The Myth of Nag Hammadi's Carbon Dating

[Leucius Charinus]

...

I think my own suggestion (of graphing the earliest extant manuscript), while different and somewhat more difficult to solve, is (also) relevant (arguably even more relevant), in terms of the eventual use in which it is pressed upon to provide guiding information (the latest possible date [terminus ad quem] that we can assign for the start of the production of any and all such mss. [the 'birth' of 'Gnostic' 'codex' 'technology'], as such is set by the earliest such extant dated mss.), so I might also make a graph plotting something like that too. Of course that's a completely different thing.

Yes of course, seeing that the origin of this ['Gnostic' 'codex' 'technology'] is probably the more important thing. FWIW I see the graph of the calibrated C14 tests on the Tchacos Codex to be the closest reflection of the distribution curve being sought here. You have already generated a few of these above, based on Krosley's data (of which I was unaware; I used Peter Head's data, which used part of Krosley's).

When the (final) UA test results are obtained, and Krosley's error in reporting fragment #4 is clarified, and when the more appropriate selection of which of these test results are to be used to calculate this terminus ad quem (probably the three papyri that Head reports as 279, 279 and 333 CE) then a final calibration graph can be prepared. It will be this graph (IMO) which will best refect what you, and I, are seeking here.

Of course I'd also say the same about the other side of the question of such phenomena; if we wanted the earliest possible date [terminus a quo] for the demise of such things, based on the extant mss., we'd need to work starting from the graph of the probable date of the latest-dated extant ms.

Agreed. I just jumped the gun in (erroneously) thinking we have more than one "Coptic Codex" with a C14 result. I would obviously like to see more C14 tests - also on the earliest Greek NT Bible codices, but I am not holding my breath on this.



LC

[Peter Kirby]

IT HAS NOT BEEN DONE BEFORE AFAIK.

I promise to get it done (whether it's been done before or not, IDK), and get back to you on that.

I don't think it's a very difficult problem, TBH. I think you'll see why it is not very complex when you see the actual representation(s).

Okay I don't think this graph is super-relevant to the larger context (as I've said), but I promised to create it.

The only thing that this graph says is "hey, given that I know N normal probability distributions [which are the multiple extant manuscripts], say that I pick a random one from among the N distributions, with equal odds of each, ... what's the graph showing the likelihood of picking x [the year] after first selecting a distribution randomly and then randomly arriving at x within the distribution?" (more or less, lol)

This is one way of combining the information regarding all the extant manuscripts, without assuming that they fit a single particular curve (not assuming that there is just one independent random variable behind all the data).


I used GeoGebra. (and, yes, let the jokes begin....)
f(x) = Normal[280,30,x]
g(x) = Normal[350,30,x]
h(x) = ( f(x) + g(x) ) / 2

This has two normal distributions, both with standard deviations of 30, with medians 280 and 350 respectively. The combined distribution is in pink, and it is (as you can see) not a normal (Gaussian) distribution. The sum of the area under each one of these curves is 1.

This is also sometimes called "mixture of Gaussians" (i.e., a mixture of normal distributions). Usually the problem is being worked in reverse, trying to find one or more curves that can "fit" the data, which shows two or more "humps." If we worked this one in reverse, we would go from doing the blind sampling (not knowing which of the two codices we were pulling sampled dates from) and to the individual probability distributions of each of the two codices.

[Peter Kirby]

I think my own suggestion (of graphing the earliest extant manuscript), while different and somewhat more difficult to solve, is (also) relevant (arguably even more relevant), in terms of the eventual use in which it is pressed upon to provide guiding information (the latest possible date [terminus ad quem] that we can assign for the start of the production of any and all such mss. [the 'birth' of 'Gnostic' 'codex' 'technology'], as such is set by the earliest such extant dated mss.), so I might also make a graph plotting something like that too. Of course that's a completely different thing.

Yes of course, seeing that the origin of this ['Gnostic' 'codex' 'technology'] is probably the more important thing.

The problem may be a bit complicated, but having a nice graphing package to take care of the messy math makes it easier.

