The Myth of Nag Hammadi's Carbon Dating

[Peter Kirby]

A third analytical curve is shown which represents both curves, on the basis that both results are in respect of the one category of test material - ie: "Gnostic Coptic codices".

I agree that the third curve represents the assumption that both original curves are describing the same 'category', in a sense (and I said as much at the end of the previous post: the very same graph would be produced to show the probable date of Thomas/Judas assuming they were both made in the same year). But that's not exactly what you want in this context, when you are interested in (a) the total extent of probable dates of any and all 'Gnostic' 'codex' 'technology', i.e. the range in which a 'Gnostic' codex might have fallen, given that we only know it is a 'Gnostic' codex, or - and this is even more germane - (b) the earliest extant example of the 'Gnostic' 'codex' 'technology'. This graph gives you neither of those things.

It takes only a child to realize that the graph of 'Gnostic' 'codex' 'technology' should not be excluding the range before the 'Thomas' dating, where the 'Judas' dating is presenting a probability of a codex before the earliest possible 'Thomas' dating.

I'd suggest looking at it with fresh eyes.

[Leucius Charinus]

A third analytical curve is shown which represents both curves, on the basis that both results are in respect of the one category of test material - ie: "Gnostic Coptic codices".

I agree that the third curve represents the assumption that both original curves are describing the same 'category', in a sense (and I said as much at the end of the previous post: the very same graph would be produced to show the probable date of Thomas/Judas assuming they were both made in the same year). But that's not exactly what you want in this context, when you are interested in (a) the total extent of probable dates of any and all 'Gnostic' 'codex' 'technology', i.e. the range in which a 'Gnostic' codex might have fallen, given that we only know it is a 'Gnostic' codex, or - and this is even more germane - (b) the earliest extant example of the 'Gnostic' 'codex' 'technology'. This graph gives you neither of those things.

Agreed. See below.

In the graphical presentation both of the two separate C14 results are displayed together with their respective median peaks and error bounds. A third analytical curve is shown which represents both curves, on the basis that both results are in respect of the one category of test material - ie: "Gnostic Coptic codices".

I think everyone understood that. As Peter said, that's a logically meaningless operation. If both of those manuscripts belong into the same category, the borders of the earlier manuscript alone determine the terminus post quem for the category. The existence of the other manuscript is meaningless for determining the earliest possible date of the category.

OK. I can see one area of misunderstanding here. I am certainly not claiming that this "combined curve" has anything to do with an "earliest possible date" for any one manuscript. My claim relates to the evidence that we have for the chronology of the entire epoch (whether that be 50 years or 500 years) during which people physically manufactured Coptic "gnostic related" codices. It seeks the median point of this entire epoch and uses the probability density results of the C14 tests (NB: unfortunately we don't have two tests atm, hence this OP) to graph a probability for the midpoint of the epoch. This is not an "earliest possible date" exercise.

If it were an "earliest possible date exercise" it would indeed be a logically meaningless operation. But it's not this. That's why I mentioned the Bunyip Bones. Such a curve on the dates of Bunyip bones provides an estimate of the peak of (or midpoint for) the entire epoch during which Bunyips existed and lived on planet earth.

It tries to provide an estimate to the question .... "When did the manufacture of gnostic (Coptic) codices PEAK in antiquity" (When did the Bunyips thrive in the past given two C14 dates for two bone samples).


Criticism of the "midpoint and normal probability range employed" for the entire EPOCH OF Coptic Gnostic Codices.

The model could be criticised using the "normal" midpoint and range. I guess I have assumed that the probability distribution for the manufacture of such codices (and for Bunyip bones) follows a normal distribution. That is, it starts small reaches a peak and then slowly declines in a similar fashion as it increased.

