Radiocarbon Dating

For something a little different, I decided a post on radiocarbon dating might be appropriate. Since I put a lot of stock in the information gleaned from radiocarbon dating, I figure it's worthwhile to describe a little bit how it's done, and more importantly, to describe the various sources of error in it. Constraining error is one of the key issues with any scientific measurement, and radiocarbon is no exception. One particular point I will make is that the error will depend a lot on specifics to each measurement (time and location). So there are periods and locations where the result has extremely large errors, and other measurements that are more trustworthy.

How it Works

The physics of radioactive dating is pretty straightforward. Carbon-14 (6 protons 8 neutrons) is a radioactive isotope with a halflife of approximately 5700 years. The characteristic decay is "beta decay" which means (roughly) that one of the neutrons in the nucleus decays into a proton and an electron. The resulting nucleus is Nitrogen-14 (7 protons 7 neutrons). The energy from the emission goes partly to the nucleus and partly to the electron that was created. Because of conservation of momentum, much more of the energy goes to the electron and it gets ejected from the atom. These ejected electrons are called "beta particles" and you can monitor the decays by detection of them.

As with all radioactive decays the density of C-14 at any time can be modeled with an exponential equation. The characteristic time for the exponential, the half-life, indicates how long it takes for half of the C-14 atoms to undergo beta decay. So if you know how many C-14 atoms are around at the beginning, you can predict how many will be there at any point in time in the future (provided of course that there are enough of them that the statistical argument makes sense.) Similarly, if you know how many there were at at the beginning, and you know how many there are now, you can predict how long ago the "beginning" was. Finally, if you know the current concentration and you know exactly how long ago you wish to measure, you can use it to determine the original concentration at that time. This last calculation will be important later.

Willard Libby proposed using the concentrations of C-14 in organic material as a means of dating a substance. C-14 is constantly being created in the upper atmosphere from interactions between high energy photons from the sun and atmospheric molecules. While an organism is alive it is constantly exchanging its carbon atoms with those in the atmosphere, so the C-14 concentration in any living being is similar to the global concentration at that time. This is because chemically isotopes behave (almost) exactly the same, so the organism does not distinguish between C-14, C-13 or C-12. After it dies, it stops incorporating carbon from the atmosphere. If we know the global concentration at the time it died (more on that later) and we can measure the concentration now, then we can calculate the date that it stopped exchanging carbon with the environment as described above. Therefore, radiocarbon analysis of the C-14 content in organic material can be used to determine the death date of organic material. For this result Libby won the Nobel Prize in Chemistry.

Now we will discuss some of the details along with the various sources of error that arise.

Carbon-14 Measurement Errors

The first error that we will look at comes from the difficulty in actually measuring the C-14 content in a sample. As with any scientific measurement there is an associated error bar. There are several ways to look for the C-14 content. One is to look for the decay by measuring the emitted beta particles. A more popular method (due to better accuracy) is to convert the entire material to a gas and run it through a charge-mass spectrometer, that can distinguish between isotopes of carbon. You can read about the various techniques here.

Both these results will have errors based on the limitations of the actual measurement technique and due to statistical problems. The statistical error is generally small compared to the measurement error. You can reduce the error by comparing results from different samples and different techniques/laboratories. But you can never make it zero.

Finding Appropriate Material

Finding appropriate organic material can be difficult. The best material (at least for the Ancient Near East region) appears to be stuff like burnt seeds and stuff like olive pits which can be found in fire pits and cooking areas. Stuff like structural wood tends to be a bad choice since it's always possible that the wood is old, having been used for a previous structure, and using it will make the date appear older than it really is.

One common form of systematic error arises from improper association of a sample with a specific archaeological stratum. In other words, you find some burnt olive pits and think they belong to the city, but it turns out they are just the remains from hundreds of years later when some nomads made a makeshift camp in the ruins.  Obviously, the more samples you have, the less likely you are to make an error like this. Yet there can be systematic errors due to associating some result with an incorrect archaeological stratum.

