spamandham

The peak is the most likely date. The problem is, it is still very unlikely. You make it sound like there's a high probability that's that date. But it isn't. The probability it is that date is small, albeit a larger small than any other given date. The proper way to use such charts is to compute the probability of the actual date falling between X and Y. It's difficult to tell what the probability that it falls on the peak date is, but eyeballing it, it looks to be less than 5%.

Yes it is. This is an ordinary probability density function normalized so that the peak is 1.0. That's what 'relative probability' is all about. Notice the legend, where it shows you the probability of the date falling within a given range? That's how the chart is intended to be used - to determine the probability of the date falling within some range. Notice that the legend shows the probability of the date being within the range 903 to 892 BCS as a mere 13.4%. The peak date is shown as 1.0. By your interpretation, there would be a 100% probability of that date. Surely you can see that isn't right.

-Jay-

No, it means that of the very small probabilities for any individual year, the year corresponding to the tallest peak has a greater, but still very small, probability than the others. However, it does not mean that that particular year has anything near a 100% probability. The "relative probability" is just a normalization to make the graph more tractable. All of the graphs shown in the original source (here) do the same thing.

Of course it's about densities. The chart represents the outputs of a Bayesian model. Bayesian models are used to determine probability distributions. Probability density functions express probability distributions in terms of integrals.

You mean 0.95 relative probability, but your mistake is in interpretting that relative probability as an absolute probability.

Repeating it won't make it true...

Others already have. For example here, or here, or here. However, possibly the most informative thing is to look at the 1-sigma and 2-sigma confidence intervals. The 2-sigma, for example, means "I have 95.4% confidence that the true value of this sample is between 918 and 823 BCE."

No, it doesn't mean nothing. It means that the high peak at 871 BCE is a little bit more probable than other dates, but certainly nowhere near 99.5% probable. You're treating it as a near-certainty, when it is no such thing. One more time - relative probability is not the same as absolute probability.

The chart represents the output of a Bayesian model developed by the authors. The model was developed to facilitate the use of statistical methods, in conjunction with some known stratigraphic data, to analyze the radiocarbon dating information obtained from testing on the Tel Rehov samples. The authors iterated the model 227,094 times, according to the original source (linked above). That's essentially like running the actual datings 227,094 times and plotting the results, only you're using a computer simulation of the dating technique with the results of the physical tests on the sample serving as the seed to the simulation. It's a very powerful tool, and can be used to improve both the accuracy and precision of the results when compared to other models. The darkened area is the plot of the results of all of those iterations. Now, in order to make all the charts in the document look consistent and easy to read, they normalize the y-axis so that whatever value turned up most in those simulations becomes nominally "1", and everything else scales accordingly. But seriously, if that "1" meant "100% probability" the way you seem to be representing it, we wouldn't need a graph. We'd be adequately served by a point on a timeline.

The chart says:
1) Based on the data collected, one can be 68.2% confident that the true date of the event occurred somewhere within the ranges 903 to 892 BCE and 885 to 845 BCE.
2) Based on the data collected, one can be 95.8% confident that the true date of the event occurred somewhere within the ranges 918 to 823 BCE.

In both intervals, 871 BCE is, of course, included.

Don't EVEN try to pull this crap. In this thread, I found this post, this post, this post, this post, this post, this post, and this post before I got bored with the exercise and quit. I'm sure there are others. Are you asking for a list? Maybe something starting with twelve drummers drumming and ending with a partridge in a pear tree? If we find everything but the partridge, do we get credit?

You've got, oh, a few hundred thousand tents with posts pounded into the soil. That disturbs the soil. A lot. Ground penetrating radar does a really, really good job at locating soil disruptions. It's used to find ancient roadways, landfills, tunnels, caves, all kinds of cool stuff. (GPR - it's not just for mine-clearing anymore...)

Deserts dessicate - they're very dry, so organic matter can dry out, essentially mummifying the lucky cadaver - finding intact graves isn't as impossible as you seem to think. Now, graves tend to disturb the soil, so GPR can find them quite effectively.

Maybe, maybe, maybe. A couple of million people, "camping" in an area of the desert that we know the location of for 38 years. 38 years is a permanent settlement. That many people need to eat - as did their animals that they brought with them. That implies crops and irrigation, and crops and irrigation imply disturbance of the surrounding environment, and disturbance of the surrounding environment is detectable.