This is probably entirely wrong on the basis that we are probably looking at a model involving EXTINCTION EVENTS. The manufacture of Coptic codices containing translations of Greek non canonical texts became extinct, it did not just die off naturally. As such the distribution may have reached a peak much later and much closer to the end of the epoch rather than its midpoint. With the analogy of Bunyip bones, the normal curve does not reflect the (real) possibility that bunyips thrived until well after the "normal" midpoint of the epoch, perhaps right up until the very last date of the evidence, but then became extinct suddenly.




LC

[Peter Kirby]

My claim relates to the evidence that we have for the chronology of the entire epoch (whether that be 50 years or 500 years) during which people physically manufactured Coptic "gnostic related" codices. It seeks the median point of this entire epoch and uses the probability density results of the C14 tests (NB: unfortunately we don't have two tests atm, hence this OP) to graph a probability for the midpoint of the epoch.

The median point is actually correct, but that's pretty much the only thing that is.

The chart's resultant curve should be wider, for what you are describing.

Your chart's third curve includes the date ranges ONLY where BOTH the 'Judas' AND the 'Thomas' codices could have been written.

Your chart's third curve should include, if you want it to represent what you want, ALL the area where EITHER the 'Judas' OR the 'Thomas' codices could have been written.

But, yes, the midpoint is correct.

The graph's third curve itself, though, as I've said before, is too narrow. And it does represent a reality, but it's not the reality that you want to represent. A reality that it does represent is the curve of the probable dates of Thomas/Judas assuming that they have the same date (and, of course, assuming that the two initial curves are correct). That's why it cuts off completely (and prematurely) when either codex doesn't have area under its curve.

I understand that you aren't trying to get the earliest extant codex's graph--that's what I'm saying you should be going for, but I understand that you aren't going for it. But I am saying that you're not even graphing the thing that you are going for, which is the range of dates in which extant 'Gnostic' codices were manufactured, including the most probable years and less probable years for said manufacture.

[Leucius Charinus]

My claim relates to the evidence that we have for the chronology of the entire epoch (whether that be 50 years or 500 years) during which people physically manufactured Coptic "gnostic related" codices. It seeks the median point of this entire epoch and uses the probability density results of the C14 tests (NB: unfortunately we don't have two tests atm, hence this OP) to graph a probability for the midpoint of the epoch.

The median point is actually correct, but that's pretty much the only thing that is.

The chart's resultant curve should be wider, for what you are describing.

Your chart's third curve includes the date ranges ONLY where BOTH the 'Judas' AND the 'Thomas' codices could have been written.

Your chart's third curve should include, if you want it to represent what you want, ALL the area where EITHER the 'Judas' OR the 'Thomas' codices could have been written.

The first and second curves are the symmetric radiocarbon age curves and the vertical axes (not shown) are (AFAIK) the output of the radiocarbon age estimate and (AFAIK) represent a probability density. The axis of the third curve shown on the graph is probability. The contributing probability densities are not added they are multiplied, and hence fall away rapidly when either contributory curve has very small probability density.

From 2010 - Questions about C14 dating, Bell Curves and averaging two independent C14 results ... http://talkrational.org/showthread.php?t=32683

To be useful the graph requires more than one, and more than two, C14 results. The more the merrier. The above graph uses 2 (in error LOL) but if we have available to us say 7 C14 tests on Coptic Gnostic codices, then the 3rd curve would be more informative - but will always remain just a probability distribution. I guess it was just designed to visually display the chronology of all the evidence (of Coptic codex manufacture) as a probability graph in time, based on the radiocarbon age.

The idea was then to run the calibration software on this (composite, derived) curve (of 2,3,4 or 100 tests), which of course will advance the dates well into the 4th century. The graph was thus intended to serve as a discussion on the bounds of the epoch in antiquity within which the manufacture of (non canonical) Coptic codices was in "full swing".




LC

[Peter Kirby]

Are you sure you completely understand all that you are saying?

And do you understand what I've been saying in reply?

I can create a proper graph later, concerning what you are interested in, if you would have any interest.

Perhaps another dialectical exercise will show why the original graph's third curve is misguided/irrelevant.