This error is entirely in the domain of the archaeologists, and it's impossible to handicap it without being involved in the actual excavation, or by scanning the detailed reports. Nevertheless, when you see large discrepancies in dates between archaeologists, chances are that the reason is because they are arguing over which stratum belongs to which set of measurements.

Constraining Initial C-14 Fraction

Libby assumed that the C-14 fraction in the atmosphere was a constant. It turns out this is not true. It can vary slightly. However, slight variations can mean big differences with regard to dating, so it's important to figure out how much carbon was in the background atmosphere at all the possible dates that the organism may have died.


The way this is done is primarily through "dendrochronology" The idea here is that you can use trees as a method of determining the C-14 concentration at any time in the past. The inner rings of a tree are not living anymore, so they do not exchange carbon. Therefore, you can cut down a long lived tree and get information on the global C-14 concentration for each year that the tree was alive, just by comparing the carbon at each ring. You know the current concentration, and you know the time, so you can get the initial concentration. Then if you have trees that died a long time ago, but were preserved, you can find overlaps with known trees. With enough work we can build a database going back thousands of years. Indeed the carbon calibration curves we have go back around 40-50 thousand years. These curves are constantly being refined, but they are pretty robust for the area in question for Biblical archaeology.

I said "global" concentration above, but that's not entirely correct. Global here means a sizeable region surrounding the area in question. There are indeed separate calibration curves for the northern and southern hemispheres, and even more local curves for time periods closer to the present (where Biblical results fall.)

Errors from Calibration Curves

While the calibration curves are pretty robust, the fact that the initial concentration varies slightly can increase or decrease the error for a given measurement. It is probably best to use an example, so here's a typical plot that you might see (taken from here).

This plot is a little busy, so let's look at the details of what's going on. The y-axis shows the amount of C-14 that was detected in the unit BP (what exactly that is doesn't matter). The red bell shape indicates the actual measurement amount (around 3000 BP) and the error associated with it, (here probably around +/- 80 BP).  The x-axis represents the dates in years BCE. The thick blue line that goes through the plot indicates the calibration curve. From this curve you can calculate the date for any given amount of BP measurement. Except not so fast. Even if you exactly knew that you had 3000 BP, you wouldn't be able to distinguish between about 1260 and 1230 BCE, since the line at 3000 intersects the blue curve twice. So, because we have measurement errors in the amount of carbon, and because the blue curve is so "wiggly" what we wind up with is a probability distribution function which is pretty complicated looking (gray region). The results on the top right summarize the plot results. You have an 8.2% probability of being between 1375 and 1340 BCE (the bump on the far left), a 87.2% probability of being between 1320 and 1129 BCE, and about a 5% probability of being somewhere else.

This plot looks about typical for results I have seen but quoted results dates tend to have errors that are smaller errors +/- 150 years. How?

"Wiggle Matching" and Bayesian Analysis

So the way to do better, as before, is by using multiple measurements. However, here what you're using are multiple measurements from different strata. To use the above example again. Let's say you find some sample that produces exactly 3000 BP. As we noted above, you can't distinguish between 1260 and 1230 BCE. But let's say you dig a bit deeper, and somewhere below you find something else that also produces exactly 3000 BP. You know that the deeper one must be older. So you can say that the deeper one is 1260 BCE and the shallower one is 1230 BCE.


"Wiggle matching" takes multiple results from as many strata as can be found and attempts to match the "wiggles" in the calibration curve as best as possible. This is essentially another massive probability calculation and it is usually done by computer codes. If you have a lot of samples from a given site, you can usually constrain the results far better than with a single sample.

But archaeologists can go even further. If you can make estimates on things like how far apart in time different strata were, or if you know from Egyptian or Assyrian chronologies when cities were destroyed (or claimed to be destroyed) then you can put those assumptions into the model as well. This can produce very accurate estimates (less than 50 years error), even for results where the error in the C-14 measurements are large. But they depend on the assumptions you put into the model and your confidence in them. These models are "Bayesian" in that they attempt to determine the probability that a given set of date measurements could produce the actual results.

