Goines On: 2021 or 2001?

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Goines thought he should first explain to the prospective 12-year-old programming whiz that his personal mnemonic

        “Mi Ki Ko Ranch” rattles Miquel

had been chosen for practical reasons, because it represented Goines’ present year, 2021. The kid might think it made more sense for a program to use the year 2001 – it seemed cleaner somehow... unless he or she chose to use 2021 as a way of attributing Goines – which Goines would have to agree would be nice.

    Of course, the kid wouldn’t bother with the mnemonic to remember the day of the corresponding month in whatever year he or she chose to base the app on. The kid’s program would just save the string of numbers indicating the day of each month on which the first Sunday fell on. For 2021:

        3-7-7   4-2-6   4-1-5   3-7-5

        January 3, February 7, March 7, April 4, etc.

    For 2001: 

        7-4-4   1-6-3   1-5-2   7-4-2

        January 7, February 4, March 4, April 1, etc. 

    As it happened, the year 2001 had the same relative sequence, just different days. The sequence was “relative” in the sense that each day of the month for 2001 was shifted 3 days earlier (or 4 days later, arithmetically speaking) than for 2021. For example, 3 days sooner than January 3 would be January 0, or January 7; 3 days sooner than February 7 and March 7 would be February 4 and March 4.
    Of course, if 2001 were used, the pattern of 400-year cycle based on 2021 would need to be replaced, because the bumped cycles for 2100, 2200, & 2300 would likely be different. Goines guessed he needed to establish whether that were so, and, if so, how so? – for his own peace of mind, if for no other reason. (The kid would of course be able to figure it out for him or herself.)

    Okay, what about 2100’s bumped cycle? The standard 28-year cycles leading up to it would be 2001–2028, 2029–2056, 2057–2084, and the cycle beginning in 2085 would be bumped at the third leap year of its 11-year sub-cycle, which, in this case, would not be a leap year, thus adding a year to the 11 to complete the sub-cycle at 2102 instead of 2101. And the sub-cycle beginning with 2103 would fit an 11-year pattern, leading to the usual 6₂-5 run for completion in the year 2124 (a total of 40 years). The bumped cycle would have been increased by 12 years to cover 2085–2124, leading to the standard 28-year cycles 2125–52 & 2153–2180, and bumping the next cycle in its otherwise standard 6₂ sub-cycle.

    He constructed a table to record what he had learned so far:

​  |———————————————————————> 

2001 2125 

2029 2153 

2057 2181 

2085  

    Goines didn’t think he needed to go any further, but he was curious whether the 2200 bumped cycle would indeed have its apparent length of 40 years. And would the 2300 bump have 12 years? He wouldn’t sleep if he didn’t figure it out.

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