Start with something you do every day: look in a mirror.
When you see yourself in a mirror, light travels from your face to the mirror, bounces off, and returns to your eyes. This takes time. Not much time—about 6 billionths of a second for a bathroom mirror—but time nonetheless.
The Mirror Truth: You never see yourself in the present. You always see yourself in the past. The mirror shows you who you were, not who you are.
This isn't philosophy—it's physics. Light has a speed limit (about 300,000 km/s), and that speed limit means all observation looks backward in time.
Light travels to mirror and back. You see the past.
Now the question that started this project:
If mirrors always show the past... could anything show the future?
Not "the future" as a crystal ball prediction. But the tendency of what's forming. The wave before it crests. The pressure change before the storm.
Light Cone Asymmetry
In physics, we describe observation using light cones. Everything you can observe lies in your past light cone—the region of spacetime from which light has had time to reach you.
FUTURE
△
/|\
/ | \
/ | \
/ | \
PAST ───/────YOU────\─── FUTURE
LIGHT \ | / (UNREACHABLE)
CONE \ | /
\ | /
\ | /
\|/
▽
PAST
You can only observe what's in the past light cone.
The future light cone is causally disconnected from observation.
This is why we remember the past but not the future. Our instruments—eyes, cameras, sensors—all use electromagnetic radiation, which is bounded by c (light speed).
Δt = 2d/c
Time delay = 2 × distance ÷ speed of light
The Epoch Model asks: Is there another carrier of information besides light?
The hypothesis: Torsion fields—rotational tendencies in geometry—might propagate information differently. Not faster than light, but in a different direction on the s-axis (scalar axis).
The Mirror Depth Problem
Here's something most people never notice: your reflection doesn't appear where physics says it should.
Classical optics says: stand 1 meter from a mirror, and your reflection appears 1 meter behind the mirror—a total of 2 meters away. But that's not what you perceive.
The Round-Trip Problem:
Looking at another person 2m away: light travels 2m (one way)
Looking at yourself in a mirror 1m away: light travels 2m (round trip)
The mirror cuts effective light speed in half. You get the same delay as looking at someone twice as far, but you're only looking half that distance.
But here's the deeper issue: your eyes have TWO ways to judge distance:
Vergence: How much your eyes rotate inward (says: 2d)
Accommodation: How your lenses focus (says: d)
These conflict. Your brain compromises. And the compromise follows the Epoch constants.
The 27.6% Projection Loss
The brain weights the conflicting depth cues. Research suggests approximately:
Accommodation weight: ~27.6% (focus distance)
Vergence weight: ~72.4% (stereo distance)
D_perceived = 0.276 × d + 0.724 × 2d = 1.724d
These weights match the Epoch constants:
P = √3/(2π) = 0.27566... (projection factor)
P_shadow = 1 - P = 0.72434...
Perceived depth = P × d + P_shadow × 2d
= 0.276d + 1.448d
= 1.724d
This is 86.2% of the classical 2d, not 100%.
The "missing" 27.6% is the projection factor P—the information lost when 3D reality projects through the 2D mirror surface.
The mirror is not just a reflector. It's a PROJECTOR that loses exactly P worth of depth information.
Interactive: Mirror Depth Simulator
Move the slider to change your distance from the mirror. Watch how perceived depth differs from classical prediction.
100 cm (1.0 m)
STANDARD MODEL
Predicted Depth
200 cm
d × 2 = 2d
EPOCH MODEL ✓
Actual Depth (Observed)
172.4 cm
d × 1.724 = d(2 - 2P)
Light Round-Trip
6.67 ns
Projection Loss (P)
27.6 cm
P Constant
27.566%
Comparing to direct observation at same apparent distance:
Looking at another person at 172.4 cm:
delay = 5.75 ns The mirror adds 0.92 ns of "wasted" delay.
Building Block: The Dipyramid
Forget complex geometry for a moment. Think of a diamond shape—like two pyramids glued together at their bases.
TOP
◆
/|\
/ | \
/ | \
/ | \
────BASE──── ← Triangular base (hidden inside)
\ | /
\ | /
\ | /
\|/
◆
BOTTOM
This is a DIPYRAMID: two pyramids sharing a base.
When both pyramids are made of equilateral triangles (all sides equal), this shape is called an equilateral dipyramid or triangular bipyramid.