Here is the relevant graph:

This graph has two different scales. The scale for the probability density functions ("PDF") has been blown up 40x on the y-axis, so that we can see what's going on, while the scale for the cumulative distribution functions ("CDF") is simply from 0 to 1.



f(x) = Normal[280, 30, x, true]
f'(x) = Normal[280, 30, x]
g(x) = Normal[350, 30, x, true]
g'(x) = Normal[280, 30, x]

All of these functions are in black. The functions f and g are cumulative distribution functions. They're telling us "the probability that the manuscript is dated earlier than this year." Because of the "earlier than" part, their graphs go up and to the right, approaching 1. The functions f' and g' are normal distributions with medians of 280 and 350, respectively, and a standard deviation of 30. They're also the first derivatives of f and g, because calculus.

Now, if we reason a little bit logically here, using our knowledge of probability, what can we say? Well, instead of attacking the problem head-on, I think we should attack the cumulative distribution function of what we want first. We should be looking at "the probability that the earliest manuscript is dated earlier than this year," because it's easier to reason about that. This value h(x) is going to be at least f(x). That's just a baseline.

But there's also a chance that the "g" manuscript came first. So we have to add this in. The way we do this is by multiplying g(x)--which is the probability that the manuscript "g" dates earlier than the year x--by the probability ( 1 - f(x) ), which is the probability that the manuscript "f" is dated x or later than x (because this is the complement of f, which is the probability that it is earlier).

This gives us the cumulative distribution function ("CDF") for the earlier of the two manuscript's dating:

h(x) = f(x) + (1 - f(x)) g(x)

This curve is represented in purple above and, as you notice, is ever so slightly to the left of "f."

And from this we know the probability density function ("PDF") of the same, which is the first derivative, because calculus.

h'(x) = Derivative[ h(x) ]

This curve is represented in pink above and, as you notice, breaks away from f for some of the earlier dates, then becomes less likely than f later.

Incidentally, you can add as many starting curves as you'd like. Here I've added a third, p, midway between the other two, at 315.

p(x) = Normal[315,30,x,true]
p'(x) = Normal[315,30,x]



To get the orange cumulative distribution function ("CDF"), we do like we did before, just with more terms:

q(x) = f(x) + (1 - f(x)) g(x) + (1 - f(x)) (1 - g(x)) p(x)

Then we get the derivative, q'(x).

Roughly speaking, this one had a much more pronounced effect on the probable date of the earliest manuscript than the one centered on 350 did.

BTW, If you're curious, the results are the same, no matter which order you do the calculations in (which one you put first, like f here, etc.).

Thank you for the opportunity to learn some interesting math.

[Leucius Charinus]

The only thing that this graph says is "hey, given that I know N normal probability distributions [which are the multiple extant manuscripts], say that I pick a random one from among the N distributions, with equal odds of each, ... what's the graph showing the likelihood of picking x [the year] after first selecting a distribution randomly and then randomly arriving at x within the distribution?" (more or less, lol)

This is one way of combining the information regarding all the extant manuscripts, without assuming that they fit a single particular curve (not assuming that there is just one independent random variable behind all the data).


I used GeoGebra. (and, yes, let the jokes begin....)
f(x) = Normal[280,30,x]
g(x) = Normal[350,30,x]
h(x) = ( f(x) + g(x) ) / 2

This has two normal distributions, both with standard deviations of 30, with medians 280 and 350 respectively. The combined distribution is in pink, and it is (as you can see) not a normal (Gaussian) distribution. The sum of the area under each one of these curves is 1.

Thanks for this. It is an interesting alternative.

Paraphrasing what you wrote above ... This is one way of combining the information regarding all the extant manuscripts .... assuming that there is not just one independent random variable behind all the data.

I think there that a reasonable case can be made to make the assumption of one such variable, by suitably defining that variable. Originally the definition was the "manufacturing of Gnostic [or non canonical] Coptic codices" in antiquity. I don't really see a problem with the principle of focussing on such a manufacturing operation in antiquity, when the dates of manufacture for various codices are provided by a C14 test.

If one were able to assume some independent random variable behind all the data, how would that effect the curve?

This is also sometimes called "mixture of Gaussians" (i.e., a mixture of normal distributions). Usually the problem is being worked in reverse, trying to find one or more curves that can "fit" the data, which shows two or more "humps." If we worked this one in reverse, we would go from doing the blind sampling (not knowing which of the two codices we were pulling sampled dates from) and to the individual probability distributions of each of the two codices.

