## FANDOM

28,067 Pages

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

 Portal Year Roulean Year Event -1441 PY 324 RC Jojiism founded. -869 PY 704 RC Viamont invades Aluvia. The reign of Pwyll II ends and the reign of Alfric begins. -779 PY 765 RC Reign of Alfrega begins. Harlune stays behind on Ispar during an expedition. -758 PY 779 RC Reign of Osric begins. -540 PY 924 RC Gharu'n armies seige the Roulean capital of Tirethas. -358 PY 1046 RC Emperor Kou unites the Sho under his rule.

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 - (1928.7053) PY = (662/441) * RC - (94441/49) PY = (1.5011) * RC - (1927.3673) PY = (683/455) * RC - (876947/455) PY = (1.5011) * RC - (1927.3560) PY = (901/600) * RC - (96377/50) PY = (1.5017) * RC - (1927.54) PY = (3/2) * RC - (1927) PY = (1.5) * RC - (1927) PY = (90/61) * RC - (116369/61) PY = (1.4754) * RC - (1907.6885) PY = (37/25) * RC - (47773/25) PY = (1.48) * RC - (1910.92) PY = (329/220) * RC - (9609/5) PY = (1.4955) * RC - (1921.8) PY = (511/342) * RC - (328471/171) PY = (1.4942) * RC - (1920.8830) PY = (3/2) * RC - (3853/2) PY = (1.5) * RC - (1926.5) PY = (239/159) * RC - (102232/53) PY = (1.5031) * RC - (1928.9057) PY = (421/281) * RC - (540964/281) PY = (1.4982) * RC - (1925.1388) PY = (218/145) * RC - (279732/145) PY = (1.5034) * RC - (1929.1862) PY = (400/267) * RC - (513986/267) PY = (1.4981) * RC - (1925.0412) PY = (91/61) * RC - (117024/61) PY = (1.4918) * RC - (1918.4262)

One thing is very clear, the slope of all of these equations is very close to 1.5, which we will express as (3/2). 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 (3/2). If we do so, we get the following equations:

 Input (RC) Best Equation Expected Output (PY) Actual Output (PY) 324 PY = (3/2) * RC - 1927 -1441 -1,441 704 PY = (3/2) * RC - 1925 -869 -869 765 PY = (3/2) * RC - 1926.5 -779 -779 779 PY = (3/2) * RC - 1926.5 -758 -758 924 PY = (3/2) * RC - 1926 -540 -540 1046 PY = (3/2) * RC - 1927 -358 -358

With this method, we can narrow the y-intercept to between -1925 and -1927. 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 = (3/2) * RC - 1926 -1440 325 PY = (3/2) * RC - 1928.5 -1441 704 PY = (3/2) * RC - 1924 -868 705 PY = (3/2) * RC - 1926.5 -869 765 PY = (3/2) * RC - 1925.5 -778 766 PY = (3/2) * RC - 1928 -779 779 PY = (3/2) * RC - 1925.5 -757 780 PY = (3/2) * RC - 1928 -758 924 PY = (3/2) * RC - 1925 -539 925 PY = (3/2) * RC - 1927.5 -540 1046 PY = (3/2) * RC - 1926 -357 1047 PY = (3/2) * RC - 1928.5 -358

The only equations which will work will be somewhere between the following:

• PY = (3/2) * RC - 1926
• PY = (3/2) * RC - 1926.5

We can repeat this entire process with the points in reverse order (e.g. 324, -1441 becomes -1441, 324) to find the equation for converting PY to RC. When all is done, the only equations which will work will be somewhere between the following:

• RC = (2/3) * PY + 1284
• RC = (2/3) * PY + (1284 + (1/3))

## Conclusion

We don't have more information to help narrow down the range, and it would make equal sense for the y-intercept to be a whole number or a decimal. However, with noting else to go on, the simplest path seems like the best choice. Therefore, when calculating dates between the Roulean and Portal Year calendars, use the following equations:

• PY = (3/2) * RC - 1926
• RC = (2/3) * PY + 1284
Community content is available under CC-BY-SA unless otherwise noted.