In my last post on the various discrepancies in the origin story of the Sappho papyrus published in 2014, I mentioned an article by Dirk Obbink published in The Times Literary Supplement on 5 February 2014. In this article, Professor Obbink stated that–as a part of the process of authenticating the Sappho papyrus–a small piece of it was subjected to radiocarbon analysis. The results of this test were reported in the following form: “The owner of the papyrus wishes to remain anonymous, but has submitted the papyrus to autopsy and multi-spectral photography, as well as Carbon 14 testing of an uninscribed portion of the papyrus sheet itself by an American laboratory, that returned a date of around 201 AD, with a plus-minus range of a hundred years.” No further information was provided.

I want to scrutinize this a bit.

The first thing to note is that this 2014 article by Professor Obbink is, as far as I know, the only time the radiocarbon analysis of this papyrus has been mentioned in print. This point in itself is quite odd. No such analysis is mentioned in Professor Obbink’s scholarly edition of the papyrus. There was an entire Brill volume dedicated to the Sappho manuscript, but, unless I miss it, there is no mention of the radiocarbon dating of the papyrus in that book either [[Correction, 10 Aug. 2019–one contribution in that volume does mention the radiocarbon dating, citing Professor Obbink’s TLS article with no additional data, p. 168]]. So this short note is all we have–no report of the location from which the sample was taken, no report of the cleaning processes used (an important point since we are allegedly dealing with cartonnage), and, most irregularly, no indication of which “American laboratory” performed the analysis.

The second curious thing is the form of the reported age: “around 201 AD, with a plus-minus range of a hundred years.” This is a very odd way to report the results of radiocarbon analysis. The phrasing is ambiguous. It could be taken to mean either “201 AD +/- 100 years” (i.e. 101-301 CE) or “201 AD +/- 50 years” (i.e. 151-251 CE). Reputable labs (like the Oxford Radiocarbon Accelerator Unit, which was not used by the anonymous owner) will usually report both a more technical quantity–the average number of “radiocarbon years before present” (see below) along with the amount of “error” or “uncertainty” in the measurement–and a specific range of possible calendar dates with a statement of probability. The latter (range of calendar dates and probability) is usually what responsible popular publications report. So, for instance, The New York Times on the recently analyzed Birmingham Qur’an leaf: “tests by the Oxford Radiocarbon Accelerator Unit indicated with a probability of more than 94 percent that the parchment dated from 568 to 645.” (Notice that even popular outlets generally name the lab that did the testing.)

But the ambiguity of the reported radiocarbon date of the Sappho papyrus is not the biggest problem. The more substantive difficulty is that–on either interpretation–this reported date of “around 201 AD, with a plus-minus range of a hundred years” is unlikely to be the result of an actual radiocarbon test. The reason is that neither of those date ranges makes much sense in light of the shape of the calibration curve for that era. What this means is that, simply because of the method of analysis, it is not at all likely for any artifact (regardless of its “real” age) to be carbon dated to either of those particular stretches of time (101-301 CE or 151-251 CE). Now let me unpack that a bit.

What is the calibration curve and why is it important for radiocarbon dating? Radiocarbon analysis involves measuring the amount of the radioactive isotope carbon-14 (¹⁴C) in a deceased organic artifact and comparing it to the amount that was present when the organism died. To translate these measurements into calendar years, scientists originally established an equation based on the rate that ¹⁴C decays. When the measured amount of ¹⁴C from the sample was put into the equation, the result was a certain number of “radiocarbon years” (¹⁴C years) before present (BP). The word “present” stood for the year 1950. This equation worked on the presumption that the level of ¹⁴C in the atmosphere is constant, but we now know that this is not the case. So, to improve their translation guide, radiocarbon scientists have tested many objects of known age, usually trees, whose exact ages can be known through dendrochronology—counting the growth rings. By testing many objects with known ages, scientists are able to determine how the levels of ¹⁴C in the atmosphere have fluctuated over the centuries and create calibration curves that help them adjust the original results of their equation for better calendar accuracy. This process of establishing calibration curves is a work in progress.

Here is a representation of a current calibration curve for the first few centuries CE. The vertical axis shows ¹⁴C years BP, and the horizontal axis shows calendar dates CE:

Notice how irregularly the curve fluctuates in the period from 101 to 301 CE: first a slight rise before a steep fall in the first quarter of the second century CE, then a nearly century-long plateau between about 130 CE and 220 CE, then another steep fall past 250 CE and then finally a notable rise into the fourth century. What this fluctuation means is that neither of the possible interpretations of the date provided by Professor Obbink “works.” If we run simulations using numbers of ¹⁴C years BP that would yield a calibrated date with a median roughly in the neighborhood of the year 201 CE, we can see the problems more clearly.

The longer range (101-301 CE) doesn’t seem consistent with the results of radiocarbon analysis because any result that includes dates in the second half of the third century will also include dates in the first part of the fourth century, reflecting the dip and rise in the calibration curve in that era. Similarly, if we try to isolate the narrower range (151-251 CE) by using an unrealistically low number of 10 for uncertainty, it is still not possible to exclude some dates before 151 CE because of the plateau in the calibration curve:

I tinkered with both the number of radiocarbon years and the amount of uncertainty (and tried earlier versions of the calibration curve), but none of my simulations produced Professor Obbink’s numbers, and it’s hard to see how any analysis would ever yield a range that could properly be reported as either “101-301 CE” or “151-251 CE.” It just doesn’t work given the atmospheric history of ¹⁴C reflected in the shape of the calibration curve.

If there is an available technical report from a lab that produced these results, I would be very curious to see it, because absent any further explanation, the numbers that Professor Obbink provided seem quite problematic. While radiocarbon dating alone can’t do the work of authenticating an ancient manuscript, the results can nevertheless provide important information for historians. Such results should thus be reported fully and accurately.