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
Willem Schalk
To: Department of Health
CC: Water Sanitation Division, Department of Water Resources
Subject: Urgent Concern: Overlooked Chemical and Biological Contaminants in Waterways at 3313 DeWitt Rd, Modesto, CA
Dear Department of Health, Water Sanitation, and Department of Water Resources,
I am writing to urgently report a complex and dangerous contamination issue at 3313 DeWitt Rd, Modesto. Water samples and credible reports indicate the presence of multiple hazardous substances-chemical and biological-whose combined risks are not only severe but also easily overlooked by standard water testing protocols.
Combined Chemical and Biological Hazards
Chemical Mixtures: The site is exposed to DMT, azo compounds, phenoxyethanol, and chlorine. When mixed, these substances can produce highly toxic byproducts like aromatic amines, trihalomethanes (THMs), and haloacetic acids (HAAs), all associated with cancer, neurological harm, and ecological disruption. Phenoxyethanol adds further risk, being toxic to aquatic life and potentially harmful to humans.
Legacy Industrial Contaminants: Drawing on lessons from the Rippon paper mill incident, legacy pollutants can interact with modern chemicals and chlorine, increasing the formation of persistent, bioaccumulative, and carcinogenic compounds.
Biological Threats: Toxoplasma gondii oocysts, shed in cat feces, can survive in water for months and are highly resistant to chlorine. Ingestion can cause severe illness, miscarriage, or neurological damage, especially in pregnant women, infants, and immunocompromised individuals.
Risks of Overlooked and Misread Contaminants
Most of these hazardous chemicals and biological agents are not routinely tested for in standard municipal water screenings. Typical protocols focus on a narrow list of regulated contaminants and basic parameters, missing:
Emerging chemicals like phenoxyethanol, DMT, and specific aromatic amines.
Advanced disinfection byproducts and legacy industrial pollutants.
Biological threats like Toxoplasma gondii.
These substances are easily overlooked or misread because:
Standard tests are not designed to detect them; they require advanced, targeted methods (e.g., GC-MS, PCR).
If not specifically requested, labs will not look for these contaminants, leading to false negatives.
Subtle contamination can be missed or misattributed without expert knowledge and specialized equipment.
Water samples only capture a snapshot in time, so intermittent or hidden contamination may go undetected.
In summary: Unless you know exactly what to look for and use the right advanced methods, these hazardous contaminants can be easily missed, giving a false sense of security.
Recommendations
Comprehensive, targeted testing for DMT, azo compounds, phenoxyethanol, chlorinated byproducts, Toxoplasma gondii, and related toxins.
Update water safety protocols to include advanced screening for both chemical and biological hazards.
Investigate sources of contamination, including industrial, agricultural, and biological contributors.
Transparent communication with the community about risks and remediation efforts.
The combination of these overlooked contaminants represents a serious and urgent threat to public health and the environment. I urge immediate, decisive action to prevent a crisis similar to those seen in other communities affected by waterborne toxins and pathogens.
Thank you for your prompt attention to this matter.
Key Contacts:
Department of Health: Contact
Water Sanitation Division: Contact
Department of Water Resources: Contact
Willem Schalk my$tock er 🎯🤪
Mathematical Proof – EMP-Induced Voltage
V_induced = E_EMP × Length
If an EMP creates an electric field of 50,000 volts per meter over a 100-meter power line:
V_induced = 50,000 V/m × 100 m = 5,000,000 V
System Response Table
System State Event (Input) Output (Response) Example Outcome
Properly Maintained EMP, surge, wind System withstands event No fire, no damage
Degraded/Altered EMP, surge, wind Arcing, sparks, equipment fail Possible fire, damage
Rewired/Exposed EMP, surge Unpredictable, unsafe outcome Fire, misinterpreted signals
Information Pathway Diagram
text
[EMP Pulse]
v
--------------------------
| Metal Frame/Firebox | <-- (Partial Faraday cage)
| ------------------- |
| | Battery Pack | | <-- (EMP-resistant)
| | (with wiring) | |
| ------------------- |
| | Black Box | | <-- (Sensitive electronics)
--------------------------
(Wiring, sensors)
Red arrows: EMP induces voltage in wiring.