Thanks for all this stuff PK.



LC

[Leucius Charinus]

I think my own suggestion (of graphing the earliest extant manuscript), while different and somewhat more difficult to solve, is (also) relevant (arguably even more relevant), in terms of the eventual use in which it is pressed upon to provide guiding information (the latest possible date [terminus ad quem] that we can assign for the start of the production of any and all such mss. [the 'birth' of 'Gnostic' 'codex' 'technology'], as such is set by the earliest such extant dated mss.), so I might also make a graph plotting something like that too. Of course that's a completely different thing.

Yes of course, seeing that the origin of this ['Gnostic' 'codex' 'technology'] is probably the more important thing.

The problem may be a bit complicated, but having a nice graphing package to take care of the messy math makes it easier.

Here is the relevant graph:

This graph has two different scales. The scale for the probability density functions ("PDF") has been blown up 40x on the y-axis, so that we can see what's going on, while the scale for the cumulative distribution functions ("CDF") is simply from 0 to 1.



f(x) = Normal[280, 30, x, true]
f'(x) = Normal[280, 30, x]
g(x) = Normal[350, 30, x, true]
g'(x) = Normal[280, 30, x]

All of these functions are in black. The functions f and g are cumulative distribution functions. They're telling us "the probability that the manuscript is dated earlier than this year." Because of the "earlier than" part, their graphs go up and to the right, approaching 1. The functions f' and g' are normal distributions with medians of 280 and 350, respectively, and a standard deviation of 30. They're also the first derivatives of f and g, because calculus.

Now, if we reason a little bit logically here, using our knowledge of probability, what can we say? Well, instead of attacking the problem head-on, I think we should attack the cumulative distribution function of what we want first. We should be looking at "the probability that the earliest manuscript is dated earlier than this year," because it's easier to reason about that. This value h(x) is going to be at least f(x). That's just a baseline.

But there's also a chance that the "g" manuscript came first. So we have to add this in. The way we do this is by multiplying g(x)--which is the probability that the manuscript "g" dates earlier than the year x--by the probability ( 1 - f(x) ), which is the probability that the manuscript "f" is dated x or later than x (because this is the complement of f, which is the probability that it is earlier).

This gives us the cumulative distribution function ("CDF") for the earlier of the two manuscript's dating:

h(x) = f(x) + (1 - f(x)) g(x)

This curve is represented in purple above and, as you notice, is ever so slightly to the left of "f."

That makes sense. The later MS is contributing its "possible earliness" to the early MS, but its not much.

And from this we know the probability density function ("PDF") of the same, which is the first derivative, because calculus.

h'(x) = Derivative[ h(x) ]

This curve is represented in pink above and, as you notice, breaks away from f for some of the earlier dates, then becomes less likely than f later.

Again not too much variation from the earliest curve.

Incidentally, you can add as many starting curves as you'd like. Here I've added a third, p, midway between the other two, at 315.

p(x) = Normal[315,30,x,true]
p'(x) = Normal[315,30,x]



To get the orange cumulative distribution function ("CDF"), we do like we did before, just with more terms:

q(x) = f(x) + (1 - f(x)) g(x) + (1 - f(x)) (1 - g(x)) p(x)

Then we get the derivative, q'(x).

Roughly speaking, this one had a much more pronounced effect on the probable date of the earliest manuscript than the one centered on 350 did.

Probably because it is closer and its contributions are more pronounced.

BTW, If you're curious, the results are the same, no matter which order you do the calculations in (which one you put first, like f here, etc.).

Yes I can understand that. All very interesting analysis.

Thank you for the opportunity to learn some interesting math. :thumbup:

Likewise !

It occurs to me that these C14 results obviously and immediately lend themselves to graphical analysis. And that there may indeed be a time when there will be multiple C14 test results available on these Coptic [non canonical] codices.

A C14 test on the NHL would be a good thing. It would be of benefit to see how C14 dating this codex compares to the present conclusion of other dating methodologies.

Another import factor not often quantified, is the "shelf-life" of the papyrus upon which the scribe wrote.