When I was a kid, I used to write to Santa Claus every year...
Just out of curiosity, which authors, and what kind of response did you get from them and from the British Museum?

No, no, no. The critical Biblical dating for Shishak's invasion falls within the 95.4% confidence interval. Crucially different.

No, I don't think anyone has accused you of putting out a fake chart. You're incorrectly interpretting a perfectly serviceable chart and people are calling you on it left and right.

And completely missing the significance of the confidence intervals.

Yes, the very center of the 95.4% confidence interval is 870.5 BCE. (It might actually drift a little if they re-ran their simulations, though.) Nobody is really arguing that the value of the center of that range is 870.5 BCE. You're shifting your argument. As long as you've been waving this chart around, you've been talking about how the chart shows that 871 BCE is the 95% probable date of the destruction of City IV (the meaning of the number on the chart), and now you're retreating to a statement you know nobody's going to dispute (the number on the chart itself).

OK. Go back up and click on the link to the original paper. (as an aside, the document at the link is just Chapter 15 of a much bigger work, which I'm very interested in reading, so thanks, LG47 for leading me to that.)
Now, at the end on page 292 (as it's numbered on the page), are the conclusions of the authors. The interesting ones are quoted below:




The current Bayesian stratigraphic model for Tel Rehov gives the following most probablestatistical results:

Larsguy47

I notice you are not using numbers. "Small"? How small are we talking. Anyway, turns out RC14 dating for this is 7 years or less. They divided up a single sample from this level into seven subsamples and then combined and averaged the results which makes it even more specific. The result is as the chart shows. The highest "relative probability" for the age of those charred cereal grains is right there where it indicates with highest relative probability between 874-867 BCE with less probability for dates in either direction. The chart is self explanatory.

If anything the 13.4% probability suggests a comparison to the larger consistent sample and they are weighing it very low as a critical probability in terms of dating, especially compared to dates c. 871BCE.

Even so this was put out to show where the calculated age or range of age a sample gives would fall on the timeline. This shows that this destructive level is most probable c. 871BCE than any other date, give or take 7 years. Why can't you just accept that?

LG47

Larsguy47

Hi NinJay. Thanks for your commentary. It was much appreciated. I have the book and looked up more information about what the chart is supposed to represent.

Page 213 of "The Bible and Radiocarbon Dating":

"How then can one decide whether a radiocarbon date in the range of 2770-2750 BP belongs to the early-middle 10th century, late 10th century of middle 9th century BCE? One possible solution is to lower the standard deviation (s, or sigma value). This can be accomplished in Groningen by high-precision radiometry (PGC), which can give a standard deviation as low as about 12 BP years, provided the sample is sufficiently large due to the sigma or the oxalic acid standard. However, multiple measurements of the same sample material, including AMS on small samples, may enable the calculation of a weighted average that can result in very low standard deviations, below 10."

Page 214: "The additional advantage in the latter case is that the average date is likely to be more accurate as well. Single C14 measurements may be some time distance away from the actual date, as indicated by the standard deviation (Mook and Waterbolk 185: 10). Multiple measurements of the same sample are likely to result in an average date with a higher precision (smaller sigma) and also a higher accuracy, in other words, closer to the real age (van de Plicht and Ruins 2001), provided the radiocarbon lab does not have a systematic bias towards older or younger dates."

The sample from City IV was a large, single sample divided into seven sub samples which were measured and then averaged. The result was as the chart shows, the highest probability between 874-867BCE, which should be closest to the actual date with a "very low standard deviation" below 10.

So the chart is not saying this is give or take 10 years for any date between 918-823 BCE, but give or take 10 years or less for 871BCE.

871BCE, of course, is right on the money since we know that date is correct based upon the correct dating for the Exodus in 1386BCE. Thus the correct dating confirms and agrees with the science.

This means the City IV fall of Rehov by Shishak c. 871BCE, give or take less than 10 years, doesn't help I. Finkelstein who needs to harmonize it with the ill-dated fixed Assyrian timeline wanting that event to make sense for Hazeal c. 835BCE. Sorry, but the closest he can get to 835BCE is 857 BCE at the most. That is still 4 years before 853BCE, the Battle of Karkar.

LG47

spamandham

The legend on the side indicates less than 55% for the range 885 to 845 (41 year range), which includes the peak. Since the graph is roughly triangular shaped over that region, and since the edges of this triangular region are at 0.6 (with the peak at 1.0), the approximate value for the year of the peak itself is:

Area under the 41 year range = 0.6*41 + 0.5*(1-0.6)*41 = 32.8

Ppeak = 55% * 1.0 / 32.8 = 1.7%

That small.