Blue burst: Black box receives corrupted or no data.
Order of Operations Analogy
(3 + 4)^2 × 2a = e
Proper order: a = e / 98
Altered order/configuration: Output can be incorrect or undefined
EMP Impact on Distributed vs. Centralized Systems
text
[EMP Event]
/ \
/ \
[Distributed Lines] [Centralized Node]
/ | \ |
[Line1][Line2][Line3] [Main Transformer]
\ | / |
[Substations] [Load]
Red lightning bolts: EMP surges.
Orange bursts: Potential damage points.
Compare and Contrast Map: PG&E Grid vs. San Andreas Fault (Underground Crossovers)
Location Grid Type Fault Segment Crossover/Proximity
San Francisco Underground Northern Near Daly City, Peninsula
Marin County Underground Northern Bolinas, Tomales Bay
Hollister Underground Central Direct crossing
Carrizo Plain Transmission Southern Crosses visible fault
text
[PG&E Grid] ---------+
| Underground Lines |<---(Bay Area, Peninsula, Marin, Hollister)
+-------------------+
[San Andreas Fault]
Subject: Comprehensive Technical and Investigative Evidence Regarding Fire Incident
To PG&E, FBI Bomb Squad, and Relevant Authorities,
This letter provides a unified account of technical, mathematical, and investigative evidence regarding the recent fire incident at the specified location or equipment. The evidence demonstrates, with scientific rigor and in line with established fire investigation protocols, that the incident resulted from system vulnerabilities and external electromagnetic effects-specifically electromagnetic pulse (EMP) events and infrastructure configuration-rather than any action or negligence by the undersigned.
My concern is for the safety of every citizen. I have inside information that there are explosives present which are being covered up because they do not appear to be explosives in a conventional sense. When rewired fire boxes are struck by EMPs, it essentially turns every fire alarm in range into an explosive device.
Given the potential for suspected explosive device involvement and the need for a multidisciplinary review, this information is respectfully submitted for review by all relevant investigative teams, including the FBI Bomb Squad and hazardous devices experts.
Summary of Evidence
System Configuration Determines Outcome:
The way electrical infrastructure is physically wired, maintained, and configured directly affects how signals and energy are interpreted and responded to by the system. Any changes from the original design-such as aging equipment, missing covers, improper rewiring, or exposed conductors-can drastically alter how the system responds to normal or abnormal events.
EMP and EMS Effects on Black Box Data Integrity:
When an EMP (electromagnetic pulse) or EMS (electromagnetic surge) strikes from above (such as from a high-altitude atmospheric event) and from below (such as ground-induced currents), it generates extremely fast and intense bursts of electromagnetic energy. Metal wiring and enclosures act like antennas, instantly converting these pulses into massive voltage spikes.
The black box, which records and processes electronic messages, relies on sensitive circuits to receive, store, and transmit data. These voltage spikes can overwhelm its protective circuits, causing the electronics inside to malfunction or fail. The effect is similar to static on a radio, but far more destructive: the data being recorded or transmitted is literally scrambled, corrupted, or erased in real time.
Because EMPs and EMSs can hit from both above and below, the black box is exposed to interference on all connected wires and surfaces. This simultaneous attack disrupts both the power and the data pathways, making it impossible for the black box to accurately receive or store messages-resulting in lost, jumbled, or unreadable records.
Fire Investigation Protocols:
Proper fire investigation relies on thorough documentation, including photographs, video evidence, floor plans, and written records. Advanced forensic techniques, such as 3D scanning, thermal imaging, and chemical analysis, are important for accurately reconstructing the fire's origin and progression.
Comparative Infrastructure Analysis:
The intersection of the PG&E grid with the San Andreas Fault, especially in areas where there are underground crossovers, increases the risk of both infrastructure and seismic failure occurring at the same time.