How long was the period between harvest and end of preparation to the day the scribe started using it? There would be a minimum period representative of the curing and preparation processes. IDK exactly what this time is. Maybe six months????

There would be a "Shelf-life" time in which the papyrus would be in storage ready to be used.

Whatever these figures are, they will need to be added to the Radiocarbon age result.



LC

[Peter Kirby]

If one were able to assume some independent random variable behind all the data, how would that effect the curve?

Well, keep in mind that the original graph wasn't assuming anything really ... it was just representing the data as we already have it. It was assuming a random sampling of N manuscripts/codices with equal weights (not giving more weight to one extant ms. or another), but that's about it.

If we try to fit it to a curve representing the function of a single independent random variable, we are making an additional assumption. One possibility (as an assumption) is a normal distribution for the probable date range of extant mss. discovered. Keep in mind that we are still making the previous assumption also (that the extant mss. that we have are a random sampling of all the possible mss. that could be extant).

When you add together normal distributions, their standard deviations are related to each other by this equation:

σ_h2 = σ_f2 + σ_g2

The square of the standard deviation is called variance; this is saying that the sum of the variances of the two original normal distributions is equal to the variance of the normal distribution that is their sum. Figuring out the mean is basically exactly what you would expect:

μ_h = ( μ_f + μ_g ) / 2

Since we aren't just adding together two normal distributions but rather finding a mean of the two, we divide the sum of the two original μ by two.

Doing the arithmetic:

h(x) = Normal[ 315, 42.4264, x ]



And, overlaid on the original pink curve ( f(x) + g(x) ) / 2.

[Peter Kirby]

I've now done the math behind dating the binding of Codex VII, more exactly.

http://peterkirby.com/beyond-the-terminus-a-quo.html

Which gives us these charts:

[Leucius Charinus]

You are being disingenuous (again); stop that.

Read my response to the OP at post #3. There is zero disingenuity in this response.

However for those who may be interested, the myth of Nag Hammadi's Carbon dating actually ended in November/December 2014 at which time two samples from Nag Hammadi Codex I underwent C14 dating.

The following from pp.117-142

TEXTS IN CONTEXT ESSAYS ON DATING AND CONTEXTUALISING CHRISTIAN WRITINGS FROM THE SECOND AND EARLY THIRD CENTURIES
EDITED BY JOSEPH VERHEYDEN – JENS SCHRÖTER – TOBIAS NICKLAS PEETERS
LEUVEN – PARIS – BRISTOL, CT
2021

DATING AND CONTEXTUALISING THE NAG HAMMADI CODICES AND THEIR TEXTS, A MULTI-METHODOLOGICAL APPROACH INCLUDING NEW RADIOCARBON EVIDENCE
H. LUNDHAUG


In collaboration with the DFG-ANR-project Coranica at the Berlin-Brandenburgische Akademie der Wissenschaften29 the ERCproject NEWCONT at the University of Oslo dated three samples from the Schøyen Collection, among them two from the cover of Nag Hammadi Codex I [30].

The owner, Martin Schøyen, generously agreed to donate a small piece of the sheepskin [31] cover as well as one small fragment of papyrus from its cartonnage for analysis. Schøyen himself cut a piece of the leather cover (Figure 1), and selected an uninscribed papyrus fragment from the cartonnage (Figure 2). The samples were then brought to the laboratory at the ETH in Zürich, where the amount of 14C in the samples were measured using accelerator mass spectrometry [32].

///

We see that this result is compatible with a calendar date for the cover of Nag Hammadi Codex I between 241 and 387 CE with a probability of 99.7% [41]

///

The laboratory test result of the papyrus fragment from the cartonnage of the cover of Codex I was a 14C BP age of 1796±2742, the greater uncertainty being caused by the fact that the fragment was too small to accommodate more than one test run. The calibrated result, with the 24±5 BP offset applied, is shown in Figure 8. This very long calendar date range of 132-381 CE (99.7%)43 is unfortunately not very helpful in determining the number of years between the production of the papyrus fragment and its re-use as cartonnage.