This is another area where you can have significant disagreement between archaeologists. They might disagree greatly between what assumptions are made. Here, we laymen are in a better position to evaluate the results, since all good archaeologists will state what assumptions, if any, are input into their models. Again though, these only show up in technical papers.

An Example: What I Found About the United Monarchy Debate

A while back I read a collection of essays in "The Bible and Radiocarbon Dating" edited by Levy and Highman, and first published in 2005. As such the results are about 10 years out of date, but that is the extent of my knowledge. The articles were highly technical, and I actually needed to learn about the topics in this post before I could properly appreciate the arguments. There were both detailed excavation reports and tons of results from radiocarbon analysis, similar to the plot I showed above.

The current main point of contention between archaeologists today (or at least in 2005) is whether or not there ever existed a united monarchy under Shlomo (Solomon). On one side is the "conventional chronology" championed first by Dever and now by Amihai Mazar which states that there indeed was such a united monarchy. The alternate view is the "low chronology" offered by Finkelstein which suggests that it never existed. At the heart of the debate are the dating of various monumental structures, specifically city gates, in various cities like Gezer and Hazor. The conventional chronology dates these to around 950 BCE which puts them in the time period of Shlomo.  The low chronology dates these to about 880 BCE and attributes them to the reign of the northern kings Omri and Ahab who were the first kings to garner international attention.

As we've noted above, a difference of less than 100 years is typically too small for radiocarbon analysis to distinguish, but each of these sites have many strata, and the articles record some of the most comprehensive attempts at carbon dating analysis to date. Nevertheless, from my perspective the results were inconclusive. Here are where the two sides differed.

1) The main source of disagreement is determining which stratum the monumental structures belong to. You can't date the structure itself, it's not organic, so you have to tie it to some organic material. As far as I know this is unresolved with Finkelstein continuing to insist it's dated to a later structure, and Mazar insisting it's an earlier structure.

2) Another source of disagreement was on the treatment of an outlier radiocarbon result. Various organic material were sent to several different labs, and one produced a date different than the others. From my memory, Finkelstein included these results in his models, but Mazar considered them an outlier and did not include them. As you can imagine this made a big difference on the results of each group's Bayesian analysis. Both groups stress the need for repeated measurements.

3) The disagreement includes anthropological models as well, specifically with regard to the appearance of specific pottery types that appear to have spread from the Philistine cities. Finkelstein thinks that it took a long time for this pottery to spread, Mazar says it spread quicker.

As you can see, when you start dealing with the details of these analyses, you very quickly get into the weeds. As a layman who is not involved in the measurements, I think it is absolutely impossible to determine who has the better argument. As such, I put the existence of the united monarchy as an unknown, and will wait until a consensus is reached on the matter.

Well Then, What Can We Know for Sure?

While the dating of monumental gates is still under question, other conclusions from archaeologists have reached a higher level of consensus. For example, the city of Yericho (Jericho) has a strong consensus that it was destroyed long before Yehoshua (Joshua) could possibly have arrived. Similarly with the city of Ai. There are fringe opinions otherwise, but overall there is very little academic debate on these matters anymore. Indeed Yericho, is a good example of carbon dating resolving a contradiction between archaeologists. As it provided enough resolution to confirm the early date proposed by Kathleen Kenyon instead of the later date proposed by Bryant Wood. You will still see apologetic answers using Bryant Wood's analysis, but this is disingenuous, and you should be able to recognize it as such.

There are other similar events which we can date, such as the destruction of major cities. Destructions tend to be easier to date because a lot of stuff tends to get burned and buried. These include sites like Ugarit and Hattusa which aren't mentioned in Biblical texts but belong to the period prior to their composition.

All in all, it pays to be cognizant of the claims being made, the associated error, and whether there's a consensus or a disagreement between the people that are closest to the measurement.