Continuity/Roulean Calendar and Portal Years

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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
(-1441, 324) (-869, 704) RC = (95/143) * PY + (16657/13)
(-1441, 324) (779, 765) RC = (441/662) * PY + (849969/662)
(-1441, 324) (-758, 779) RC = (455/683) * PY + (876947/683)
(-1441, 324) (-540, 924) RC = (600/901) * PY + (1156524/901)
(-1441, 324) (-358, 1046) RC = (2/3) * PY + (3854/3)
(-869, 704) (779, 765) RC = (61/90) * PY + (116369/90)
(-869, 704) (-758, 779) RC = (25/37) * PY + (47773/37)
(-869, 704) (-540, 924) RC = (220/329) * PY + (422796/329)
(-869, 704) (-358, 1046) RC = (342/511) * PY + (656942/511)
(-779, 765) (-758, 779) RC = (2/3) * PY + (3853/3)
(-779, 765) (-540, 924) RC = (159/239) * PY + (306696/239)
(-779, 765) (-358, 1046) RC = (281/421) * PY + (540964/421)
(-758, 779) (-540, 924) RC = (145/218) * PY + (139866/109)
(-758, 779) (-358, 1046) RC = (267/400) * PY + (256993/200)
(-540, 924) (-358, 1046) RC = (61/91) * PY + (117024/91)

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:
RC = (95/143) * PY + (16657/13) RC = (0.6643) * PY + (1281.3077)
RC = (441/662) * PY + (849969/662) RC = (0.6662) * PY + (1283.9411)
RC = (455/683) * PY + (876947/683) RC = (0.6662) * PY + (1283.9634)
RC = (600/901) * PY + (1156524/901) RC = (0.6659) * PY + (1283.6004)
RC = (2/3) * PY + (3854/3) RC = (0.6667) * PY + (1284.6667)
RC = (61/90) * PY + (116369/90) RC = (0.6778) * PY + (1292.9889)
RC = (25/37) * PY + (47773/37) RC = (0.6757) * PY + (1291.1622)
RC = (220/329) * PY + (422796/329) RC = (0.6687) * PY + (1285.0942)
RC = (342/511) * PY + (656942/511) RC = (0.6693) * PY + (1285.6008)
RC = (2/3) * PY + (3853/3) RC = (0.6667) * PY + (1284.3333)
RC = (159/239) * PY + (306696/239) RC = (0.6653) * PY + (1283.2469)
RC = (281/421) * PY + (540964/421) RC = (0.6675) * PY + (1284.9501)
RC = (145/218) * PY + (139866/109) RC = (0.6651) * PY + (1283.1743)
RC = (267/400) * PY + (256993/200) RC = (0.6675) * PY + (1284.9650)
RC = (61/91) * PY + (117024/91) RC = (0.6703) * PY + (1285.9780)

One thing is very clear, the slope of all of these equations is very close to .67. This means we can express the slope as (2/3). 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):

  • RC = (2/3) * PY + (1281.3334)
  • RC = (2/3) * PY + (1283.25)
  • RC = (2/3) * PY + (1283.6667)
  • RC = (2/3) * PY + (1284)
  • RC = (2/3) * PY + (1284.3334)
  • RC = (2/3) * PY + (1284.6667)
  • RC = (2/3) * PY + (1285)
  • RC = (2/3) * PY + (1285.6667)
  • RC = (2/3) * PY + (1286)
  • RC = (2/3) * PY + (1291)
  • RC = (2/3) * PY + (1293)

To determine which equation works best, we can input the PY dates we have, and see how the RC output compares to expected value. Below is a table for each equation, and all of its inputs and outputs:

Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1281.3334) 324 320.6667
-869 RC = (2/3) * PY + (1281.3334) 704 702
-779 RC = (2/3) * PY + (1281.3334) 765 762
-758 RC = (2/3) * PY + (1281.3334) 779 776
-540 RC = (2/3) * PY + (1281.3334) 924 921.3334
-358 RC = (2/3) * PY + (1281.3334) 1046 1042.6667
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1283.25) 324 322.5833
-869 RC = (2/3) * PY + (1283.25) 704 703.9167
-779 RC = (2/3) * PY + (1283.25) 765 763.9167
-758 RC = (2/3) * PY + (1283.25) 779 777.9167
-540 RC = (2/3) * PY + (1283.25) 924 923.25
-358 RC = (2/3) * PY + (1283.25) 1046 1044.5833
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1283.6667) 324 323
-869 RC = (2/3) * PY + (1283.6667) 704 704.3334
-779 RC = (2/3) * PY + (1283.6667) 765 764.3334
-758 RC = (2/3) * PY + (1283.6667) 779 778.3334
-540 RC = (2/3) * PY + (1283.6667) 924 923.6667
-358 RC = (2/3) * PY + (1283.6667) 1046 1045
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1284) 324 323.3334
-869 RC = (2/3) * PY + (1284) 704 704.6667
-779 RC = (2/3) * PY + (1284) 765 764.6667
-758 RC = (2/3) * PY + (1284) 779 778.6667
-540 RC = (2/3) * PY + (1284) 924 924
-358 RC = (2/3) * PY + (1284) 1046 1045.3334
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1284.3334) 324 323.6667
-869 RC = (2/3) * PY + (1284.3334) 704 705
-779 RC = (2/3) * PY + (1284.3334) 765 765
-758 RC = (2/3) * PY + (1284.3334) 779 779
-540 RC = (2/3) * PY + (1284.3334) 924 924.3334
-358 RC = (2/3) * PY + (1284.3334) 1046 1045.6667
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1284.6667) 324 324
-869 RC = (2/3) * PY + (1284.6667) 704 705.3334
-779 RC = (2/3) * PY + (1284.6667) 765 765.3334
-758 RC = (2/3) * PY + (1284.6667) 779 779.3334
-540 RC = (2/3) * PY + (1284.6667) 924 924.6667
-358 RC = (2/3) * PY + (1284.6667) 1046 1046
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1285) 324 324.3334
-869 RC = (2/3) * PY + (1285) 704 705.6667
-779 RC = (2/3) * PY + (1285) 765 765.6667
-758 RC = (2/3) * PY + (1285) 779 779.6667
-540 RC = (2/3) * PY + (1285) 924 925
-358 RC = (2/3) * PY + (1285) 1046 1046.3334
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1285.6667) 324 325
-869 RC = (2/3) * PY + (1285.6667) 704 706.3334
-779 RC = (2/3) * PY + (1285.6667) 765 766.3334
-758 RC = (2/3) * PY + (1285.6667) 779 780.3334
-540 RC = (2/3) * PY + (1285.6667) 924 925.6667
-358 RC = (2/3) * PY + (1285.6667) 1046 1047
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1286) 324 325.3334
-869 RC = (2/3) * PY + (1286) 704 706.6667
-779 RC = (2/3) * PY + (1286) 765 766.6667
-758 RC = (2/3) * PY + (1286) 779 780.6667
-540 RC = (2/3) * PY + (1286) 924 926
-358 RC = (2/3) * PY + (1286) 1046 1047.3334
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1291) 324 330.33334
-869 RC = (2/3) * PY + (1291) 704 711.6667
-779 RC = (2/3) * PY + (1291) 765 771.6667
-758 RC = (2/3) * PY + (1291) 779 785.6667
-540 RC = (2/3) * PY + (1291) 924 931
-358 RC = (2/3) * PY + (1291) 1046 1052.3334
Input (PY) Equation Expected Output (RC) Actual Output (RC)
-1441 RC = (2/3) * PY + (1293) 324 332.3334
-869 RC = (2/3) * PY + (1293) 704 713.6667
-779 RC = (2/3) * PY + (1293) 765 773.6667
-758 RC = (2/3) * PY + (1293) 779 787.6667
-540 RC = (2/3) * PY + (1293) 924 933
-358 RC = (2/3) * PY + (1293) 1046 1054.3334


Conclusion

References

<references />

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