Dissertation: The Diamond of Truth—A Geometric and Perceptual Model for Overlapping Realities and Geographies
Abstract
This dissertation introduces a novel geometric and perceptual framework for understanding how the world can be constructed from a single, foundational region—the "truth corner"—using layered, rotating, and mirrored triangular grids. The model evolves from a simple triangular section to a dynamic, diamond-shaped (octahedral) structure, where perception, symmetry, and spatial relationships create a complex, interconnected reality. The work explores the mathematical, geographic, and cognitive implications of this model, including how real-world locations overlap within the truth corner and how symmetry both enables and complicates perception.
1. Introduction
Traditional models of geography and perception assume a fixed, objective world mapped with regularity and symmetry. This work challenges that paradigm by proposing that our experience of the world can be generated from a single triangular region—the "truth corner"—through processes of layering, rotation, and mirroring. This approach not only reimagines spatial relationships but also explores how perception, symmetry, and cognitive mapping interact to create a reality that is both interconnected and ambiguous.
2. The Truth Corner and Triangular Grids
2.1 Defining the Truth Corner
The "truth corner" is a triangular section located in the high Arctic, encompassing regions such as Nunavut, Ellesmere Island, the Boothia Peninsula, the Central Arctic Ocean, North Slope of Alaska, and Chukotka in Russia. In a 3x3 grid model, each side of the triangle is approximately 6,667 km, covering an area of about 19 million km².
2.2 Layered Triangular Grids
By dividing the world into triangular grids (e.g., 2x2, 3x3, 5x5), we can layer these grids atop each other. The top grid is fixed, while the middle and bottom grids rotate—one clockwise, one counterclockwise—causing their triangular sections to periodically overlap the truth corner.
3. Overlap Dynamics and Geographic Mapping
3.1 Overlap Mechanism
Locked Top Layer: Always covers the same geographic regions.
Rotating Layers: As the middle and bottom grids spin, their triangles sweep across the truth corner, creating dynamic overlaps.
Cumulative Coverage: Over a full cycle, every triangle from the rotating grids will, at some point, overlap the truth corner.
3.2 Geographic Locations
Base Locations (Truth Corner):
Nunavut, Canada (Arctic Archipelago, Resolute Bay)
Ellesmere Island, Canada
Boothia Peninsula, Canada
Central Arctic Ocean
North Slope, Alaska, USA
Chukotka, Russia
Overlapping Locations (as grids rotate):
Greenland
Iceland
Svalbard, Norway
Northern Scandinavia
Northern Siberia (Yakutia)
Barents Sea
Northwest Territories, Canada
Bering Strait Region
Hudson Bay, Canada
Various sectors of the Arctic Ocean
4. Scaling and Measurement
4.1 Ruler-Based Sizing
3x3 grid: Triangle side ≈ 6,667 km; area ≈ 19 million km²
2x2 grid: Triangle side ≈ 10,000 km; area ≈ 43 million km²
5x5 grid: Triangle side ≈ 4,000 km; area ≈ 6.9 million km²
On a 12-inch globe, a 3x3 triangle would be about 2 inches per side.
5. The Diamond (Octahedral) Model
5.1 Structure
The truth corner forms the base of a pyramid.
Mirroring this pyramid both above and below creates a diamond (octahedron) with three layers up, three down, and the "eye" or central truth section in the middle.
The apexes represent the most focused truths; the base spans the broadest area.
5.2 Perceptual and Symmetry Implications
A central observer at the "eye" can perceive both ends of the diamond as if they are adjacent, due to the mirroring effect.
Symmetry creates the illusion of continuity, but also introduces ambiguity—edges appear to connect, even though they are not physically adjacent.
6. Cognitive and Experimental Implications
6.1 Testing the Model
Virtual Reality (VR): Build environments based on this model, allowing users to navigate and perceive the world from different "truth sections."
Psychophysical Testing: Gradually remove symmetry and track perceptual thresholds for spatial coherence.
Quantitative Analysis: Measure navigation accuracy, object recall, and subjective reality ratings.
6.2 Adaptation and Perception
The model predicts that even partial removal of symmetry (10–20%) can radically alter perception.
Individuals may construct unique, context-driven maps of reality, especially when symmetry is disrupted.
7. Example Table: Diamond Layers and Geographic Mapping
Layer Direction Description/Location Example
Top (+3) Upward Apex (e.g., North Magnetic Pole)
Middle (+2) Upward Central Arctic Ocean
Upper Base (+1) Upward Ellesmere Island, Nunavut
Eye (0) Center Truth Corner (Nunavut/Arctic)
Lower Base (-1) Downward Boothia Peninsula, northern Alaska
Middle (-2) Downward Chukotka, Siberia
Bottom (-3) Downward Opposite pole/antipode region
8. Conclusion
This dissertation presents a comprehensive geometric and perceptual model for how the world can be constructed from a single, foundational region. By layering, rotating, and mirroring triangular grids, and by conceptualizing the truth corner as the center of a diamond (octahedral) structure, we gain new insights into the interconnectedness of geography, the nature of perception, and the role of symmetry. This model not only offers a novel way to visualize overlapping realities, but also provides a framework for experimental testing and cognitive exploration.
Estimated Word Count: ~1,160 words