The Voynich Ninja

(16-05-2021, 04:24 PM)Anton Wrote: You are not allowed to view links. Register or Login to view.The plus-minus is not 95% confidence

Anton, the figures quoted are 2 sigma.

Check e.g.Fig 5 leaf 68 (no solvent).

Top right tables of figures give the ranges, also marked on the bottom of the chart. "95.4% probability" : 1396-1457 (fits with range marked on bottom of chart). The difference is 61, which is +/- 2 = 4 sigma. So sigma = 15. Roughly!

There seems to be a bit of weighting or rounding going on and I don't know the meaning of the "93.8%" in brackets so simple calculations are not exact. Maybe some skew or kurtosis in the graph too.

Note also there is an error in the section "Averaging the Results to increase Precision"
"the measurement from solvent treated Leaf #68 was excluded from this average."

In fact it was the solvent untreated sample that was excluded.

The weak methodological point in the report (and here I agree with Rich, notwithstanding that he erroneously treats the dating) is that weighted averaging (page 3). The asumption in which it was made is clearly stated:

Quote:Given the clustering of the dates for the four Soxhlet treated samples, and the nature of the object (a book), one can argue that in fact, a single object was measured 4 times

Now, while I myself used to like the idea that we deal with a "single object", I have to admit that there are arguments towards the opposite, namely that this is not a single object, but rather a collection of different objects which may have been produced at different time, and bound only later. In this light, it makes no sense to average those results.

Furthermore, this statement is strange:

Quote:Note that the measurement from solvent treated Leaf #68 was excluded from this average

I'm not sure whether that means that they averaged three solvent-cleaned folios (8, 26 and 47) or three solvent-cleaned (8,26,47) with one uncleaned (68), but either case it's methodologically inconsistent.

In any case, even with this drawback, the three Herbal folios are pretty consistent, with high probability being from ~1390 to ~1450. The Astro folio is just uncertain between 1308-1362 and 1385-1436. There's good chance that it's pretty older than Herbal folos.

It's a pity that they did not take more samples from sections other than Herbal. But I guess that Beinecke would not be particularly glad to have the VMS cut in pieces for the sake of scientific combustion.

Let's say we can assume that Pharma does not pre-date Herbal, because they re-use leaves and roots from Herbal there. Zodiac and Balneo are probably of the same date, because they re-use nymphs. If we assume that the You are not allowed to view links. Register or Login to view. nymph is the same hand, then Recipes fall into the same time period. Astro/Cosmo may be something different in time, since I think there are no direct stylistic links between those and other sections.

(16-05-2021, 05:41 PM)DONJCH Wrote: You are not allowed to view links. Register or Login to view.Anton, the figures quoted are 2 sigma.

No, it's one sigma (for the uncalibrated figures). For the calibrated curves, they give both one sigma and two sigma. For the normal distribution, one sigma is 68,2% probability, two sigmas is 95,4. Applying the calibration curve makes the calibrated distribution two-modal (quite unfortunately!), so they break the uncalibrated interval into two calibrated intervals (one for each mode). For example, folio 68: uncalibrated it's within one sigma (plus-minus) with 68,2% probability, and within two sigmas with 95,4% probability. However, the uncalibrated one sigma interval maps to two calibrated intervals - one is 1324-1345, the other is 1393-1422. The probability to fall into the former is 26,1%, into the latter - 42,1% (26,1+42,1 = 68,2). Same logic applies for the two-sigma interval.

That's how those results are to be read.

(16-05-2021, 06:05 PM)DONJCH Wrote: You are not allowed to view links. Register or Login to view.Note also there is an error in the section "Averaging the Results to increase Precision"
"the measurement from solvent treated Leaf #68 was excluded from this average."

In fact it was the solvent untreated sample that was excluded.

I don't think so. Would they exclude the untreated sample, the left peak of the weighted curve would have been much more manifested. They just got rid of the "inconvenient" curve which is expressly two-modal.

Another thing, I have the forms for You are not allowed to view links. Register or Login to view. and You are not allowed to view links. Register or Login to view. but the others seem to be missing, is it the same for everybody?

Same here, but the only (more or less) valuable information these forms contain is the weight of the samples and the place whence they were taken, so one does not lose much information by not having the remaining two forms.

EDIT: This information is present in the report, all the same.

(16-05-2021, 06:20 PM)Anton Wrote: You are not allowed to view links. Register or Login to view.That's how those results are to be read.

Okay, I do understand all that. I think initially we were talking about 2 different things, uncalibrated vs calibrated.

I see they do indeed quote 1 sigma for the uncalibrated, so I was wrong and you were right, but it still surprises me that the calibrated results end up with higher precision.

(16-05-2021, 06:20 PM)Anton Wrote: You are not allowed to view links. Register or Login to view.I don't think so.

Regarding the solvent treatment, they say in several places that it was necessary so I can only regard the quoted sentence as a mistake.

Under Chemical Treatment
"The results indicated that the solvent extraction was necessary, so it was adopted for all subsequent samples."

Under Accelerator Mass Spectrometry
"The two measurements of Leaf #68 indicate a younger radiocarbon age for the sample that did not undergo solvent extraction. This pattern is consistent with the accumulation of more recent carbon, perhaps from handling."

Under Averaging the results to increase precision
"Given the clustering of the dates for the four Soxhlet treated samples, and the nature of the object (a book), one can argue that in fact, a single object was measured 4 times. The mean and combined error of these four measurements was calculated using the formulae shown below. The results were 516 ± 18 radiocarbon years BP."

Soxhlet treated = solvent extracted.
If you use the solvent extracted value of 550 for f68, you get the correct mean of 516. If you use the solvent untreated value of 488, you get a mean of 499.5, which is incorrect.

Figure 6 shows the 4 samples used. f68 has the value 550 and the prominent first peak of the age distribution.

Hence I conclude that the solvent extraction was used in all cases for the 4 final samples.

(16-05-2021, 07:14 PM)DONJCH Wrote: You are not allowed to view links. Register or Login to view.but it still surprises me that the calibrated results end up with higher precision

It's not with higher precision (if we speak of individual folio results). Basically what they do they take the one-sigma interval of the uncalibrated distribution and, mapping it against the calibration curve, show what's the respective calibrated interval would be. Next, they take the two-sigma interval of the uncalibrated PDF, and, mapping it against the calibration curve, show what's the respective calibrated interval would be.

The uncalibrated PDF (and hence its parameters such as mean and sigma) has its own precision, which is determined by the precision of the experimental measurement, I'm not exactly sure which it is, but the worst figure mentioned in the report in this respect is 0,6%, which looks quite satisfactory, I guess.

(16-05-2021, 07:34 PM)DONJCH Wrote: You are not allowed to view links. Register or Login to view.Figure 6 shows the 4 samples used. f68 has the value 550 and the prominent first peak of the age distribution.

Hence I conclude that the solvent extraction was used in all cases for the 4 final samples.

Ah, my bad, I somehow thought that they averaged the calibrated results, while in fact they averaged uncalibrated results and mapped the outcome against the calibration curve.