Last modified: 4024_31_6.1751 UCY

UCY is an alternative calendar system that solves the Gregorian calendar's fractional week problem using 8-day weeks and octal notation. Anchored to astronomical reality while maintaining perfect computational regularity.

A calendar system that:

• Contains complete weeks in every year (no fractional weeks)
• Uses 8-day weeks (0-7 in octal notation)
• Creates years of 360 days (45 weeks) or 368 days (46 weeks)
• Follows a natural 368-368-360 pattern (~365.24 day average)
• Anchors to spring equinoxes (not arbitrary dates)
• Employs a measurement-based algorithm instead of fixed leap year rules
• Exhibits stability (repeating 27+ year pattern)

The Gregorian calendar divides 365.2421875 days by 7-day weeks = 52.177... weeks per year—an eternally fractional value that creates:

• Dates drifting through weekdays
• Complex leap year algorithms
• Irregular months (28/29/30/31 days)
• Week numbers that don't align with year boundaries
• Computational complexity in date arithmetic

UCY asks: What if we designed a calendar from mathematical first principles?

• 8-day weeks: Optimal week length enabling complete-week years while tracking the tropical year
• Octal notation: Base-8 matches 8-day structure naturally
• Clean division: 360÷8=45 weeks, 368÷8=46 weeks (no remainder)
• No special cases: No months, no leap day insertions, no irregular patterns

• Datum: Spring equinox after Julius Caesar's death (March 21, 44 BCE = Year 0)
• Equinox alignment: Year starts stay within ~4 days of the equinox and align to 8-day boundaries via a measurement-based threshold (no lookup tables)
• Dynamic determination: Measurement-based threshold algorithm (no lookup tables)
• Deep-time accuracy: Algorithm tested against astronomical data spanning millennia

• Natural: Following astronomical math instead of fixed rules yields a remarkable generational stability
• Generational: A simple pattern holds for over 27 years at a time
• Predictable: Reducing the cognitive load of calendar tracking from an annual check to a generational one
• Validated: Empirical analysis across millennia validates the stability pattern
• Consistent: Zero unexpected calendar changes within generational runs

• Constant-time calculations: No iteration through previous years required
• No lookup tables: Algorithm adapts dynamically to actual tropical year
• Clean implementation: <100 lines of Python

pip install -r requirements.txt

Requirements: skyfield, pytest

Note: On first run, Skyfield will download the NASA JPL DE431t ephemeris (~3.5 GB) to ~/.skyfield-data. See ucy.md for implementation details and optimization options.

from ucy import to_ucy, to_parts, to_utc
import skyfield.api as sf

# Get current UCY date
ts = sf.load.timescale()
now = ts.now()
ucy_date = to_ucy(now.tt)
print(ucy_date)  # e.g., "4024_31_6.1751"

# Get UCY components
year, week, day, nano = to_parts(now.tt)
print(f"Year {year:o}, Week {week:02o}, Day {day:o}")

# Convert UCY back to UTC
utc_iso = to_utc("4024_31_6.1751")
print(utc_iso)  # e.g., 2025-10-11T14:55:34Z

UCY dates use octal notation: year_week_day.fraction

Example: 4024_31_6.1751

• Year: 4024 (2068 in decimal)
• Week: 31 (25 in decimal)
• Day: 6
• Fraction: .1751 (position within day)

├── ucy.py                    # Core implementation
├── test_ucy.py               # Test suite
├── test_cases.py             # Test case data
├── generator.py              # Reference table generator
├── ucy.md                    # Main documentation
├── MEDITATION.md             # Philosophical exploration
├── requirements.txt          # Dependencies
└── LICENSE                   # GPL v3

# Quick check
pytest

# Full suite (include slow tests)
pytest -m ""

Tests validate:

• Historical dates
• Deep time accuracy
• Year boundary alignment
• No consecutive short
• Generational stability

• ucy.md: Main documentation with four layers—poetic rules, historical context, technical specs, and philosophical Q&A
• MEDITATION.md: Deep exploration of time, mathematics, and human systems

• Astronomy computations use Skyfield by Brandon Rhodes
• Ephemerides from NASA JPL (DE431t) accessed via Skyfield
• This project is unaffiliated with NASA/JPL; names are used for attribution

This is a complete, self-contained reference implementation. To explore:

1. Read the main documentation
2. Examine the implementation
3. Run the tests
4. Reflect on the meditation

GPL v3 - See LICENSE for details.

@software{ucy,
  author = {Pat Bierkortte},
  title = {UCY: A More Humane Calendar Hiding in Plain Sight},
  year = {2025},
  url = {https://github.com/pbierkortte/UCY},
  email = {hello@patbierkortte.com}
}