# Analysis of Radiocarbon Dating Statistics in Reference to the Voynich Manuscript - Part 2

- Knox and McFaden 1997, Radiocarbon, Vol.39 No.1, p.193-204.
- Stolk, K. H. and Henk, B 1989, Radiocarbon, Vol.31 No.12, p.169-178.
- Stuiver and Reimer, 1989, Radiocarbon, Vol.31 No.3, p.812-823.

Graph of calibrated dates on charcoal and wood for New Zealand prehistory (A)

compared with graphs of calibrated dates on charcoal for South Australia (B)

and British Columbia (C) prehistory.

Note the correspondence between the peaks and troughs of the non-ambiguous regions () of the tree ring calibration curve. For a single 14C age, non-ambiguous regions of the curve correspond to a single calendar date, while ambiguous regions have multiple calendar dates. The calendar years are the number of years before 1950. (D) Range of dates for the VM –512 to –546.

The 2SD (1404 – 1438) range of dates for the Voynich Manuscript (VM) lies on the double peak D of the distribution graph C close to an ambiguous region of the curve. I modeled, using a least squares fit to a straight line, the raw 14C BP data from BP -486 to -586 from the 2004 tree ring curve http://www.radiocarbon.org/IntCal04%20files/IntCal04_rawdata.csv. The curve had a correlation coefficient = 0.98, a slope= 2.77. The error in the precision of the calendar date is determined by the reciprocal of the slope of the curve. The 1SD error in the mean BP calendar estimate for the VM is 8.5 years. The 1SD error in the 14C BP age is 8.5 * 2.77 or 24 years. The non linearity of the tree calibration curve, whether exascerbated by SCD or not, influences the magnitude of the 1 and 2 SD estimates of the calendar year errors. Steep regions of the curve will indicate small errors and flat regions will signify large errors.

Table 1 below, gives additional examples of the problems that result when the 1 and 2 SD ranges about an estimated mean 14C BP age are used to determine calendar age ranges from the tree ring calibration curve. All the parchment samples are from the Beinecke Library and were analyzed by the U. of Arizona. The ages of samples (1-4) are known, the Vinland map has been dated to ~1434. The data from which this table was constructed came from Table 2 in http://www.webexhibits.org/vinland/paper-donahue02.html.

14C BP age ± one sigma | Calibrated age, AD one sigma | Calibrated age, AD two sigma | Known age | Calendar age ± 1SD | Calendar age ± 2SD | |
---|---|---|---|---|---|---|

Sample-1 | 405 ± 25 | 1444-1482 | 1437-1620 | 1434 | 1463 ± 19 | 1528 ± 91 |

Sample-2 | 443 ± 25 | 1438-1466 | 1427-1485 | 1446 | 1455 ± 17 | 1456 ± 29 |

Sample-2 | 443 ± 25 | 1438-1466 | 1427-1485 | 1446 | 1455 ± 17 | 1456 ± 29 |

Sample-3 | 399 ± 25 | 1444-1488 | 1438-1620 | 1457 | 1466 ± 22 | 1519 ± 91 |

Sample-4 | 313 ± 25 | 1521 -1639 | 1491-1645 | 1495 | 1580 ± 59 | 1568 ± 77 |

Vinland map | 467 ± 27 | 1423-1445 | 1411-1468 | 1434 | 1434 ± 11 | 1439 ± 28 |

- The results for samples 1 and 3, show that SCD, due to the non-linearity of the calibration curve, gives different estimates for the 1 and 2 SD ranges.
- The measured 14C BP age of each sample has approximately the same 1SD error ~25 years, but as a result of SCD, due to the non-linearity of the calendar curve, the 1SD calendar age error varies from 11 to 59 years and the 2SD error varies from 28 to 91years. The age of the parchment samples ranged from 1434-1495, 61 years.

The current method of stating the estimated error for the calendar year from a single 14C BP age is over-simplified and as I indicated in my paper, Analysis of Radiocarbon Dating Statistics in Reference to the Voynich Manuscript, an increase in the error estimate for the 14C BP age estimate is justified and, depending on its magnitude, could would lead to a proportional increase in the calendar year error estimate.