To get any more precise would require having access to the actual data that went into making the graph. You're more than welcome to perform your own calculation and justify your results.

The graph indicates a 105 year 95% probability range. Why are we wasting time on this graph if you have a different source you are really using?

I agree. Sadly, I'm having to explain it to you nonetheless.

I don't know where you're getting the +- 7 year business from. The probability it lies in the range 871 +- 7 years is approximately (where again, it's roughly triangular and the edge values are about 0.8 this time)

1.7% * (( 1.0 + 0.8) /2) * 15 = 23%

Look, it's clear to anyone with any background in statistics or probability you have no idea what you're talking about. You are making a fool of yourself on this subpoint.

How can we take any of your argument seriously, when you have demonstrated obstinate ignorance regarding one of its cornerstones? This is just silly.

-Jay-

Blast. This is the point where I wish I'd paid Amazon for the overnight shipping...

Sure. This is the best you can do with the equipment and a good, large sample. On Page 275, the authors clarify a little more:

"A sample consisting of 25 grams C that is measured routinely for two days (2700 minutes) in specific counters of the Groningen laboratory can give a low standard deviation of 9 C-14 years BP for modern samples and 12 C-14 years for samples of abour 5000 years old. (Mook and Waterbolk 1985:12)."

Note that a large sample here is 25 grams of carbon, and that the low end of the possible standard deviations is 9 years for a modern sample, such as one of the hamburgers my pop incinerated at the last family cookout. Note also that the words "specific counters" here is specifically referring to the Proportional Gas Counters at Groningen, not the Accelerator Mass Spectrometers.

Yep. Nothing controversial here. That's what the Bayesian model accomplishes with it's use of the Markov Chain Monte Carlo draws.

And here the train goes off the tracks...

Quoting from page 275-276 of the source material:

"Stratum IV was the last Iron Age IIA City at Tel Rehov. Datable organic material was only found in Locus 5498 in the form of charred cereal grains, representing the destructive end of City IV. The seven AMS dates from this single sample of cereal grains (Basket 54702) are placed in the model, with the ‘R_Combine’ command determining the weighted average."

It is not clear from the material in Chapter 15 of the book that the Stratum IV sample was "large" in the same sense of the term that we need for PGC to work. We know that the grain sample from L 5498 in Stratum IV yielded seven AMS dates, and we know that AMS is suited for small samples. We also know, from page 275 that for purposes of PGC, 25 grams of carbon is a "large" sample. This implies that the grain sample in question was somewhere much less than 25 grams of carbon, so the sample in total may not have been as large as you might think. (Serious question, since I won't have my copy of the book for another day or so - precisely how large was the sample from L 5498 in Stratum IV?)

No. The chart quite clearly shows it's 1-sigma and 2-sigma ranges. The 1-sigma range, which you're claiming to be +/- 10 years or less is really +/- about 26 years, and the 2-sigma range is +/- about 48 years. What you've done is made the invalid assumption that because the equipment and the protocols are capable of yielding a 1-sigma value of less than 10 years under very , it has actually done so in this case. The authors quite clearly state the 1-sigma (68.2%) and 2-sigma (95.4%) confidence intervals for the destruction of City IV on the chart, and restate the 2-sigma range in their conclusion #6 on page 292. The 1-sigma range is absolutely not 871 BCE +/- 10 years.




The radiocarbon dates available for Stratum IV relate only to the destruction at the end of City IV’s lifespan. The availability of samples for radiocarbon dating in archaeology are, unfortunately, more likely to come from fires or destruction events than from ordinary daily life. The sampled Bayesian destruction date of City IV (Fig. 15.8) has the highest probability in the 1-sigma range of 903– 892 (13.4%), 885–845 BCE (54.8%), extended in the 2-sigmarange to 918–823 BCE. Though it seems very unlikely that the Shishak campaign would have been responsible for the destruction of City IV, there are various other candidates later in time. As there are no younger Iron Age stratigraphic data from Tel Rehov, the available 14C data are insufficient to favour a certain decade within the above 2range of 920–815 BCE. The sampled Bayesian time-span for City IV is 28–55 years in the 1-sigmaand 2-sigmaranges, respectively (Fig. 15.8)."


