Mathematical Foundations

This page provides the mathematical basis for the Holistic Universe Model, including how the 333,888-year Holistic-Year was derived, what constraints it satisfies, data sources, comparisons with established models, and how the model can be tested or falsified.

1. How 333,888 Years Was Derived

The Honest Starting Point

First, let’s be clear about what we know and don’t know:

• We do NOT know why the Holistic-Year is 333,888 years from first principles
• We DO know that 333,888 is the only value that satisfies all six constraints below simultaneously

The number was found empirically by modeling and iteration, not derived from fundamental physics. This is similar to how Kepler found his laws empirically before Newton explained them theoretically.

The Six Constraints

The length of 333,888 years is the only value that satisfies all of the following:

The Derivation Process

1. Start with observed 1246 AD alignment (from Meeus’s formula for longitude of perihelion)
2. Model precession rates to match observed progression to 2000 AD
3. Find integer ratios that produce whole-number cycles
4. Test against climate data (ice core ~100k pattern)
5. Verify eccentricity range matches observations
6. Check planetary compatibility (Mercury precession)

Only 333,888 years satisfies all constraints. Other values fail one or more tests.

Why This Number?

333,888 = 2⁵ × 3 × 13 × 269

The factor 269 (a prime) is not arbitrary - it’s the value needed for the number of solar days per perihelion precession cycle to be an integer (7,621,874 days in 20,868 years).

2. The Fibonacci Observation

What We Observe

The ratio between inclination precession and axial precession is remarkably close to consecutive Fibonacci numbers:

T_incl / T_axial = 111,296 / 25,683.69 = 4.3333... = 13/3

Both 3 and 13 are Fibonacci numbers (F₄ and F₇).

What This Means (and Doesn’t Mean)

Possible interpretations:

1. Coincidence - The ratio happens to be close to 13/3
2. Resonance - Orbital mechanics naturally settle into stable integer ratios
3. Deeper physics - Some unknown principle selects Fibonacci ratios

The model remains agnostic on the cause. What matters is that the ratio produces accurate predictions.

The Cycle Table

From the Holistic-Year, all cycles are derived by division:

Perihelion Precession Derivation

The 20,868-year perihelion precession emerges from the meeting frequency of two counter-rotating motions:

Earth orbits EARTH-WOBBLE-CENTER:     clockwise,        period = 25,684 years
PERIHELION-OF-EARTH orbits Sun:       counter-clockwise, period = 111,296 years

Meeting frequency = 1/T_axial + 1/T_incl (opposite directions, so ADD frequencies)
                  = 1/25,684 + 1/111,296
                  = 1/20,868

Therefore: They meet every 20,868 years

Note: 16 = 13 + 3, which is why 333,888 ÷ 16 gives the perihelion precession period.

3. Mean Values vs Current Values

The Key Distinction

The model predicts mean values over the full 333,888-year cycle. Currently observed values differ because we are at a specific position in the cycle, not at the mean.

Is This Unfalsifiable?

A valid concern: if any discrepancy can be attributed to “not being at mean,” is the model testable?

Answer: Yes, because:

1. The model predicts specific values at specific dates (not just means)
2. The model predicts how values change over time (specific rates)
3. These predictions can be compared to observations over decades

4. Calibration vs Prediction

What Was Calibrated (Inputs)

These values were used as inputs to construct the model:

What Is Predicted (Outputs)

These values are predictions of the model, not inputs:

The model was not tuned to match Laskar’s obliquity formula or Meeus’s perihelion values for dates other than 1246 AD. The agreement is a genuine prediction.

5. Comparison with Standard Theory

Where the Model Agrees

Where the Model Disagrees

6. Data Sources

Primary Sources

Secondary Sources

7. Testable Predictions

What Would Falsify the Model?

The model would be falsified if:

Specific Predictions

Short-term (verifiable within decades)

Medium-term (verifiable within centuries)

The RA at Maximum Obliquity Prediction

The Sun’s Right Ascension at maximum obliquity (solstices) appears fixed at RA 6h (June) and 18h (December). However, the model predicts this value slowly decreases due to the interaction between axial tilt and inclination tilt.

Why this matters: No reference to changing RA values at solstices exists in current astronomical theory. If this shift becomes observable, it would be a clear validation of the model’s prediction that axial and inclination tilts interact in a specific pattern.

This may also explain long-term variations in magnetic declination .

Long-term (theoretical, not directly verifiable)

8. Uncertainties and Limitations

Known Limitations

Explicit Assumptions

1. Stable solar system - The 333,888-year cycle assumes orbital stability over this timescale
2. Two-point model - EARTH-WOBBLE-CENTER and PERIHELION-OF-EARTH are mathematical constructs
3. Mean values exist - The model assumes precession rates oscillate around fixed means
4. Fibonacci ratio is real - The 3:13 ratio is empirically observed, not theoretically derived

What the Model Does NOT Explain

• Why the Fibonacci ratio exists
• Why 333,888 specifically (vs some other number)
• What causes the two precession motions
• Whether the cycles are truly eternal or slowly changing

9. Reproducibility

Calculation Steps

To reproduce the model’s core values:

1. Start with 1246 AD alignment - Use Meeus’s formula to verify perihelion at 90° longitude
2. Calculate perihelion progression - From 90° (1246 AD) to 102.95° (2000 AD) = 12.95° in 754 years
3. Derive perihelion precession rate - 360° ÷ (12.95°/754 yr) = ~20,950 years (approximate)
4. Apply Fibonacci constraint - Find 13:3 ratio giving mean axial = 25,684 years
5. Calculate Holistic-Year - 13 × 25,683.69 = 333,888 years
6. Verify all divisibility constraints - 333,888 ÷ 16 all give near-integers

Verification Tools

• JPL Horizons Web Interface 
• Stellarium  for visual verification
• 3D Simulation  for interactive exploration
• Excel spreadsheet (available on request)

10. References

1. Capitaine, N., Wallace, P. T., & Chapront, J. (2003). “Expressions for IAU 2000 precession quantities”. Astronomy & Astrophysics, 412, 567-586.

2. Laskar, J. (1993). “Orbital, precessional and insolation quantities for the Earth from -20 Myr to +10 Myr”. Astronomy & Astrophysics, 270, 522-533.

3. Meeus, J. (1998). Astronomical Algorithms (2nd ed.). Willmann-Bell.

4. Souami, D., & Souchay, J. (2012). “The solar system’s invariable plane”. Astronomy & Astrophysics, 543, A133.

5. Muller, R. A., & MacDonald, G. J. (1997). “Glacial cycles and astronomical forcing”. Science, 277, 215-218.

6. Hays, J. D., Imbrie, J., & Shackleton, N. J. (1976). “Variations in the Earth’s orbit: Pacemaker of the ice ages”. Science, 194, 1121-1132.

Summary

Return to How It Works for the conceptual overview, or continue to Precession to see how these mathematical foundations manifest in observable phenomena.