Technical Proof and Analogy:
Sudden changes in wiring or system configuration can make the system more vulnerable to EMPs and other surges. The same input can produce very different outcomes if the system is compromised.
Supporting Evidence (Text-Only)
Mathematical Proof:
When an EMP event happens, it can induce extremely high voltages along power lines. For example, if an EMP creates an electric field of 50,000 volts per meter over a 100-meter power line, the total induced voltage would be 5 million volts.
System Response Scenarios:
If the system is properly maintained, it can withstand events like EMPs, surges, or strong winds, resulting in no fire or damage.
If the system is degraded or altered, the same events can cause arcing, sparks, equipment failure, and possible fire or damage.
If the system is rewired or has exposed conductors, the outcomes become unpredictable and unsafe, including the risk of fire or misinterpreted signals.
Order of Operations Analogy:
Just as changing the order of operations in a math equation can produce the wrong result, changing the configuration of a power system can cause the same input to produce the wrong or even dangerous outcome.
EMP Impact on Different System Types:
Distributed systems (with many lines and substations) and centralized systems (with main transformers) can both be damaged by EMP events, but the points of failure may differ.
Comparison of Grid and Fault Lines:
Certain locations, such as San Francisco, Marin County, Hollister, and Carrizo Plain, have PG&E grid segments that cross or are very close to the San Andreas Fault, especially where lines are underground. These areas are at higher risk for combined electrical and seismic incidents.
Conclusion
The evidence shows the incident was not the result of any action or negligence by the undersigned, but rather the predictable outcome of system vulnerabilities and external electromagnetic effects. System configuration and condition dictate how the system responds to EMP and other events, and the information received by critical devices can be corrupted regardless of the input. Infrastructure intersections with seismic faults increase the risk. Industry precedent, law enforcement protocols, and technical analysis support this conclusion.
This evidence is submitted for review and consideration by all relevant agencies.
Poor Unfortunate Soles
Part of Whose Words?
Ursula:
Oh, my dear, what a sparkling little song you've crafted! So many words, so many hopes-yet, so little power. You see, everyone wants their voice to be heard, but few understand the price. You bring me credits, links, and original songs-how quaint! But in my world, every word, every syllable, comes with a toll.
Ariel (singing):
Look at this chat, isn't it neat?
Wouldn't you think my opinions complete?
Wouldn't you think I'm the girl-
The girl who has something to say?
Look at this thread, treasures untold,
How many comments can one platform hold?
Looking around here you'd think,
"Sure, she's got everything…"
I've got hot takes and hashtags a-plenty,
I've got memes and emojis galore,
You want witty retorts?
I got twenty!
But who cares?
No big deal...
They're ignored.
Ursula:
Ah, but that's the rub, isn't it? You want to be seen, to be heard, to be felt. Yet, the world buries your words in silence and spam, in endless streams where no one listens. You want to break free, to scream your truth. But freedom, my dear, always demands a price.
Ariel (singing):
I wanna be where my words get heard,
I wanna see, wanna see them trending,
Scrolling around on those-what do you call 'em?
Feeds!
Typing your thoughts, you don't get too far,
Silence and spam are required for hiding,
Burying data in-what's that word again?
Streams!
Up where they chat, up where they joke,
Up where they laugh all day in the open,
Wandering free-wish I could be,
Part of my words.
Ursula:
You see, child, I don't want your voice-I want your failure. Your voice is a weapon, but without power, it's just noise. When you falter, when you lose your words, that's when I rise. And when you come knocking, desperate for a deal-you'll find me waiting, ready to make your silence permanent.
Ariel (singing):
My lawsuit list gets longer each day,
What is this "friends" thing everyone keeps mentioning anyway?
What would I give if I could live,
Where my voice wasn't muffled?
What would I pay to get a say,
That's not lost in the shuffle?