Suppose we have 2 initial curves with 4sigma (practically almost 100%) intervals of 250 to 450 and of 500 to 700 respectively.

Your multiplication would leave no area under the resultant curve, or it would take miniscule overlap around 475 and represent that as the highest point on the curve when in fact it should be low since it is outside both initial curves with over 99.9% confidence.

Do you see?

Someone misguided you if someone said that this was the appropriate math for what you want.

[Leucius Charinus]

Are you sure you completely understand all that you are saying?

Not 100%. It's been well over 40 years since I did university level statistical mathematics.

And do you understand what I've been saying in reply?

Kind of. I can see you have a point about what to do with the outlying results.
You make this clear in the exercise below.

I can create a proper graph later, concerning what you are interested in, if you would have any interest.

OK. Sure I am interested. The whole thing was the ability to depict not just one, but a series of C14 results (obviously for the same category of evidence)

Perhaps another dialectical exercise will show why the original graph's third curve is misguided/irrelevant.

Suppose we have 2 initial curves with 4sigma (practically almost 100%) intervals of 250 to 450 and of 500 to 700 respectively.

Your multiplication would leave no area under the resultant curve, or it would take miniscule overlap around 475 and represent that as the highest point on the curve when in fact it should be low since it is outside both initial curves with over 99.9% confidence.

Do you see?

Well your example makes it pretty clear there is a problem when the distributions are as disjoint as that.

While this is a valid comment, I kind of expected that the range of all the distributions would not be disjoint. (Because of the nature of the Age curve)

NB: Your example = 2 initial curves with 4sigma. But is this the sigma of radiocarbon age curve?

Someone misguided you if someone said that this was the appropriate math for what you want.

It is more likely that my input specifications were inappropriate for the someone who prepared the graph.
Here is the posts with the specifications used in the graph.

You can see from this that the 3rd curve reflects the probability that both documents were produced in a 20 years span centered on that date.
The 20 years looks a bit arbitrary.

http://talkrational.org/showpost.php?p= ... stcount=82

OK, I made a graph of this. Here it is. The blue and red curves are normal distributions centered on the dates you gave, with standard deviation 60 years. The value of the brown curve at a given date is the probability that both documents were produced in a 20 years span centered on that date. For example, at 300 it's .013, which means there's a 1.3% change that both documents were produced in the period 290-310.

Please be aware that the units of the brown curve (probability) are NOT the same as the units of the blue and red curves (probability density). Really they shouldn't be plotted on the same graph. If you integrate the blue and red curves over some date range you get the probability that document was produced in that range. If you integrate the brown curve, you get crap (it's already integrated).

You could pick something other than a 20 year interval. If you pick a very short interval the brown curve has more or less the same shape, but its amplitude (peak value) gets very small. If you pick a large range the peak value goes close to 1 and it becomes very broad (nearly just a straight line at 1). If you think about it you can see why.

Instead you might want to see a plot of the probability that both documents were produced within some time of the midpoint between 290 and 348 (in other words a plot of the peak value of the brown curve as a function of the range). I can make that one too if you ask nicely. I expect it will be 70% when the range is about 200 years, 90% if it's 300.

So there may be a better and more natural way to graphically present a probability curve for multiple C14 dates. IT HAS NOT BEEN DONE BEFORE AFAIK. That does not mean that the principle behind it is illogical or invalid. Quite obviously the test material must be of the same category in order to make a valid comparison.

It may even be preferable to use as input data the results of the calibrated date range. The whole point of the exercise was to derive some sort of [valid] probability curve that combines the results of n C14 tests results (where n>1). The idea is that one [valid] picture is worth a thousand words. The focus here was on the manufacture of Coptic codices in antiquity.

So of course I would be interested to explore this further. In time. And also of course, to better understand the specifications of how to "combine" two (or more) C14 distributions (either prior to or after calibration). Whether such a specification is valid, and what may be interpreted from it. etc.



LC

[Peter Kirby]

NB: Your example = 2 initial curves with 4sigma. But is this the sigma of radiocarbon age curve?

