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A Conflict in the Avatar World's Cycle of Years and Why It Happened
I discussed in my last post how the Avatar world probably uses a combination of elemental and animal years to have a cyclical system, much like the traditional Chinese sexagenary cycle. In that post I also argued that the fan theory of the elemental years standing for Avatar eras is unworkable, due to the difficulty of coding historical events (like Avatar birth and death years) into a mathematical and astronomical calendar,.and due to the notation of the years in writing.
That is not to say my theory is without its problems. I ran a quick simulation and realized that my interpretation contradicts evidence from the show: the years Superior Mighty Monkey (the year at the time of "The Library") and Cultivated Commanding Dragon (the year of the darkest day in Fire Nation history) cannot both exist in the calendar system I'm proposing.
This is because my first assumption was that the elemental and animal years are combined just like the real-life Chinese sexagenary cycle. In the sexagenary cycle, the ten-item element list and the twelve-item animal list are simply placed side by side, rinse and repeat, until the ends of the two lists match up and the beginning year returns. Since the shorter element list will end sooner, it just starts up again and the first element (甲, yang wood) cycles back to match up with the eleventh animal (戌, dog). The least common multiplier of 10 and 12 being 60, the same element-animal combination will repeat itself every 60 years. To illustrate:
Element - Animal
1. 甲 (yang wood) - 1. 子 (rat)
2. 乙 (yin wood) - 2. 丑 (ox)
3. 丙 (yang fire) - 3. 寅 (tiger)
.
.
.
10. 癸 (yin water) - 10. 酉 (rooster)
1. 甲 (yang wood) - 11. 戌 (dog)
2. 乙 (yin wood) - 12. 亥 (pig)
3. 丙 (yang fire) - 1. 子 (rat)
...
Now, this was my default assumption with the Avatar calendar system as well, given the similarities between the two. Unfortunately, this creates the conflict I've described above: Cultivated Commanding Dragon and Superior Mighty Monkey can't coexist in this system.
To understand why, take a gander at the example years I've written above for the Chinese calendar. Notice anything about the numbers on the left and right columns? 1 on the elemental list matches 1 on the animal list, and so on... and then 1 on the elemental list, and 11 on the animal list. Then 3 on the elemental list, and 1 on the animal list.
There are 60 different element-animal combinations in this system, but it's not every possible combination (which would be 120). That's because the order within each list doesn't change--the lists are just laid alongside each other and repeated until the ends match up, remember. This means that, because the highest common denominator of 10 and 12 is--try calculating it--2, an odd number on the element list can only match up with an odd number on the animal list, and an even number on the element list can only match up with an even number on the animal list.
To get a feel for that, it might help to think of the 10-item element list as a five-part list with two items in each part, and the 12-item animal list as a six-part list also with two items in each part. Each part matches up with its counterpart in the other list, so that we have a two-two-two match on each side. 2m+1 on the element list can only meet 2n+1 on the animal list, and 2p on the element list can only meet 2q on the animal list (m and n being integers of 0 or larger, and p and q being natural numbers).
Below is a simple diagram I drew to show that relationship, with the blue column standing for the element list, the red for the animal list, and the compartments divided with orange lines showing the two-item parts. Sorry it's so ugly, but hopefully it illustrates the point.
Now, moving on to the calendar in the Avatar world, the exact same thing happens if we assume this calendar uses the same method as the Chinese one. The only difference is that the highest common denominator is now--try calculating!--4 instead of 2, since we're talking 16 and 12 instead of 10 and 12. So the same relationship applies, except now the relationship isn't between even and odd numbers, but a range of four numbers depending on their difference from a multiplier of four. So 4n + 1 on the element list can only meet 4m+1 on the animal list, 4n + 2 can only meet 4m + 2, and so on.
Which brings us back to the ever-elusive Cultivated Commanding Dragon. Since Superior Mighty Monkey" is the year the Gaang discovered the calendar, let's take "superior mighty" as the first on the element list and "monkey" as the first on the animal list. According to the Avatar era names compiled on the Avatar Wiki, that makes "cultivated commanding" the seventh element and "dragon" the ninth animal. The remainder of seven divided by four is three (4m + 3 where m=1). The remainder of nine divided by four is two (4n + 2 where n = 2). This means "cultivated commanding" and "dragon" cannot match in the system I have assumed.
The easiest way to get around this difficulty is to say that "Cultivated Commanding Dragon year" is a mistake. The creative team was on a schedule, after all, while fans have years and years to analyze this stuff, assuming a show that is not quickly forgotten and/or fans with enough time on their hands.
Still, I'd like to eschew the easy way out in this particular case because there is something else I don't like about the system I've assumed. I like it a lot better than the Avatar epoch-animal year system hypothesized by the Avatar Wiki, for all the reasons I've stated in my previous post on the subject. However, I don't like that the years cycle back in only 48 years. In a 48-year cycle, living until your birth year comes around again can't be anything very rare, nor does it denote as much wisdom and experience as a 60-year cycle. The cultured commanding dragon year business is just an additional reason to seek an alternative.
