Although some translations of Plato's work give the statement that the Atlanteans would meet every fifth and sixth year, one translation explicitly states the fourth and fifth year gathering at their capital seaport.
This historical view is important because if our Atlantean ancestors added a "leap-day" every fourth and fifth year during such "social gatherings" -- together with adding a jubilean "super leap-day" every fifty years to a 365-day solar calendar, the calendrical result would equal the True Tropical Solar Year value of 365.2422 days a year.
Today's Gregorian Calendar -- which replaced the Julian Calendar of 365.25 days a year nearly four centuries ago, equals only 365.242 days a year. Although the Gregorian Calendar is quite accurate, falling short by only one day every 5000 years from the True Tropical Solar Year value, it uses a time counting formula wherein historians must remember not to use the 4-year leap-day rule in century years -- unless the year is divisible by 400.
Remembering not to count the leap-day event every century -- unless the century is divisible by 400, is a time-keeping rule that spans a long time between calendrical events. Many social and environmental factors could make historians forget this somewhat complicated time keeping rule -- in fact, although the calendrical rule can be found in many encyclopedias, most people are probably not even aware that it exist.
For example, if the historical archives and time-keeping habits of Western Civilization were corrupted by a catastrophic environmental event and had to start over again, the 4-year leap-day rule may be remembered by some survivors -- but would the additional rule about not adding a leap-day every century unless it was divisible by 400 be remembered or understood by surviving historians?
So far, the Gregorian Calendar has worked just fine -- but was it the first solar calendar designed to remind time-keepers about leap-day rules beyond the 4-year event?
Perhaps not, because the fourth and fifth year gathering event documented by Plato -- together with other calendrical data, suggest the idea that the Atlanteans once used leap-day rules long before the leap-day rule of even the Julian Calendar.
Conventional history portrays that the astronomer Sosigenes designed the leap-day rule of the Julian Calendar -- however, that calendrical rule became effective about the same time when the Romans met the Armoricans near Brittany.
What makes this historical view truly important is that the Romans may have followed a time-keeping habit of the Armorican/Atlantean culture which used leap-day rules to balance calendrical time.
For example, a 7-day weekly counting formula can only add up to 364 days a year. So in order to "balance" a 364-day count to a 365-day year count, our ancestors added an extra "pass over" day -- or a day that was not a week day, but was rather a "year" day to the annual count of time.
The total stairway count of 364 "day-steps" on the main pyramid at Chichen Itza in the Yucatan Peninsula is a good example of how ancient time-keepers used "temple tools" to help keep public time. An ancient "calendar stick" from the British Isles wherein four edges that totaled 364 markings is another example of how annual time was once kept by our ancestors. Both devices allowed for an extra year-day ceremonial event to make a 365-day year.
Both the Julian and Gregorian Calendars do not use the year-day event because, in the aftermath of the Biblical flood, surviving time-keepers forgot how to balance the 7-day weekly count system with a full 365-day year -- so the days of the week retrograde through the years.
When it was learned that the solar year needed even more balancing, another extra day formula was a natural decision for time-keepers.
When to inter calculate an extra day count onto a 365-day solar calendar must of taken many years of celestial measuring. Incidentally, the business number symbol "#" probably originated from the "cross-hatch" design of counting and measuring calendrical time within a square grid.
According to Plato, the numerical reason why the Atlanteans met every four and five years was that "they were showing equal respect for (the) even number and odd".
(One possible reason why some translations state a five and six year gathering of the Atlanteans may be because the Roman letter value of four (IV), if read backwards from right to left, like some early Mediterranean alphabets were used, would give the value of six (VI) instead -- so perhaps portions of those translations may be incorrect.)
Also according to Plato, the reason why the Atlantean maritime kingdom -- and their time-keeping ways, disappeared from history was because of a catastrophic world-wide event that engulfed the trans-continental kingdom.
That catastrophic world-wide event was probably the result of gravitational and atmospheric reactions caused by a rogue comet crashing into the Sun.
In the aftermath of such a major event, the surviving "lost tribes" of the former Atlantean realm regrouped and some calendrical knowledge of the leap-day habit may have appeared as a 4-year leap-day rule of the Julian Calendar and the 50-year Jubilean ceremony of the Old Testamemt.
So perhaps the antediluvian age from before the Biblical flood was the era in which the Atlanteans used a very accurate leap-day formula that may have lasted for centuries. The next important question to ask would be how many centuries did the Atlanteans live as a maritime kingdom? The answer awaits more research.
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