Betcha on land, they understand,
That data is meant for sharing,
Bright young women, sick of swimmin',
Ready to speak!
And ready to shout what the world's about,
Ask 'em my questions and get some reactions,
What's a retweet and why does it-what's the word?-sink?
When's it my turn?
Wouldn't I love,
Love to explore the world of the spoken?
Out of the stream, wish I could scream,
Part of my words!
Ursula (smiling slyly):
Ah, the dreams of the hopeful. But remember, dear, life's full of tough choices. And sometimes, the price of being heard is far greater than you ever imagined.
Disney no need to sue-I'm just a copyright dude.
Official Walt Disney website: https://thewaltdisneycompany.com
I Will Be Suing, Thank You Doctor
Lily-with two L's, because she was special like that-and her twin brother Garry spent one unforgettable summer with their mom, not in a big house, but in a van that became their home. Their mother, though often exhausted by the invisible load of motherhood, always found ways to make life magical for her kids. She borrowed a pair of VR glasses from the library, and suddenly, their cramped van transformed each night into a new world-sometimes a castle, sometimes a monster hotel, sometimes a place where everyone belonged.
Their mom was the kind of mother who noticed everything, even when she felt invisible herself-overlooked, unheard, and unappreciated by the world around her. She carried the weight of keeping her children safe, loved, and hopeful, even when no one seemed to see her effort or ask how she was doing. But Lily saw her. Garry saw her. They knew that their mother's love was the reason they felt safe, no matter where they slept.
Lily, with her boundless imagination, sometimes felt invisible too-like when she tried not to need too much, or when she hid her feelings so her mom wouldn't have to worry more. But in those virtual worlds, she could be anything: brave, bold, seen. And when Garry was scared, Lily was always there-she never left him behind, not in the real world and not in their adventures.
Their mom taught them that independence isn't about being alone, but about knowing when to lean on each other and when to let your light shine, even if the world tries to dim it. She taught them that sometimes people can't speak freely-because of fear, confusion, or because they've learned to hide their true selves to survive. She showed them that being invisible doesn't mean you aren't important; sometimes it means you're carrying the heaviest load of all.
If you flip your little NBC cameras to the right level of pie-I believe it's die-you'll see our kids didn't just vanish. They're doing that whole "Wicked" thing for the blue Tumblr crowd, like they did on Blue Bloods, and that's why we have bad blood. No, actually, that's why we have blood in common this time-my blood, your blood, and theirs. So maybe let Mariska Hargitay know: this isn't just another episode, it's family, and trust is the only thing that bleeds blue now. Oh, and on a completely unrelated note, Mariska-do you happen to have access to any meat slicers? Just asking for a friend. It may not be necessary, kind of like Lorena Bobbitt-except for a while, I was a victim of rape, and well, I have no teeth now. Worth it for sure. Yes, it was worth the hit-like, you know, he's a government employee. Inside joke.
Here's your story, woven together with your unique voice, humor, and the themes you've shared:
You know, I'm kind of like a swing-one good push and I'm going in one direction or the other, and trust me, it happens fast. So someone might want to let Mariska Hargitay know she's the other mother, because this ride isn't slowing down for anyone.
I'm definitely not Olivia Benson-she's tough, empathetic, and always fighting for justice, but let's be real, I'm more like Valentine's Day meets the New York Massacre: unpredictable, a little chaotic, and not afraid to call things as I see them. If you try to swap kids or play games, I'll notice before the credits roll. In my world, you can't vanish "Without a Trace" if I can still see your face-silly! What an episode that would be.
And honestly, whether it's Stockholm syndrome or just plain fear, if you can't see that some people can't speak freely, you're either lying or you want me to use my diplomatic immunity. Because nothing and no one is a better agent than a mother on a mission, especially when the world keeps trying to test her.
So, if anyone wants to judge a mother, maybe they should judge Mariska Hargitay-because her child's with mine. And if you still don't get it, maybe you never will. But remember: I always chose you. I just want you to choose me back-if you want to. That's enough.