regards,

NinJay

-Jay-

Well, vanishingly small as it turns out. For many intents and purposes, you can treat the chart as a function of a continuous random variable, with the probability of any interval, say, 885 to 845 is the integral of the function between those two values. If we set the interval at just a gnat's eyelash to the left of 871 to just a gnat's eyelash to the right of 871, our integral approaches the area under a zero width curve, and the area under a zero width curve is, well, zero.

regards,

NinJay

Larsguy47

Sorry, but the range of error is less than 10 years by the method used because they divided the single sample found at level City IV into seven subsamples. When they do that and then "average" the dates it is closer to the actual date to less than ten years. Otherwise depending upon method it varies from 7-20 years. So there wasn't a lot of flexibility in the first place. The 870.5 mid-range "relative probability" is thus the best possible dating for that event available from science. That means it is prudent to work from that date outward when comparing chronologies.

Per the KTU 1.78 BCE eclipse dating that would fix-date the 1st of Akhenaten to 1386BCE, Shishak's invasion would be dated to 871BCE, which is precisely on target. Thus the improved fixed dating confirms the reliability of this particular sample and its results. This event occurred in 871BCE and the RC14 from a large sample found at this destructive level comes up with the same dating based upon the most advanced dating available for RC14 applications to chronology.

It's interesting to me that when science tends to confirm the Bible, then something is wrong with the science, but when it contradicts the Bible then something is wrong with the Bible.

I'm just the opposite! When science agrees with the Bible, then the science is "expert" but when it doesn't, they are incompetent or flawed. So it's the same old game. People hold out for their own views. But it's nice to hear the other sides, which can be reassuring or unsettling!

LG47

spin

The text has nothing to do with Akhenaten. It was found at Ugarit and written in Ugaritic. The Egyptians didn't use Ugaritic. In fact they weren't particularly good at Western Peripheral Akkadian the lingua franca in the Amarna letters and KTU 1.78 has nothing to do with the Amarna cache. There is just no way despite all the claptrap about Egyptian universities (howls of uproarious laughter) that you can seriously relate this text to Egypt, let alone to Akhnaten.



This is just your bias constructing a straw man. When science can confirm the bible then one can say the bible got something right. When science shows the bible got something wrong then one can say the bible got something wrong.

Just to show your bias:
And we've noticed.

You are unable to say anything meaningful about science with this gooey kid's stuff.

It's not the other side, Dave. It's the real world.

Scholarship doesn't hold out for its own views. It holds out for what is the best fit and when something fits better what it held before is washed away.

However, because you have this book around your neck like an albatross, you suffer the consequences. You cannot understand science. You can merely abuse it. You play with things you can't really appreciate, as a means to your apologetic ends. So it's the same old game.

spamandham

You still fail to understand radiometric dating, and don't even appear to be trying. If you start with a single sample, there are uncertainties related to the environment that are not overcome by dividing the sample into parts and averaging the results. The raw results are calibrated based on estimates of the amount of C14 in the air as a function of calendar date, but there is still residual uncertainty even after calibration.

The only reason to break up a sample is to ensure proper methods are followed and to make sure there is not contamination in handling (to make sure someone didn't screw up). This improves our trust in the final results, but it does not reduce the standard deviations, because in the case of C14 dating, the uncertainty is virtually entirely related to environmental, rather than resulting from handling or measurement technique (assuming accelerator-based mass-spectroscopy, which eliminates virtually all error related to counting C14).

Further, you seem obsessed with the idea of "there is one true date, and so we pick the date that is most likely and assume that's it". This is not valid in any branch of science. You MUST assume the entire range of possible dates, and work from there. In this case, we are talking about a 95% range of nearly 100 years. You could assume a smaller range, but that then increases the likelihood you are wrong.

It has already been shown to you numerically how unlikely it is that the actual date is the exact date of the peak in the graph. You demanded to know this, and it was provided to you, and you summarily ignored it.

Your quack approach ensures no-one serious will pay any serious attention to the rest of your argument. You are repeatedly making a fool of yourself, ignoring all patient attempts to explain RC dating to you, making unreasonable demands, and then ignoring them when they are met. I've lost patience with you and am simply enjoying rubbing it in over and over.

You can claim Bible persecution all you want, but it is your flawed reasoning that betrays you. The Bible is not automatically discounted here as a historical source. For fuck's sake, Finkelstein and Silberman are both Jewish. This is not some kind of evil atheist conspiracy among archaeologists. Ugh.