Radiocarbon age = Radiocarbon years = conventional radiocarbon age = RCYBP

And it also is basically equivalent to the C-14 content ratio, although different units are used.

This kind of expression is always expressed as a 1-sigma interval (a normal distribution with mention of the median and of the length of one standard deviation). That's just part of the definition of the conventions of such expressions.

...

However, you can use whatever confidence level you want (whatever percentage amount you want, which amount falls inside a particular date range, of the total area under the curve), when talking about calibrated calendrical date ranges.

Most typically we are interested in the 1-sigma (68%) and the 2-sigma (95%) intervals of the calibrated date ranges.

But nothing stops us from calculating a 3-sigma (99.7% of the area under the curve) interval.

Or indeed a 4-sigma (99.997% of the area under the curve) interval.

The more area under the curve, the longer the interval (range of dates). Generally speaking, higher confidence involves larger date ranges (when speaking of the same curve, naturally ... not when comparing two different curves, because one might be really "tight" and the other extremely "wide").

[perseusomega9]

I have to ask, what's the deal with the bird?

[Peter Kirby]

All emphasis below mine.

It is more likely that my input specifications were inappropriate for the someone who prepared the graph.
Here is the posts with the specifications used in the graph.

You can see from this that the 3rd curve reflects the probability that both documents were produced in a 20 years span centered on that date.
The 20 years looks a bit arbitrary.

http://talkrational.org/showpost.php?p= ... stcount=82

OK, I made a graph of this. Here it is. The blue and red curves are normal distributions centered on the dates you gave, with standard deviation 60 years. The value of the brown curve at a given date is the probability that both documents were produced in a 20 years span centered on that date. For example, at 300 it's .013, which means there's a 1.3% change that both documents were produced in the period 290-310.

Please be aware that the units of the brown curve (probability) are NOT the same as the units of the blue and red curves (probability density). Really they shouldn't be plotted on the same graph. If you integrate the blue and red curves over some date range you get the probability that document was produced in that range. If you integrate the brown curve, you get crap (it's already integrated).

You could pick something other than a 20 year interval. If you pick a very short interval the brown curve has more or less the same shape, but its amplitude (peak value) gets very small. If you pick a large range the peak value goes close to 1 and it becomes very broad (nearly just a straight line at 1). If you think about it you can see why.

Instead you might want to see a plot of the probability that both documents were produced within some time of the midpoint between 290 and 348 (in other words a plot of the peak value of the brown curve as a function of the range). I can make that one too if you ask nicely. I expect it will be 70% when the range is about 200 years, 90% if it's 300.

With the slight difference that I did not detect that this graph represented a 20-year [+/- 10 year] range of the conjunction of the dates of 'Thomas'/'Judas' (instead of just 1 as I guessed from the visual), I don't think I am out of line to say that I appear to have been spot-on in my assessment of the kind of thing represented by the third curve.

What your graph does show (whether it was meant to or not) is what the likely date is for both Tchacos and NHL (given their starting curves), assuming that they were made in the same year.

I agree that the third curve represents the assumption that both original curves are describing the same 'category', in a sense (and I said as much at the end of the previous post: the very same graph would be produced to show the probable date of Thomas/Judas assuming they were both made in the same year).

Your chart's third curve includes the date ranges ONLY where BOTH the 'Judas' AND the 'Thomas' codices could have been written. ..... A reality that it does represent is the curve of the probable dates of Thomas/Judas assuming that they have the same date (and, of course, assuming that the two initial curves are correct).

Sorry if this is a little obnoxious.

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).

...

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.

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.

[Leucius Charinus]

I have to ask, what's the deal with the bird?

https://www.youtube.com/watch?v=S0ZbykXlg6Q

It's an Australian kingfisher which "laughs" and as such appeals to my own sense of humour.

FWIW I have found that a sense of humour is absolutely essential element in the exploration of church dogma and in the ultra-serious field of BC&H.





LC