Continuity/Roulean Calendar and Portal Years: Difference between revisions

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One thing is very clear, the slope of all of these equations is very close to 1.5. Its only the y-intercept that varies. If we round the y-intercept to the nearest whole number, third, or quarter, we are left the following equations (duplicates removed):
One thing is very clear, the slope of all of these equations is very close to 1.5. Its only the y-intercept that varies. We have determined that the y-intercept is somewhere between around -1,907 and -1,930. One way to further narrow this down is to find the equation that best works for each point, given that the slope is 1.5. If we do so, we get the following equations:
* PY = (1.5) * RC - (1,907.6667)
* PY = (1.5) * RC - (1,911)
* PY = (1.5) * RC - (1,918.5)
* PY = (1.5) * RC - (1,921)
* PY = (1.5) * RC - (1,921.75)
* PY = (1.5) * RC - (1,925)
* PY = (1.5) * RC - (1,926.5)
* PY = (1.5) * RC - (1,927)
* PY = (1.5) * RC - (1,927.5)
* PY = (1.5) * RC - (1,927.3334)
* PY = (1.5) * RC - (1,928.75)
* PY = (1.5) * RC - (1,929.25)


The is one more piece of information we have to work with: we know that the event which took place in 704 RC, the Viamontian invasion of Aluvia, took place on the 4th of Solclaim.<ref name=TheReignOfAlfrega>1999/11 [[Release]] - [[The Reign of Alfrega]]</ref> we also know from [[Microsoft Zone Archive/Asheron's Lore/A Brief History for Travelers|A Brief History for Travelers]] that Solclaim is the 5th of 12 months on the Roulean calendar. Expressed as a decimal, that is 0.4167. So that event took place on 704.4167, almost exactly.
{|class="wikitable"
|bgcolor=#d0d0d0| '''Input (RC)'''
|bgcolor=#d0d0d0| '''Best Equation'''
|bgcolor=#d0d0d0| '''Expected Output (PY)'''
|bgcolor=#d0d0d0| '''Actual Output (PY)'''
|-
| 324 || PY = (1.5) * RC - (1,927) || -1441 || -1,441
|-
| 704 || PY = (1.5) * RC - (1,925) || -869 || -869
|-
| 765 || PY = (1.5) * RC - (1,926.5) || -779 || -779
|-
| 779 || PY = (1.5) * RC - (1,926.5) || -758 || -758
|-
| 924 || PY = (1.5) * RC - (1,926) || -540 || -540
|-
| 1046 || PY = (1.5) * RC - (1,927) || -358 || -358
|}
 
With this method, we can narrow the y-intercept to between -1,925 and -1,927. However, this is not perfect, because we are only using whole numbers. In actuality, an event could occur at any point in the year, not just the new year's day. So for example, the event that occurred in 324 RC could have occurred anywhere between 324 and 325 RC. And it's corresponding PY could be anywhere between -1440 and -1441 PY.
<br /><br />
<br /><br />
With that in mind, the correct equation should take an input of 704.4167 RC should return a value between -868 an -869 PY.
That expands the possible equations to the following:
<br /><br />
{|class="wikitable"
This narrows our y-intercept to between about -1,924.67 and -1,925.5.
|bgcolor=#d0d0d0| '''Input (RC)'''
<br /><br />
|bgcolor=#d0d0d0| '''Equation'''
One way to further narrow this down is to take our known RC values, input them into the equations, and see how close the output is to our known PY values.
|bgcolor=#d0d0d0| '''Output (PY)'''
|-
| 324 || PY = (1.5) * RC - (1,926) || -1440
|-
| 325 || PY = (1.5) * RC - (1,928.5) || -1441
|-
 
| 704 || PY = (1.5) * RC - (1,924) || -868
|-
| 705 || PY = (1.5) * RC - (1,926.5) || -869
|-
 
| 765 || PY = (1.5) * RC - (1,925.5) || -778
|-
| 766 || PY = (1.5) * RC - (1,928) || -779
|-
 
| 779 || PY = (1.5) * RC - (1,925.5) || -757
|-
| 780 || PY = (1.5) * RC - (1,928)|| -758
|-
 
| 924 || PY = (1.5) * RC - (1,925) || -539
|-
| 925 || PY = (1.5) * RC - (1,927.5) || -540
|-
 
| 1046 || PY = (1.5) * RC - (1,926) || -357
|-
| 1047 || PY = (1.5) * RC - (1,928.5) || -358
|-
|}
 
The only y-intercept that works for all of the given dates is going to be between -1,926 and -1,926.5.


== Conclusion ==
== Conclusion ==

Revision as of 10:05, 4 March 2015

In early 2003, Turbine released a timeline called The History of Auberean. We are presented with several events, and the year the occurred on both the Portal Year and Roulean calendars:

Portal Year Roulean Year Event
-1441 PY 324 RC Jojiism founded.<ref name=HistoryOfAubereanVol3>2003/03 The History of Auberean/Volume III: The Fall From Grace (-1,804 to -891)</ref>
-869 PY 704 RC Viamont invades Aluvia. The reign of Pwyll II ends and the reign of Alfric begins.<ref name=HistoryOfAubereanVol4>2003/03 The History of Auberean/Volume IV: Shifting Ways (-888 to -574)</ref>
-779 PY 765 RC Reign of Alfrega begins. Harlune stays behind on Ispar during an expedition.<ref name=HistoryOfAubereanVol4 />
-758 PY 779 RC Reign of Osric begins.<ref name=HistoryOfAubereanVol4 />
-540 PY 924 RC Gharu'n armies seige the Roulean capital of Tirethas.<ref name=HistoryOfAubereanVol5>2003/03 The History of Auberean/Volume V: New Arrivals (-540 to 13)</ref>
-358 PY 1046 RC Emperor Kou unites the Sho under his rule.<ref name=HistoryOfAubereanVol5 />