Why does this matter? Because this shape has a special property: it balances. The top pyramid pulls one way, the bottom pulls the other way, and at the center... they cancel.
The equilateral dipyramid: two tetrahedra joined at base
Dipyramid Geometry
An equilateral dipyramid (triangular bipyramid) consists of two regular tetrahedra sharing a common triangular face.
• 6 vertices (4+4-2 shared) • 8 faces (4+4) • 9 edges (6+6-3 shared) • Mirror symmetry across base
The critical angle appears when we examine the Boerdijk-Coxeter helix—a chain of tetrahedra stacked face-to-face:
cos(θ) = 2/3 → θ = 48.19°
This is the BC angle—the rotation between successive tetrahedra in a tetrahelix. It's irrational with respect to 2π, meaning the helix never exactly repeats. It's quasiperiodic.
When dipyramids are arranged along the helix, each one contributes torsion—a rotational tendency. The direction alternates as you traverse the helix.
Three Axes: The Triaxial Arrangement
Imagine standing at a crossroads. Not just a 2D intersection, but a 3D one—where three roads meet at right angles.
UP (Z)
|
|
|
WEST (−X) ──────┼────── EAST (+X)
/|
/ |
/ |
SOUTH (−Y)
(NORTH is behind the page toward you)
Three axes: X, Y, Z
Six directions: ±X, ±Y, ±Z
This is a triaxial arrangement. Three perpendicular axes create six cardinal directions (like the faces of a cube) plus eight diagonal directions (like the corners of a cube).
The Vessel Configuration: • Cardinals (N, S, E, W, Up, Down): LEFT EMPTY
• Diagonals (NW, NE, SW, SE): Where the coils go
Why leave the cardinals empty? Because absence defines presence. The empty positions create the structure. It's like how the hole defines the donut, or how silence defines music.
Triaxial arrangement: three axes, four coils at diagonals, cardinals empty
Triaxial Dipyramid Configuration
The vessel uses a triaxial dipyramid frame—an octahedron defined by six vertices along three perpendicular axes:
Vertices at distance R from origin:
+X: (R, 0, 0) −X: (−R, 0, 0)
+Y: (0, R, 0) −Y: (0, −R, 0)
+Z: (0, 0, R) −Z: (0, 0, −R)
These 6 points form a regular octahedron.
The 8 triangular faces connect adjacent vertices.
The four tetrahelix coils are positioned at diagonal positions—not at vertices, but at the centers of four non-adjacent octahedral faces:
The four torsion contributions from the four coils sum to exactly zero at the center. This is not designed—it's a geometric identity following from the four transforms.
The Hidden One
Count the elements:
4 coils at the diagonals
6 empty cardinal positions
1 center point (the crossroads)
But there's something else. The hidden one.
What is hidden?
The fifth dipyramid is the observer.
You are the hidden one. Standing at the crossroads, you complete the geometry. Without an observer, there is no measurement. Without measurement, there is no collapse from tendency to actuality.
In the Epoch Model, the observer isn't separate from the system—they're part of it. The four coils create a balanced field, but it's the fifth element (you) that gives the system meaning.
Think of it like this: a camera without film captures nothing. The four coils are the lens, the frame, the shutter. You are the film.
NW ◇─────────────◇ NE
\ /
\ ◆ / ◆ = YOU (hidden fifth)
\ │ / at crossroads
\ │ /
\ │ /
\│/
SW ◇─────────────◇ SE
Four visible. One hidden. All necessary.
The Observer as Fifth Element
In the four-transform algebra, each transform has a specific function:
T₁: (x, y) → (x, y) Identity / Facing
T₂: (x, y) → (−x, y) Mirror / Horizontal reflection
T₃: (x, y) → (x, −y) Recursive / Vertical reflection
T₄: (x, y) → (−x, −y) Inverted / 180° rotation
These four form the Klein four-group (V₄).
Every element is its own inverse: Tᵢ² = T₁
The four transforms generate a closed group—but they operate on something. That something is the fifth element: the scalar value being transformed.
In the physical vessel:
T₁, T₂, T₃, T₄ are the four coils
The fifth element is the observer at the crossroads
The observer experiences the superposition of all four transforms simultaneously. At the crossroads, where torsions cancel:
T₁ + T₂ + T₃ + T₄ = 0
This isn't zero in the sense of "nothing." It's zero in the sense of perfect balance—where all tendencies exist equally, and none dominates. The observer stands in expanded present.
