add RationalPrimeCalendar.md

Author: Rick Hull

RationalPrimeCalendar.md

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+# Rational Prime Calendar
+
+*A rational basis for a calendar based on 61 day periods*
+
+The Gregorian calendar is a 400-year-old hack job.
+February's weird.
+July-August breaks the pattern,
+and no one can remember which months have 31 days.
+But there's a better way, hidden in prime factorization.
+
+## Considerations
+
+* Solar day (roughly 24 hours for the earth to rotate)
+* Solar year (365.2425 solar days for the earth to orbit the sun)
+* Lunar cycle (29.53 days for 8 distinct moon phases, roughly 12x annually)
+
+It's impossible to coordinate or synchronize these 3 cycles perfectly.
+But we can devise a system to accommodate them and minimize tradeoffs.
+We also want to consider historical calendars, particularly the current
+Gregorian calendar and less so the prior Julian calendar.
+
+## Approach
+
+If a solar year is considered to be 366 days, this factors to 61 * 3 * 2,
+which naturally suggests (6) 61-day periods, or alternately (61) 6-day periods.
+Perhaps we should have 6 day weeks, but that will be for another proposal.
+
+We can split each 61-day period into alternating months of 30 and 31 days,
+in either order.  This provides some alignment with the lunar cycle as well
+as traditional calendars.
+
+### The Prime Insight
+
+* **61 is prime**; indivisible, mathematically fundamental
+* Each of 6 periods of 61 days can be split into **pairs of months, 30 + 31**
+* 12 months matches the **lunar cycle** of roughly 30 days
+* 12 months allows clean **divisibility by 4** (seasons, business quarters)
+* 12 months matches **tradition**
+* **Resist entropy**: a regular pattern of pairs in a predictable order
+
+### Leap Year
+
+We can retain the Gregorian approach to leap years, which solves the problem
+of accounting for the remaining 0.2425 days in a solar year as years go by.
+We'll pick one month out of twelve that will have an extra day roughly every
+4 years.  If 366 days is our starting basis, then the leap month will have
+a one-day deficit in most years.
+
+## Specifics
+
+For explication, a leap year is considered the base case, and a "normal year"
+is handled specially, in some sense, even though leap years are less frequent.
+
+### Base Case (Leap Year)
+
+* Always alternate 30-31
+
+Thus:
+
+1.  30 (January)
+2.  31 (February)
+3.  30 (March)
+4.  31 (April)
+5.  30 (May)
+6.  31 (June)
+7.  30 (July)
+8.  31 (August)
+9.  30 (September)
+10. 31 (October)
+11. 30 (November)
+12. 31 (December)
+
+* August through September retain their traditional lengths
+* Halloween, Oct 31
+* New Year's Eve, Dec 31
+
+### Normal Year
+
+* February has a day removed
+
+Thus:
+
+1.  30 (January)
+2.  30 (February)
+3.  30 (March)
+4.  31 (April)
+5.  30 (May)
+6.  31 (June)
+7.  30 (July)
+8.  31 (August)
+9.  30 (September)
+10. 31 (October)
+11. 30 (November)
+12. 31 (December)
+
+* Retain all base case benefits
+* February continues as the traditional leap month
+* Start the year with 30-30-30 and alternate after that
+
+### Compared to Gregorian
+
+* Most February weirdness is gone
+* Gregorian July-August flip
+  - Gregorian starts big-small, pairwise
+  - August is due to be small but is big
+  - Pattern is small-big after that
+  - Pairwise: big-small, big-big, small-big
+* Rational Prime maintains 30-31 throughout
+* August through December are identical to Gregorian month lengths
+* January through July mismatch the Gregorian pattern
+
+| Feature  | Gregorian | Rational Prime
+| -------- | --------- | --------------
+| February | 28/29     | 30/31
+| Jul-Aug  | 31-31     | 30-31
+| Pattern  | Irregular | Cleanly alternating
+
+### Why This Matters
+
+* Predictable patterns (no more "30 days hath September" mnemonics)
+* Business quarters are equalized
+* Cultural continuity (Halloween, New Year's Eve preserved)
+* Mathematical elegance
+
+### What Changes, What Stays
+
+Preserved from Gregorian calendar:
+
+* 12 month structure
+* Months of alternating 30 and 31 lengths
+* August-December lengths (dates like Halloween and New Year's Eve)
+* Leap year frequency and concept
+* February as the leap month
+
+Fixed from Gregorian calendar:
+
+* February: awkward 28/29 becomes rational 30/31
+* July-August 31-31 pattern reversal becomes logical 30-31 within pattern
+* Unpredictable patterns become clean alternation
+
+### Cultural Considerations
+
+This proposal is deliberately intended as a replacement for the Gregorian
+calendar, primarily within the Western cultural tradition.
+Other cultural traditions or calendars are welcomed yet will probably be
+considered out of scope.
+
+### Implementation and Adoption Challenges
+
+This proposal is not intended to address local or global adoption.
+It is merely to lay out a more desirable scheme than the status quo.
+Adoption will have both costs and benefits.
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+# Rational allocation of 365 (+1) days into 12 months
+# 366 / 6 =  61, so every 2 months add up to 61 in a leap year
+# Alternate 30 and 31 days, in either order, in a leap year
+# Pick a 31 month to have a day removed in most years
+# Most years will have a 30-30-30 sequence and otherwise alternate
+# February is the traditional leap month, so start January at 30 days
+# This retains the traditional month lengths from Aug-Dec
+# This removes most of the weirdness of February in Gregorian calendar
+# This removes the weird 31-31 sequence for Jul-Aug in Gregorian calendar
+
+1: 30
+2: 30 (+1 LY)
+3: 30
+4: 31
+5: 30
+6: 31
+7: 30
+8: 31
+9: 30
+10: 31
+11: 30
+12: 31