With multiple matching pairs of dates, we can determine the equation to convert between calendars. All we have to do is treat the pairs of dates as coordinates of points, and find the equation for the line that intersects those points. We will determine the equation for each set of points:

Point A Point B Equation
324, -1441 704, -869 PY = (143/95) * RC - (183227/95)
324, -1441 765, -779 PY = (662/441) * RC - (94441/49)
324, -1441 779, -758 PY = (683/455) * RC - (876947/455)
324, -1441 924, -540 PY = (901/600) * RC - (96377/50)
324, -1441 1046, -358 PY = (3/2) * RC - (1927)
704, -869 765, -779 PY = (90/61) * RC - (116369/61)
704, -869 779, -758 PY = (37/25) * RC - (47773/25)
704, -869 924, -540 PY = (329/220) * RC - (9609/5)
704, -869 1046, -358 PY = (511/342) * RC - (328471/171)
765, -779 779, -758 PY = (3/2) * RC - (3853/2)
765, -779 924, -540 PY = (239/159) * RC - (102232/53)
765, -779 1046, -358 PY = (421/281) * RC - (540964/281)
779, -758 924, -540 PY = (218/145) * RC - (279732/145)
779, -758 1046, -358 PY = (400/267) * RC - (513986/267)
924, -540 1046, -358 PY = (91/61) * RC - (117024/61)

If we solve the division within the parentheses, we see these equations are all fairly similar. Below is a table with the equations, where the division has been solved to four decimal places:

Equation is similar to:
PY = (143/95) * RC - (183227/95) PY = (1.5053) * RC - (1,928.7053)
PY = (662/441) * RC - (94441/49) PY = (1.5011) * RC - (1,927.3673)
PY = (683/455) * RC - (876947/455) PY = (1.5011) * RC - (1,927.3560)
PY = (901/600) * RC - (96377/50) PY = (1.5017) * RC - (1,927.54)
PY = (3/2) * RC - (1927) PY = (1.5) * RC - (1927)
PY = (90/61) * RC - (116369/61) PY = (1.4754) * RC - (1,907.6885)
PY = (37/25) * RC - (47773/25) PY = (1.48) * RC - (1,910.92)
PY = (329/220) * RC - (9609/5) PY = (1.4955) * RC - (1,921.8)
PY = (511/342) * RC - (328471/171) PY = (1.4942) * RC - (1,920.8830)
PY = (3/2) * RC - (3853/2) PY = (1.5) * RC - (1,926.5)
PY = (239/159) * RC - (102232/53) PY = (1.5031) * RC - (1,928.9057)
PY = (421/281) * RC - (540964/281) PY = (1.4982) * RC - (1,925.1388)
PY = (218/145) * RC - (279732/145) PY = (1.5034) * RC - (1,929.1862)
PY = (400/267) * RC - (513986/267) PY = (1.4981) * RC - (1,925.0412)
PY = (91/61) * RC - (117024/61) PY = (1.4918) * RC - (1,918.4262)

One thing is very clear, the slope of all of these equations is very close to 1.5. Its only the y-intercept that varies. We have determined that the y-intercept is somewhere between around -1,907 and -1,930. One way to further narrow this down is to find the equation that best works for each point, given that the slope is 1.5. If we do so, we get the following equations:

Input (RC) Best Equation Expected Output (PY) Actual Output (PY)
324 PY = (1.5) * RC - (1,927) -1441 -1,441
704 PY = (1.5) * RC - (1,925) -869 -869
765 PY = (1.5) * RC - (1,926.5) -779 -779
779 PY = (1.5) * RC - (1,926.5) -758 -758
924 PY = (1.5) * RC - (1,926) -540 -540
1046 PY = (1.5) * RC - (1,927) -358 -358

With this method, we can narrow the y-intercept to between -1,925 and -1,927. However, this is not perfect, because we are only using whole numbers. In actuality, an event could occur at any point in the year, not just the new year's day. So for example, the event that occurred in 324 RC could have occurred anywhere between 324 and 325 RC. And it's corresponding PY could be anywhere between -1440 and -1441 PY.

That expands the possible equations to the following:

Input (RC) Equation Output (PY)
324 PY = (1.5) * RC - (1,926) -1440
325 PY = (1.5) * RC - (1,928.5) -1441
704 PY = (1.5) * RC - (1,924) -868
705 PY = (1.5) * RC - (1,926.5) -869
765 PY = (1.5) * RC - (1,925.5) -778
766 PY = (1.5) * RC - (1,928) -779
779 PY = (1.5) * RC - (1,925.5) -757
780 PY = (1.5) * RC - (1,928) -758
924 PY = (1.5) * RC - (1,925) -539
925 PY = (1.5) * RC - (1,927.5) -540
1046 PY = (1.5) * RC - (1,926) -357
1047 PY = (1.5) * RC - (1,928.5) -358

The only y-intercept that works for all of the given dates is going to be between -1,926 and -1,926.5.

Conclusion

References

<references />

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