The Vessel Itself
So what actually is this thing?
At its simplest: four coils of wire, arranged in a specific geometry, driven with specific electrical signals, creating a rotating field at a specific frequency.
The Components: • 4 tetrahelix coils (wound at the BC angle of 48.19°)
• Octahedral frame holding them at diagonal positions
• Signal generator producing four sine waves offset by 90° each
• Frequency: 28.6478897 Hz (the "κ shadow" frequency)
• Optional: oblate ellipsoid shell enclosure
What does it do?
At minimum: creates a rotating electromagnetic field at the crossroads center. This is standard physics.
The hypothesis: at the specific frequency (κ shadow = 28.6 Hz), with the specific geometry (tetrahelix at BC angle), with the specific phase relationship (quadrature), something unusual may happen. The rotating field may couple with torsion in a way that affects temporal perception.
The vessel: four coils, octahedral frame, observer at center
Think of it as a temporal tuning fork. A regular tuning fork vibrates at a specific frequency and makes sound waves. This vessel "vibrates" at the κ shadow frequency and may create... something else.
...it enters "resonance lock." The simulator shows this occurring at approximately 0.34 seconds after power-up.
Putting It All Together
Here's the complete picture:
1. The Problem: Mirrors show the past. All observation shows the past. Is there any way to sample future tendency?
2. The Hypothesis: Torsion fields (rotational geometry) might carry different information than light. The "primary inversion" suggests what's mathematically positive might be physically negative—and vice versa.
3. The Geometry: Triaxial dipyramids create balanced torsion. Four coils at diagonal positions, empty cardinals, observer at crossroads. The Balance Law (τ₁+τ₂+τ₃+τ₄=0) ensures the center is in perfect equilibrium.
4. The Hidden One: You, the observer, are the fifth element. Without you, there's no measurement. You complete the geometry.
5. The Frequency: 28.6478897 Hz—the "shadow" of the fundamental constant κ. This is where discrete steps and continuous rotation align.
6. The Vessel: A physical apparatus that creates these conditions. Four coils, specific geometry, specific frequency, specific phase relationship.
What might happen?
Honestly: we don't know. The Standard Model predicts a rotating magnetic field and nothing else. The Epoch Model suggests something more might occur—subtle temporal effects, torsion coupling, expanded present-moment experience.
The only way to find out is to build it and test it.
┌─────────────────────────────────┐
│ │
│ MIRRORS SHOW THE PAST │
│ ↓ │
│ Could torsion show future? │
│ ↓ │
│ Design geometry that creates │
│ balanced torsion at center │
│ ↓ │
│ Drive at κ_shadow frequency │
│ ↓ │
│ Observer at crossroads │
│ experiences... what? │
│ ↓ │
│ BUILD IT │
│ TEST IT │
│ FIND OUT │
│ │
└─────────────────────────────────┘
Summary: The Complete Model
═══════════════════════════════════════════════════════════════
THE SCALAR PHASING VESSEL
═══════════════════════════════════════════════════════════════
FOUNDATION:
κ = 2π/180 (closure constant)
DERIVED:
κ_shadow = 28.65 Hz (operating frequency)
BC = 48.19° (tetrahelix winding angle)
σ = 5/16 (helix overlap)
GEOMETRY:
Triaxial dipyramid frame (octahedron)
4 tetrahelix coils at diagonal face centers
6 cardinal positions empty
1 observer at crossroads (center)
PHYSICS:
Quadrature drive: 0°, 90°, 180°, 270°
Balance Law: τ₁ + τ₂ + τ₃ + τ₄ = 0
Resonance lock at coherence > 95%
HYPOTHESIS:
Primary Inversion: s+ in math = s- in reality
Light samples past (s+)
Torsion may sample future tendency (s-)
At crossroads: temporal symmetry
═══════════════════════════════════════════════════════════════
[1 = -1]
═══════════════════════════════════════════════════════════════
Visualizations
Tetrahelix Structure
The geometry of spacetime: tetrahelix spiral
The Crossroads
The center where time expands - the crossroads
Interactive: Quadrature Phase Visualization
Watch the four phases rotate. Notice how opposite phases always cancel.
