Saturday, January 26, 2013

Geometry Expressed, Hidden In Ancient Design


If the late character of our sources may incite us to doubt the authenticity of this tradition, there remains that, in its spirit, it is in no way out of character, as can be seen by reading or rereading what Plato says about the sciences fit for the formation of philosophers in book VII of the Republic, and especially about geometry at Republic, VII, 526c8-527c11. We should only keep in mind that, for Plato, geometry, as well as all other mathematical sciences, is not an end in itself, but only a prerequisite meant to test and develop the power of abstraction in the student, that is, his ability to go beyond the level of sensible experience which keeps us within the "visible" realm, that of the material world, all the way to the pure intelligible. And geometry, as can be seen through the experiment with the slave boy in the Meno (Meno, 80d1-86d2), can also make us discover the existence of truths (that of a theorem of geometry such as, in the case of the Meno, the one about doubling a square) that may be said to be "transcendant" in that they don't depend upon what we may think about them, but have to be accepted by any reasonable being, which should lead us into wondering whether such transcendant truths might not exist as well in other areas, such as ethics and matters relating to men's ultimate happiness, whether we may be able to "demonstrate" them or not.See: Frequently Asked Questions about Plato by Bernard SUZANNE


Academy was a suburb of Athens, named after the hero Academos or Ecademos. The site was continuously inhabited from the prehistoric period until the 6th century A.D. During the 6th century B.C., one of the three famous Gymnasiums of Athens was founded here. Moreover, it is recorded that Hippias, the son of Peisistratos, built a circuit wall, and Cimon planted the area with trees which were destroyed by Sulla in 86 B.C. In 387 B.C. Plato founded his philosophical school, which became very famous due to the Neoplatonists, and remained in use until A.D. 526, when it was finally closed down by emperor Justinian.


I relay some thoughts I have had with regard to an emergent process.  I think it incorporates a view I have about the geometries hidden in nature that are designed toward expression of some of the historical understanding of this need to apply "fundamentals."  These constructs are in  ephemeral states of existence as if expressed as an idea.  As idea, these become matter orientated views as "a method of approach."

 Learning to identify the schematic usage of geometrical design as an inherent basis of expression, was to understand that intent had this basic design as a malleable feature in the nature of probabilistic outcomes of experience?

In order for us to understand this "world view" as applied to the nature of the reality, it is assumed such fundamentals(all basic models) reveal some of the ways in which we will adopt the reality as expressed?  We are active participants regardless aren't we,  which might mean, there is still some room with which to form, "a more comprehensive view of the type of fundamentals" necessary for such a world view?


IN that sense, the basis of geometrical exploration, as a set of possible outcomes, was to see schematically, that such usage was necessary in understanding what Einstein was able to reveal once adopting, Grossmann's realizations.

By pointing toward Riemann's realization, and this underlying framework of experience as a possible outcome of a universal expression, showed the way to this projector type of geometry, as a dynamical view of this "gravitation inclusion," as a process toward forming that intent.

So of course historical analysis became an important function for me so as to look at the way in which such a historical school,  might have used this method in order to attain the desired student. One who would  face the continuing  search for  such fundamentals. Of course nothing said this is "set in stone." I am laughing right now.  I will use such a structure so as to show you this method.


This was revealed to me in the statement of Hameroff and Penrose, as a process in the cyclic expression of the universe. Using, geometrical design. Looking at emergence as geometrical underlying process of the universe in expression. This was to see an underlying format of constructive phases of experience.

So, not by the idea that such singularity as the nature of such expression, but that by such intent, is an outcome toward the nature of the geometry as dynamical views of as, K minus or plus, as metric aversions of the dynamical process of out comes as the universe in such expression?



While I cannot say for certain, these are the tendencies of Plato, in my thoughts it was for him, to seek and define reality in pursuance of foundation building blocks. Although too, it may not  be true to today's world, it was sufficient then to describe reality as it contained the "ancientness of belief" about an astronomical processes that existed in nature.

While again it may not have been the best way, it reveals some deeper thinking about alchemist methods as they were adopted and transformed. This  in Greek culture of the philosophers arose from one generation to the next.  It then became a method by which one could internalize transformation.

Such model building was to build the ideological,  by the discussing of these analogical methods to purify oneself of the grossness of nature embedded within the material world?

 How much finer such methods then  but to distillate the process for what begins as to it's beginning,  exists as a some, " Prima Materia."  This then became matter defined as the grossness of our experiences,  could lead from any asymmetrical notion of this symmetry in the beginning?




Logic is the art of thinking; grammar, the art of inventing symbols and combining them to express thought; and rhetoric, the art of communicating thought from one mind to another, the adaptation of language to circumstance.Sister Miriam Joseph
The quadrivium comprised the four subjects, or arts, taught in medieval universities after the trivium. The word is Latin, meaning "the four ways" or "the four roads". Together, the trivium and the quadrivium comprised the seven liberal arts.[1] The quadrivium consisted of arithmetic, geometry, music, and astronomy. These followed the preparatory work of the trivium made up of grammar, logic (or dialectic, as it was called at the times), and rhetoric. In turn, the quadrivium was considered preparatory work for the serious study of philosophy and theology.

So while it may be fleeting that such a design may indicate the unification of the Trivium with the Quadrivium, such a completion was inherently significant not just for the presence of adaptation in any school.

Intuitive knowledge is free from partiality or dualism; it has overcome the extremes of stressing subject or object. It is the vision of a world-synthesis, the experience of cosmic consciousness where the Infinite is realised not only conceptually but actually. (p233) Lama Anagarika Govinda, Creative Meditation and Multidimensional Consciousness, 1977


In my thoughts such a design was necessary as  to impose a "model design" that indicated that such adaption in Plato's school amounted to something so solid? A method.

Such integration was necessary so as to realize that such a model built was to survive not only the objective world as a solid,  but was also to realize that such unification could exist within ourselves. Bringing together this liberal arts as a measure of success was to delineate each subjective facet of experience so as to realize that one could transcend the material world, by such realizations which may have took one back to the beginning.

While in this sense artistic expressionism of Raphael's picture in the heading of this site, such a realization was to signify that such a pursuat was necessary and represented the coming together of Aristotle and Plato in the very centre of that world. It required us to become closely associated to the "beginning point" of what was allowed in terms of what is self evident as an inductive deductive process of unfolding.

This was our internal teacher/student dialogue that becomes necessary in order to proceed with dealing with the  truths as they come to us in our realizations.

It was the uniqueness of the individual to which although each truth revealed it's successes with regard to that individual's development, in the larger scheme of things,  it asked us to proceed with a method so as to deal with the science of life? To be inquisitive, but grounded in this teacher/student relationship so as to move forward and experience the world.



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