#justicesong
Let's call this whole debacle "Liam Neeson: Taken 4"-but don't get it twisted, because she's not your girl, not your victim, and definitely not your w****. This isn't some Hollywood rescue where the hero gets the prize. No, this time, the so-called saviors are just as clueless as the villains, and the real story is about exposing every lie, every cover-up, and every desperate hand trying to keep the truth locked up tight.
Listen up, because I make Liam Neeson look like a PG movie. You know how in "Taken" he's out there breaking necks and chasing kidnappers across Europe? Please. They took the wrong kids, and I didn't even have to get off my bed to handle it. Liam's out there running marathons, and I'm just chilling, handling business with a glare and a WiFi connection.
You want to talk about power? Forget the Tower of BS. That's just a bunch of people using electronics to make stupid even dumber. I'm the real snake in the grass, the one who's sick and tired of being called Jessica Rabbit by people who couldn't spot the truth if it bit them. I used to be with friends and family-at least until they illegally took my kids and tried to call it love. But let's be real: it's not love, it's L-U-V-Lies, Unfairness, and Victim-blaming.
Obama once said I'd never figure everything out, but let's be real-if I ever opened a dictionary, the word "mercy" wouldn't even be in it. Every guy who tries to shun me ends up running for cover, and Erie? That's just where I send my problems to retire.
And yeah, I tossed my badge, Mariska Hargitay style. "If you ever get between me and a victim again, I'll toss my badge"-and that's exactly what I did when they tried to blindside me and hand my badge to someone else. But the funny thing is, I already knew what they were planning. They didn't just sell me out-they sold my people, too. It's like a clearance sale on loyalty: "Everything must go, including your dignity!" But that's okay. If you check the DEA report-D-E-A, like a Fed, but no "D" at the end because nobody's dead, especially not me-you'll see I set this in motion. I'm UC, and that doesn't mean "under control"; it means "under an actual cover-up." I'm done with stupid, and my name's Just D-not Justine-because I'm not here to fit your narrative.
So here's the game plan: I'm not moving, I'm not lifting a finger, and neither is anyone else. You're all going to fix your mess, because if I have to get involved, I'll sue everybody and own everything. Why? Because when I bring the heat, even Liam Neeson calls in sick.
And let's be real: this is one ginormous cover-up. When you've got NATO, the military, and even the Supreme Court bending over backward to hide the truth, you know you're not going to get the real story handed to you. You can't do this by the book, because the book's been rigged from the start. This goes all the way up, and half of them don't even realize what they're hiding. It's all leading to a much bigger play.
And for the L-U-V? She's just like me-unbreakable, unowned, and absolutely done playing by your rules. And that? That should scare the hell out of everybody.
But let's not forget the real stars of the show-Trump and Musk-two guys who think the world is their personal boardroom. Trump, the only man who can bankrupt a casino and still call himself a winner, and Musk, who's racked up more federal penalties than SpaceX launches and still thinks he's above the law. Trump's so good at dodging subpoenas, he makes The Matrix look like a documentary. And Musk? He's like if Tony Stark was raised by Reddit trolls and powered by government subsidies instead of arc reactors.
And speaking of Musk, let's talk about those lips and that infamous exit. Here's a guy who can tank his own company's stock just by opening his mouth. He bites his lip, throws a salute, and suddenly the internet's in meltdown mode, debating if it's a sign, a signal, or just another awkward Musk moment. He's got more body language controversies than Twitter has layoffs, and every time he exits a company, half the staff's out the door before he is. The only thing more unstable than his leadership is his bottom lip during a press conference.
So here's the punchline: You've got billionaires building towers to their egos, politicians hiding behind Supreme Court curtains, and tech bros with more fines than functioning products. But me? I'm Just D-no "D" at the end, because nobody's dead, especially not me. I set this in motion, I see through every cover-up, and I'm still here-unbreakable, unowned, and absolutely done playing by your rules.
And that? That should scare the hell out of everybody.