Footnotes:

30. The third sample was taken from Schøyen MS 193, commonly known as the Crosby-Schøyen Codex. For the results and details of the dating of this sample, see H. LUNDHAUG, The Date of MS 193 in the Schøyen Collection: New Radiocarbon Evidence, in Bulletin of the American Society of Papyrologists 57 (2020) 219-234.

31. ROBINSON, Construction of the Nag Hammadi Codices (n. 17), p. 172.

32. I visited the Schøyen Collection together with Lance Jenott on 9 April, 2014, when the samples were taken. I then took the samples to Berlin, from where they were taken to the lab at ETH in Zürich by Tobias J. Jocham of the Coranica project. The first test run was conducted in November 2014 and the second and third runs in December 2014.

41. Due to the remaining uncertainties with regard to the historical levels of atmospheric 14C in this region I prefer to use the full 3σ probability range. The 1σ and 2σ probability ranges are as follows: 1σ: 256-299 CE (45.9%), 318-340 CE (22.3%); 2σ: 249-357 CE (90.5%), 366-380 CE (2.1%).

https://www.academia.edu/50918807/Datin ... ence_2021_

[Leucius Charinus]

In scholarship, there are some things that are known to be true, some things that are known to be false, some things that are simply unknown (whether true or false), and some matters of opinion and speculation that are keenly debated. But there are also things that are known to be false that are often taken as true, and of such things it is said: "If you repeat a lie often enough, people will believe it, and you will even come to believe it yourself."

One of these urban legends is the idea that the texts or the cartonnage of the Nag Hammadi Library have been examined with C-14 radiometric dating.

http://peterkirby.com/nag-hammadi-carbo ... -myth.html

I don't think you're going to like this essay very much, Pete...

As it turns out there were in fact C14 radiometric dating results from the physical material in the Nag Hammadi Library (as indicated above). The Myth of Nag Hammadi's Carbon Dating is itself a myth.

Do you intend to update your essay to reflect this fact?

DATING AND CONTEXTUALISING THE NAG HAMMADI CODICES AND THEIR TEXTS

III. CONCLUSION

Each text in the Nag Hammadi Codices has a number of possible contexts of interpretation, and we need to choose whether to read them in their hypothetical contexts of authorship, with all the problems that entails in terms of textual fluidity, or we may read them as texts in use, in the form in which they have been preserved to us, thus shedding light on the context in which the manuscripts were produced. Analyses of their cartonnage and colophons indicate that the Nag Hammadi Codices were produced and used by monastics in the fourth and fifth centuries. Radio carbon dating of the leather cover of Nag Hammadi Codex I is compatible with these indications when interpreted in light of Codex I’s scribal connections with Codices XI and VII, the latter of which contains the only certain terminus post quem of any Nag Hammadi Codex. Radio carbon dating does not, and cannot, provide us with a silver bullet for manuscript dating, but it does provide us with valuable added data that can fruitfully be used in conjunction with other dating methods. Radiocarbon dating of samples from the other Nag Hammadi Codices could no doubt contribute valuable additional evidence that may prove especially valuable with regard to those Nag Hammadi Codices that are not connected by scribal overlap to either Codices I or VII, for which our main evidence for their date of production is currently their association and general similarity with Codices I, VII, and XI.

University of Oslo Hugo LUNDHAUG
Faculty of Theology
Postboks 1023 Blindern
NO-0315 Oslo
Norway

https://www.academia.edu/50918807/Datin ... ence_2021_

[Peter Kirby]

In scholarship, there are some things that are known to be true, some things that are known to be false, some things that are simply unknown (whether true or false), and some matters of opinion and speculation that are keenly debated. But there are also things that are known to be false that are often taken as true, and of such things it is said: "If you repeat a lie often enough, people will believe it, and you will even come to believe it yourself."

One of these urban legends is the idea that the texts or the cartonnage of the Nag Hammadi Library have been examined with C-14 radiometric dating.

http://peterkirby.com/nag-hammadi-carbo ... -myth.html

I don't think you're going to like this essay very much, Pete...

As it turns out there were in fact C14 radiometric dating results from the physical material in the Nag Hammadi Library (as indicated above).

You're quoting something from 2015. At that time, there weren't.

Do you intend to update your essay to reflect this fact?

Yeah, but it doesn't really change the point made by the essay when it was written.