Has the Riddle of the Sphinx been solved?
The Turning Point
Theturningpoint: Nature, Science, Philosophy, Symbolism, Geometry... Pyramids of Giza
Nonspecific Euclidean Geometry
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Some commentators have noted that it takes a “certain amount of faith” to go forward in geometric studies because these foundational axioms lay outside proof… Nonspecific Geometry will be developed to add “characteristics or description” to these fundamental abstractions that do not interfere with their usage as elements of geometric construction. In fact, with this new approach, clarity emerges which requires less faith on the part of the investigator and delivers rich possibilities.
Point, line, and plane are the undefined terms that provide the underpinnings and beginnings for geometry. They are undefined in the sense that they are axiomatic – that is, they have no proof or definition – they just exist as being “self evident” abstractions:
Point: The most fundamental concept in geometry. It specifies location or position in space and has zero width, length or height. It is not possible to physically see a point, and it is usually depicted as a dot.
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Line: A point in motion creates a line. It has length, but no width or height.
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Plane: A line swept at right angles to its own direction forms a surface called a plane. Planes are two-dimensional and have length and width but no height. A plane extends indefinitely in all directions.
DOES IT MAKE ANY SENSE THAT POINTS HAVE NO DIMENSION (SIZE)?
HOW CAN POINTS REALLY LOCATE ANYTHING IF ONE CANNOT SEE OR CONCEPTUALIZE
THEM IN REALITY? LOGICAL DILEMMA…
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A COUNTER INTUITIVE LIMIT CONDITION HAS BEEN IMPOSED ON GEOMETRIC
CONSTRUCTION (GEOMETRY MADE OF POINTS).
RATHER THAN EMPLOY AN “ARTIFICIAL LIMIT,” ONE CAN DEVELOP A MORE NATURAL CONSTRUCT FOR GEOMETRIC ENTITIES – LET THEM BE DYNAMIC AND REFLECT INFINITIES - THIS INSIGHT IS KEY TO UNDERSTANDING GIZA:
NONSPECIFIC POINT (INFINITELY CONTRACTING SPHERE - INFINITESIMAL) MOMENTARILY FROZEN IN STATE OF INFINITE SHRINKAGE SPECIFIES ZONE OF UNCERTAINTY IN ABSOLUTE POSITION (ω).
THE WHEREABOUTS OF THE NONSPECIFIC POINT AT THIS INSTANT IS “BLURRED” DUE TO (ω). NO ABSOLUTE POSITION WILL EVER BE FOUND. THUS, ANY ARBITRARY "SUB" RESOLUTION POINT CAN BE THOUGHT TO BE VIBRATING IN A ZONE OF UNCERTAINTY AT THIS MOMENT… THIS CONDITION NEVER CEASES…
NONSPECIFIC LINE (INFINITELY CONTRACTING CYLINDER - INFINITESIMAL) MOMENTARILY FROZEN IN STATE OF INFINITE SHRINKAGE SPECIFIES ZONE OF UNCERTAINTY IN ABSOLUTE POSITION (ω).
THE WHEREABOUTS OF THE NONSPECIFIC LINE AT THIS INSTANT IS “BLURRED” DUE TO (ω). NO ABSOLUTE POSITION WILL EVER BE FOUND. THUS, ANY ARBITRARY "SUB" RESOLUTION LINE CAN BE THOUGHT TO BE VIBRATING IN A ZONE OF UNCERTAINTY AT THIS MOMENT… THIS CONDITION NEVER CEASES…
NONSPECIFIC PLANE (INFINITELY CONTRACTING CYLINDERS/LINES - INFINITESIMALS) MOMENTARILY FROZEN IN STATE OF INFINITE SHRINKAGE SPECIFY ZONE OF UNCERTAINTY IN ABSOLUTE POSITION (ω).
THE WHEREABOUTS OF THE NONSPECIFIC PLANE AT THIS INSTANT IS “BLURRED” DUE TO (ω). NO ABSOLUTE POSITION WILL EVER BE FOUND. THUS, ANY ARBITRARY "SUB" RESOLUTION PLANE CAN BE THOUGHT TO BE VIBRATING IN A ZONE OF UNCERTAINTY AT THIS MOMENT… THIS CONDITION NEVER CEASES…
In a sense, nonspecific geometric elements can be said to be constantly "searching for a center" - an absolute position that never really exists... An argument could be made that sub resolution geometry finds a statistical center that equates to current views of limited geometric entities.
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See website blog "mini" lessons for a more comprehensive discussion of the above descriptions and how they relate to the tenets of Perennial Philosophy and the union of opposites by way of the middle path.