Therefore my next post on the subject (yes, I'm writing three posts about the calendar of a fictional world. Go me!) I'll talk about ways to fix the calendar system.
That is not to say my theory is without its problems. I ran a quick simulation and realized that my interpretation contradicts evidence from the show: the years Superior Mighty Monkey (the year at the time of "The Library") and Cultivated Commanding Dragon (the year of the darkest day in Fire Nation history) cannot both exist in the calendar system I'm proposing.
This is because my first assumption was that the elemental and animal years are combined just like the real-life Chinese sexagenary cycle. In the sexagenary cycle, the ten-item element list and the twelve-item animal list are simply placed side by side, rinse and repeat, until the ends of the two lists match up and the beginning year returns. Since the shorter element list will end sooner, it just starts up again and the first element (甲, yang wood) cycles back to match up with the eleventh animal (戌, dog). The least common multiplier of 10 and 12 being 60, the same element-animal combination will repeat itself every 60 years. To illustrate:
Element - Animal
1. 甲 (yang wood) - 1. 子 (rat)
2. 乙 (yin wood) - 2. 丑 (ox)
3. 丙 (yang fire) - 3. 寅 (tiger)
.
.
.
10. 癸 (yin water) - 10. 酉 (rooster)
1. 甲 (yang wood) - 11. 戌 (dog)
2. 乙 (yin wood) - 12. 亥 (pig)
3. 丙 (yang fire) - 1. 子 (rat)
...
Now, this was my default assumption with the Avatar calendar system as well, given the similarities between the two. Unfortunately, this creates the conflict I've described above: Cultivated Commanding Dragon and Superior Mighty Monkey can't coexist in this system.
To understand why, take a gander at the example years I've written above for the Chinese calendar. Notice anything about the numbers on the left and right columns? 1 on the elemental list matches 1 on the animal list, and so on... and then 1 on the elemental list, and 11 on the animal list. Then 3 on the elemental list, and 1 on the animal list.
There are 60 different element-animal combinations in this system, but it's not every possible combination (which would be 120). That's because the order within each list doesn't change--the lists are just laid alongside each other and repeated until the ends match up, remember. This means that, because the highest common denominator of 10 and 12 is--try calculating it--2, an odd number on the element list can only match up with an odd number on the animal list, and an even number on the element list can only match up with an even number on the animal list.
To get a feel for that, it might help to think of the 10-item element list as a five-part list with two items in each part, and the 12-item animal list as a six-part list also with two items in each part. Each part matches up with its counterpart in the other list, so that we have a two-two-two match on each side. 2m+1 on the element list can only meet 2n+1 on the animal list, and 2p on the element list can only meet 2q on the animal list (m and n being integers of 0 or larger, and p and q being natural numbers).
Below is a simple diagram I drew to show that relationship, with the blue column standing for the element list, the red for the animal list, and the compartments divided with orange lines showing the two-item parts. Sorry it's so ugly, but hopefully it illustrates the point.
Now, moving on to the calendar in the Avatar world, the exact same thing happens if we assume this calendar uses the same method as the Chinese one. The only difference is that the highest common denominator is now--try calculating!--4 instead of 2, since we're talking 16 and 12 instead of 10 and 12. So the same relationship applies, except now the relationship isn't between even and odd numbers, but a range of four numbers depending on their difference from a multiplier of four. So 4n + 1 on the element list can only meet 4m+1 on the animal list, 4n + 2 can only meet 4m + 2, and so on.
Which brings us back to the ever-elusive Cultivated Commanding Dragon. Since Superior Mighty Monkey" is the year the Gaang discovered the calendar, let's take "superior mighty" as the first on the element list and "monkey" as the first on the animal list. According to the Avatar era names compiled on the Avatar Wiki, that makes "cultivated commanding" the seventh element and "dragon" the ninth animal. The remainder of seven divided by four is three (4m + 3 where m=1). The remainder of nine divided by four is two (4n + 2 where n = 2). This means "cultivated commanding" and "dragon" cannot match in the system I have assumed.
The easiest way to get around this difficulty is to say that "Cultivated Commanding Dragon year" is a mistake. The creative team was on a schedule, after all, while fans have years and years to analyze this stuff, assuming a show that is not quickly forgotten and/or fans with enough time on their hands.
Still, I'd like to eschew the easy way out in this particular case because there is something else I don't like about the system I've assumed. I like it a lot better than the Avatar epoch-animal year system hypothesized by the Avatar Wiki, for all the reasons I've stated in my previous post on the subject. However, I don't like that the years cycle back in only 48 years. In a 48-year cycle, living until your birth year comes around again can't be anything very rare, nor does it denote as much wisdom and experience as a 60-year cycle. The cultured commanding dragon year business is just an additional reason to seek an alternative.
Therefore my next post on the subject (yes, I'm writing three posts about the calendar of a fictional world. Go me!) I'll talk about ways to fix the calendar system.