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

Over the ages, the concentration of 14C in the atmosphere varies. The conversion of 14C BP age measurements to calendar years requires the use of a tree ring curve constructed by estimating the 14C BP age of tree rings from trees of known age. McFaden et.al. (1994, Radiocarbon, Vol.36 No.2, p.221-236), tested the tree ring curve by plotting the frequency of C14 BP measurements from a random selection of charcoal and wood specimens (BP –100 to –1400 years) from New Zealand, Australia and British Columbia against their estimated BP calendar age (Figure 1). The three resultant histograms show that each region has a very similar distribution of peaks and troughs that correlate with changes in slope of the tree ring calibration curve. McFaden et.al. attributed this finding to Stochastic Calibration Distortion (SCD) and not human activity. SCD is the artificial clumping or spreading of calendar dates and is considered due to the interaction of the error in the 14C measurement of the tree ring samples with the changes in slope of the calibration curve. There are several papers in the literature related to SCD and 14C BP dating:

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

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.

1. 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.
2. 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.