Western psychological interpretations According to the psychologist David Fontana, its symbolic nature can help one "to access progressively deeper levels of the unconscious, ultimately assisting the meditator to experience a mystical sense of oneness with the ultimate unity from which the cosmos in all its manifold forms arises."[26] The psychoanalyst Carl Jung saw the mandala as "a representation of the unconscious self,"[citation needed] and believed his paintings of mandalas enabled him to identify emotional disorders and work towards wholeness in personality.[27] See: Mandala
It would be hard for one to see the subjectivity of one's experiences so that they may say, that such a thing could be misleading. If you believe in a way with which consciousness may have some kind of structure then how would you describe that structure? All you see is a body with a brain, or, words that let you know that some kind of intelligence exists behind the tapping of the keys that represented words that materialize here.
Escher Drawing Hands, 1948.
But the idea here is more then that. I became convinced that such methodicalness from a visual representation could be more then the sum of it's part because in a way, it could encapsulate a lot of things. I grasp on to visual reasoning so as to imply that we can receive pictures that are complete unto themself( complete knowledge of), yet hold greater meaning as the symbol is seen in context of an examination of life.
...underwriting the form languages of ever more domains of mathematics is a set of deep patterns which not only offer access to a kind of ideality that Plato claimed to see the universe as created with in the Timaeus; more than this, the realm of Platonic forms is itself subsumed in this new set of design elements-- and their most general instances are not the regular solids, but crystallographic reflection groups. You know, those things the non-professionals call . . . kaleidoscopes! * (In the next exciting episode, we'll see how Derrida claims mathematics is the key to freeing us from 'logocentrism'-- then ask him why, then, he jettisoned the deepest structures of mathematical patterning just to make his name...)
* H. S. M. Coxeter, Regular Polytopes (New York: Dover, 1973) is the great classic text by a great creative force in this beautiful area of geometry (A polytope is an n-dimensional analog of a polygon or polyhedron. Chapter V of this book is entitled 'The Kaleidoscope'....)"
So lets say "you are present" with a experience in your dream time that is totally off the wall. Who is it's manufacturer to have detailed such a scene so as to speak to something quite personal to you, and with it, help you to see the error of your ways? How is complete knowledge gained? You knew better already?:)
Felix Klein on intuition
It is my opinion that in teaching it is not only admissible, but absolutely necessary, to be less abstract at the start, to have constant regard to the applications, and to refer to the refinements only gradually as the student becomes able to understand them. This is, of course, nothing but a universal pedagogical principle to be observed in all mathematical instruction ....
I am led to these remarks by the consciousness of growing danger in Germany of a separation between abstract mathematical science and its scientific and technical applications. Such separation can only be deplored, for it would necessarily be followed by shallowness on the side of the applied sciences, and by isolation on the part of pure mathematics ....
Perhaps you can write a visual interpretation of an image that would likely pass as close to the image that is being described. Do you find familiarity with it or have you see it some where else?
Intuition and Logic in Mathematics by Henri Poincaré
On the other hand, look at Professor Klein: he is studying one of the most abstract questions of the theory of functions to determine whether on a given Riemann surface there always exists a function admitting of given singularities. What does the celebrated German geometer do? He replaces his Riemann surface by a metallic surface whose electric conductivity varies according to certain laws. He connects two of its points with the two poles of a battery. The current, says he, must pass, and the distribution of this current on the surface will define a function whose singularities will be precisely those called for by the enunciation.
The dream is a little hidden door in the innermost and most secret recesses of the soul, opening into that cosmic night which was psyche long before there was any ego consciousness, and which will remain psyche no matter how far our ego consciousness extends.... All consciousness separates; but in dreams we put on the likeness of that more universal, truer, more eternal man dwelling in the darkness of primordial night. There he is still the whole, and the whole is in him, indistinguishable from nature and bare of all egohood. It is from these all-uniting depths that the dream arises, be it never so childish, grotesque, and immoral. Carl Jung
By 'dilating' and 'expanding' the scope of our attention we not only discover that 'form is emptiness' (the donut has a hole), but also that 'emptiness is form' (objects precipitate out of the larger 'space') - to use Buddhist terminology. The emptiness that we arrive at by narrowing our focus on the innermost is identical to the emptiness that we arrive at by expanding our focus to the outermost. The 'infinitely large' is identical to the 'infinitesimally small'. The Structure of Consciousness John Fudjack - September, 1999
Is there not some understanding here of what is gained by a deductive/inductive realizations with regard to our interactions with the world? Is there not some sense here of something topologically significant on a abstract level, that explains this aspect of consciousness? I call it a toposense?
If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.
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