Ldecola tries it with the Gregorian year. How does it hold up against theAbysmal?
This intrepid soul has made a valiant attempt, however, I suspect this is a task without a satisfying resolution.
For me, the fundamental part of the problem here is that the systems being used, atomic time, clock time, calendar time, are numbered in different ways. The Gregorian itself uses three different numbering systems, which differ from the system used with clocks. If one of these systems was chosen and used throughout, at least it would be consistent.
As an aside, the flowchart defines the year numerically as 365.25 days, which is the duration of the Julian Calendar’s year, amended to 365.2425 days with the Gregorian Calendar. The rule eliminates 3 leap year days every 400 years, which more closely aligns the Gregorian Year with the Solar Year.
What’s in a Numbering?
Digital clocks count elapsed time using cardinal numbers beginning with 0 (colloquially, natural numbers) 0, 1, 2…; four of the calendar months are named after their Roman numerals September (VII), October (VIII) November (IX) and December (X); days of the month are ordered using ordinal numbers beginning with 1st (colloquially, whole numbers) 1st, 2nd, 3rd…; years are numbered beginning with 1 (whole numbers), both to count and order the years.
seconds, minutes, hours: 0, 1, 2, …
days of the month: 1st, 2nd, 3rd, …
months of the year: VII, VIII, IX, X
years: 1, 2, 3, …
In addition, the Gregorian suffers from the disharmony between the 7-day week, the irregular months, and the year. The day and week are always in a harmonious 7:1 ratio. The irregular months (31/28/31/30/31/30/31/31/30/31/30/31 days) define irregular semesters (181/184 days), terms (120/123/122 days), and quarters (90/92/92/91 days) of the year.
For comparison, here’s how theAbysmal Calendar scales up from Caesium-133 to the Year.
22 x 7 x 13 + 1
60 x 60 x 24x =
27 × 33 × 52
2 × 32 × 5 × 72 × 47 × 44,351
theAbysmal Year
Because theAbysmal Calendar harmonizes the 7-day week with the rest of the year, the measures are regular: 7 days per week, 4 weeks per month, 13 months per year, 13 weeks per quarter, 26 weeks per semester, 52 weeks a year.
A year is 364 + 1 days.
A semester is 182 days.
A quarter is 91 days.
A month is 28 days.
A fortnight is 14 days.
A week is 7 days.
A day is 86,400 seconds.
A second is 9,192,631,770 Caesium atom vibrations (Cs).
Why stop there? Why not continue scaling our measures of time down to the smallest theoretical measurement?
Planck Time
A single Caesium vibration (Cs133) equals 2,017,799,100,000,000,000,000,000,000,000,000 times Planck time ( tP).
Let’s express these things in terms of their prime factors:
days per year (different calendar systems):
365 = 5 × 73
= 22 × 7 × 13 + 1 (13-month calendars, including theAbysmal)
= 192 + 4 (Bahā’i)
= 23 × 32 × 5 + 5 (Haab’, Coptic)
leap year days per year (theAbysmal):
+1/4 – 1/128
seconds per day:
86,400 = 27 × 33 × 52
Caesium vibrations per second:
9,192,631,770 = 2 × 32 × 5 × 72 × 47 × 44,351
Planck Time for a single Caesium vibration:
2.0177991 × 1033 = 233 × 36 × 533 × 89 × 311
To take advantage of the prime factors that repeat themselves, we could scale up using 2, 32, and 5, as these are common throughout, provided the year is divided into 360 + 5 days, which is a whole other possibility explored elsewhere.
Even Divisions of theAbysmal Year
Year
= 364 Days + 1 Day
= 52 Weeks = 26 Fortnights = 13 Months = 4 Quarters = 2 Semesters
Semester = 182 days = 26 Weeks
Quarter = 91 Days = 13 Weeks
Month = 28 Days = 4 Weeks
Fortnight = 14 Days = 2 Weeks
Week = 7 Days
Day = 86,400 seconds
second = 9,192,631,770 Cs133
Cs133 = 2,017,799,100,000,000,000,000,000,000,000,000 tP.
Rethinking Time 