organum. That is from the most profound understanding emanating from Plato’s School of Athens referenced in his dialogue the Symposium. (Shelley’s translation for English speakers.) This distinction is necessary when attempting to decode how energy and aesthetics are conformable classes of notions. If tragedy is the unresolved working through of crisis, this is understandable from the preconscious reference point understood in the immediacy of dream state, which is without the conscious narrative characteristic of inwardly “spoken” thought. This is why “form” of music and visual arts coheres with the story form of connections from dreams. (Also explains mythos of sphinxes and gargoyles imaginary complexes.) Comedy then becomes the coming home in Plato’s (Homer’s Odyseus, Dante’s Commedia.) sense. This is not the purgation or abreaction associated with Aristotle’s or Bacon’s Organum.
Now from the reference frame of energy, Schiller’s discussion on free energy and must be interpolated. Interestingly, this ties into dreaming as well. Relevant to this, Augustine asks why adornments that are unnecessary from the standpoint of sheer survival are even in existence. Schiller asks why do animals frolic? Why is there harmony, or free energy? Is this Keat’s truth that is beauty? Isn’t the natural order a continuum of ever expanding free energy over and above what is required to maintain the system? So there is the bad infinite entropic approach of a linear expansion trapped in a tragic fixed framework as opposed to a step function which appears to draw upon new forms of energy and redefines the bounds of the system. Playfulness is the expression of this excess in the system. Creativity is its natural conclusion and return to itself on a re-created level. Dreams, plays, art, and drama are the devices that work through the variety of experience which ever expands as humanity promotes a harmonically coherent form of its governance.

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