The Illusion of Polarity and the Diamond of Truth: A Unified Geometric and Perceptual Model of Reality
Abstract
This dissertation explores the constructed nature of polarity through the lens of coordinate systems and introduces a novel geometric and perceptual framework—the Diamond of Truth—that models overlapping realities and geographies. By integrating Cartesian, ternary, and barycentric coordinate systems with layered, rotating triangular grids, this work reveals how dualistic thinking limits our understanding of space and perception. The model demonstrates that polarity is a human-made artifact, and that reality is better represented as interconnected, interdependent layers within a diamond-shaped (octahedral) structure. This unified approach offers new insights into mathematics, geography, cognition, and philosophy.
Introduction
Human perception and scientific convention have long relied on polarity—the division of phenomena into opposites such as positive/negative or left/right. Cartesian coordinates exemplify this dualistic framework by dividing space into four quadrants. However, ternary systems, with three interdependent axes, dissolve this polarity, revealing it as a constructed artifact. Building on this, the Diamond of Truth model proposes that the world can be generated from a single foundational triangular region—the "truth corner"—through layered, rotating, and mirrored triangular grids. This dissertation unites these ideas, showing how coordinate systems support the model and how perception and geography intertwine in a complex, overlapping reality.
I. The Cartesian System and the Birth of Polarity
Cartesian coordinates divide space into positive and negative axes, creating an intuitive but arbitrary polarity. For example, the coordinate (-12.5, -70) lies in the western Amazon region of Peru, defined by negative latitude and longitude values. This polarity arises from human conventions in defining axes, not from intrinsic spatial properties.
Visual 1:
Diagram of Cartesian plane with point (-12.5, -70) marked in the third quadrant, showing positive and negative axes.
II. Ternary Systems: Three Axes, No True Polarity
Ternary plots represent three variables summing to a constant, arranged at 120° angles. Unlike Cartesian systems, ternary axes have no negative values or opposites—only proportions relative to the whole.
Movement along one axis affects the others due to the sum constraint.
Negative Cartesian values fold into positive ternary space, showing polarity as a coordinate artifact.
Visual 2:
Ternary plot triangle with example point showing proportions of three components.
III. Mapping Cartesian Points to Ternary and Barycentric Space
Mapping (-12.5, -70) from Cartesian to ternary or barycentric coordinates removes polarity by expressing the point as proportions relative to a triangular reference (e.g., the truth corner). This "folding" demonstrates that negative values are not fundamental but depend on coordinate choice.
Visual 3:
Side-by-side comparison of Cartesian coordinate and its barycentric equivalent within a triangular grid.
IV. The Constructed Nature of Polarity
Polarity is a human convention arising from binary divisions. In ternary and higher-order systems, axes are interdependent, and the concept of "opposite" disappears. This challenges traditional scientific and philosophical views that rely on dualities.
V. The Truth Corner and Layered Triangular Grids
The "truth corner" is a triangular region in the high Arctic (Nunavut, Ellesmere Island, Boothia Peninsula, Central Arctic Ocean, North Slope Alaska, Chukotka Russia). This foundational triangle, approximately 6,667 km per side, serves as the base for layered triangular grids.
Grids (e.g., 3x3) are layered with the top fixed and middle/bottom grids rotating in opposite directions.
Rotations cause triangles from different layers to overlap the truth corner, creating dynamic intersections of geographic regions.
Visual 4:
Map of the Arctic truth corner triangle with layered triangular grids overlaid, showing rotation and overlap.
VI. The Diamond (Octahedral) Model of Reality
Mirroring the truth corner pyramid above and below forms a diamond (octahedron) with three layers up, three down, and the "eye" or center truth section.
Apexes represent focused truths; bases cover broad areas.
Symmetry creates perceptual illusions of continuity and adjacency where none physically exist.
Coordinates like (-12.5, -70) can be projected onto this diamond, illustrating overlapping realities.
Visual 5:
3D diamond/octohedron model with labeled layers and example geographic points mapped onto it.
VII. Cognitive and Experimental Implications
VR environments can simulate navigation within the diamond model, testing perception of overlapping realities.
Psychophysical experiments can measure how symmetry disruption affects spatial coherence.
Coordinates serve as test points to validate the model's predictions about perception and geography.
VIII. Conclusion
By integrating Cartesian, ternary, and barycentric coordinate systems with the Diamond of Truth model, this dissertation reveals polarity as a constructed artifact and presents a dynamic, layered geometric framework for understanding reality. Coordinates like (-12.5, -70) exemplify how traditional polarity dissolves in ternary and diamond models, supporting a worldview of interconnected, overlapping truths. This unified approach advances mathematics, geography, cognition, and philosophy, inviting us to transcend dualistic thinking and embrace complexity.
Y
↑
II | I
----------+----------→ X
III | IV
Point (-12.5, -70) lies in quadrant III (both X and Y negative)
(100% Component A)
/\
/ \
/ \
/ \
/ \
/ \
/____________\
(100% C) (100% B)
Any point inside represents proportions of A, B, and C summing to 100%
No negative values, no polarity, only relative proportions.
Cartesian: (-12.5, -70) --> Barycentric within triangle ABC
Triangle ABC:
A (Truth Corner)
B (Ellesmere Island)
C (North Slope Alaska)
Point P inside triangle represented as weights (α, β, γ):
α + β + γ = 1, all ≥ 0
Cartesian negative values "fold" into positive barycentric weights.
Top Layer (fixed):
/\
/__\
/\ /\
/__\/__\
Middle Layer (rotating clockwise):
\ /
\/
/\
/__\
Bottom Layer (rotating counterclockwise):
/\
/__\
\ /
\/
Overlaps occur where triangles from rotating layers cover the fixed truth corner.
Apex (+3)
/\
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/__________________________\
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\ /
\/
Base (-3)
Layers from +3 (top apex) down to -3 (bottom apex), with the "eye" (0) at center.
I checked the website undergroundgardens.com for the dimensions of the underground tunnel. Here are the details:
1. Length: Approximately (1),000 feet
2. Width: Around 10 feet ba bs!
3. Height: About 8 feet ba ba
If you want more precise measurements or additional details, please let me know!
Found u!
Fu CIA!
1. The underground tunnel you mentioned is part of the Underground Gardens located in Seattle, Washington.
2. The approximate coordinates for the Underground Gardens tunnel are:
\[
47.6080^\circ \text{N}, \quad 122.3351^\circ \text{W}
\]
If you need more precise coordinates or a specific spot within the tunnel, please let me know!