This is a proposal for a replacement to the traditional Gregorian calendar, which was adopted by Western cultures in 1582 to replace the Julian calendar from Roman times. I submit this proposal for feedback, suggestions, and inquiry into prior proposals of a similar or identical nature.
A rational basis for a calendar upon 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 (366 days)
Always alternate 30-31
Month
Length
Jan
30
Feb
31
Mar
30
Apr
31
May
30
Jun
31
Jul
30
Aug
31
Sep
30
Oct
31
Nov
30
Dec
31
Total
366
August through December retain their traditional lengths
Halloween, Oct 31
New Year’s Eve, Dec 31
Typical Year (355 days)
February has a day removed
Month
Length
Jan
30
Feb
30
Mar
30
Apr
31
May
30
Jun
31
Jul
30
Aug
31
Sep
30
Oct
31
Nov
30
Dec
31
Total
365
Retain all base case benefits
February continues as the traditional leap month
Start the year with 30-30-30 and alternate after that
Review
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: 3x big-small, 1x big-big, 2x small-big
Rational Prime maintains 30-31 throughout
August through December are identical to Gregorian month lengths
January through July mismatch the Gregorian pattern
Days Per Month
Month
Gregorian
Rational Prime
Jan
31
30
Feb
28⁄29
30⁄31
Mar
31
30
Apr
30
31
May
31
30
Jun
30
31
Jul
31
30
Aug
31
31
Sep
30
30
Oct
31
31
Nov
30
30
Dec
31
31
Total
365⁄366
365⁄366
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.
The intention is merely to lay out a more desirable scheme than the status quo.
Adoption will have both costs and benefits.
Rational Prime Calendar
This is a proposal for a replacement to the traditional Gregorian calendar, which was adopted by Western cultures in 1582 to replace the Julian calendar from Roman times. I submit this proposal for feedback, suggestions, and inquiry into prior proposals of a similar or identical nature.
Below is a reproduction of https://github.com/rickhull/compsci/blob/master/RationalPrimeCalendar.md
Rational Prime Calendar
A rational basis for a calendar upon 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 (366 days)
Always alternate 30-31
August through December retain their traditional lengths
Halloween, Oct 31
New Year’s Eve, Dec 31
Typical Year (355 days)
February has a day removed
Retain all base case benefits
February continues as the traditional leap month
Start the year with 30-30-30 and alternate after that
Review
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: 3x big-small, 1x big-big, 2x small-big
Rational Prime maintains 30-31 throughout
August through December are identical to Gregorian month lengths
January through July mismatch the Gregorian pattern
Days Per Month
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. The intention is merely to lay out a more desirable scheme than the status quo. Adoption will have both costs and benefits.