Coherence between many lines of evidence: Part I

An important hallmark of good science is coherence across many different, independent measurements. It is simply a fact of living in the real world that no single way of measuring something works in all cases. For example, a bathroom scale might be a good way to measure my own mass. But, if I want to determine the mass of a spoonful of flour, I will need to use a different kind of scale.

Different measurements rely on different assumptions. If the starting assumptions are wrong, then a measurement will produce nonsensical results. If I want to measure my mass on the earth, I can use a standard scale. But, if I were on the moon, this scale would give me an incorrect result since the scale is calibrated assuming earth-gravity.

Let’s examine this issue in the context of one particular measurement problem: how to calculate the age of old sample using Carbon dating. First, a brief introduction/review of how carbon dating works: There are several “isotopes” of carbon. Isotopes are different versions of the same element with different numbers of neutrons (neutral particles) in the nucleus. Neutrons have no effect on the chemical properties of an element, but they can affect how stable it is. Unstable elements will decay over time. Carbon 14 (C14) is an unstable isotope of carbon with a half-life of ~5730 years. This means that if I have a sample of C14, after 5730 years I will have half as much. Even though C14 decays away, new C14 is produced in the atmosphere from cosmic rays bombarding Carbon 12 (C12). Living plants breath in the C14 and are eaten by animals. The carbon 14 becomes a part of these living things and continues to replenish as long as they are alive. But, as soon as they die, no new C14 enters the specimen and the fraction of C14 continues to decline. Knowing the atmospheric concentration of C14, we can figure out how long ago this plant or animal died from how much of that C14 decayed away [1].

Let’s think about some of the challenges involved in Carbon dating. Then we’ll peruse the literature and see how these challenges are dealt with.

1) What determines the initial Concentration of C14 and is it constant?

The fraction of Carbon 14 in the atmosphere is determined by the rate it is produced in the atmosphere and the rate at which it decays. New C14 is produced by cosmic rays bombarding the atmosphere. In order for carbon dating to work, this concentration should be stable and well-known. If it is not stable and relatively constant, then the method would not work.

2) Is the decay rate constant? Are there factors that could change it?

Another potential challenge to the accuracy of radiometric dating is the decay rate of C14, itself. If this decay rate was not constant, we could not use it as a reliable clock.

We don’t need to rely on physical assumptions, even well motivated assumptions, to verify these underlying premises of carbon dating. We can actually cross-check these assumptions *directly* against other sources of evidence. Carbon dating is the not the sole technique we have available for determining age. It exists alongside other, categorically different dating methods [2]. The more independent measurement methods we have, the more confidence we can place on the broad conclusions.

So what are some of the complementary measurement techniques for determining ages?

As most people know, trees grow in seasonal cycles and their trunks show a pattern of concentric rings corresponding to periods of growth and rest. There is one ring per year. Moreoever, the sizes of tree rings vary with fluctuations in local and global climate. These unique, yearly patterns allow us to line up tree rings from younger trees with those of older trees and we can work our way backward. Using the overlap between successive generations of trees we can patch together a timeline extending back more than ten thousand years. This lining up process has its challenges and pitfalls, but the people who do the work are able to use precision measurement techniques. In any case, this technique does not depend on carbon-14 levels in the atmosphere. Nor does it depend on the constancy of radioactive decay rates. [3]

Tree rings fall into a class of dating methods called “incremental dating techniques” because they exhibit a pattern of countable bands, each band corresponding to one yearly cycle. Two other incremental methods that I would like to discuss are varves and ice cores. Varves are seasonal sediment layers that build up in certain lakebeds [4]. The varve record goes much further back than the tree ring record: close to 50,000 years of banding patterns. Several particular sets of varve records play critical roles as calibration samples for carbon dating. Ice cores are vertical columns of ice, carefully drilled out of large glaciers. Like tree rings and varves, the ice forms a banding pattern, due to seasonal thaw and refreezing cycles [5]. The ice core record goes back even further yet: several hundred thousand years. There are many other relative and absolute dating methods that we can use to compare and cross-check carbon dating. I hope to address others. But, for this article, let’s stop here.

Now, let’s take a look at our carbon dating method. We can take trees that died in particular years in the tree-ring record and compare their age in the tree-ring record with the fraction of carbon-14 remaining [6]. Likewise, we can take samples found in varves and compare the C14 age with the year of the corresponding sediment layer the sample was buried in. Here is a composite of varve data taken from Lake Steel in Minnesota and Lake Suigetsu in Japan,  various tree ring data, and their corresponding carbon 14 concentration (source: Davidson and Wolgemuth) [7]:


Over a span of ~10,000 years of tree rings and and 50,000 years of varves, we see a smooth, mostly linear relationship with the logarithm of  C14 concentration: The older the tree, the less the C14. In other words, the age given by trees and varves is pretty well consistent with the C14 concentration. And here is the key point: if either of our above two assumptions about carbon dating (known atmospheric concentrations and constant decay rate) were significantly wrong, the C14 concentrations would diverge from the other methods. Instead of a straight line, the above graph would fluctuate wildly, with no rhyme or reason. This is clearly not the case.

What makes these methods nice is their complementarity. There are many factors that can bias varve and tree data, but those factors have little to do with the nuclear physics governing Carbon-14 decays. Likewise, even if carbon-14 decay rates were completely different in the past, one would be hard pressed to explain why this effect would simultaneously increase (or decrease) the number of tree rings or sediment layers in the record.

At this point, an astute reader might notice that the graph of C14 concentration versus varves is not a perfectly straight line. There are small fluctuations. And, more importantly, in the older samples (>20,000 years) the yellow points are starting to bend slightly downward away from a straight line. Don’t worry, I won’t dust this under the carpet. As you will recall, we never expected carbon dating to work perfectly. All measurement techniques are inherently imperfect. What scientists and informed scientific readers ask is: (1) How imperfect are these methods and (2) can we understand those imperfections? In short, are they good enough? With any good scientific method we should be able to quantify how good they are compared with the accuracy we need. And this takes us to the most exciting point:

Using a large number of complementary measurement techniques can even help us to understand the imperfections and limitations of each individual technique. Coherence does not just reinforce our confidence in a measurement; it helps us to systematically understand it.

First, we need to understand which factors are varying over time. If the plot above jitters a bit, what is causing the jitter? Is it the carbon dating or the tree rings or the varves or ice cores? Well, fortunately we have at least four different measurements techniques. If two of them agree with each other but not the third one, then we have good reason to believe that the third one is the “odd man out” so to speak. We can plot deviations of C14 age from tree-ring age, for example, and we get the black graph below on the plot below.  The y-axis (on the left side) shows the percent difference between the measured concentration and the expected concentration of C14 for a sample of a given age. Sometimes there is more C14 than there should be (and we would underestimate the age). Sometimes there is less than there should be (and we overestimate the age). But, note the magnitude of the fluctuations. The majority of the variations are within 10% of the correct age, with a few deviations as large as around 20%. If we don’t trust these particular tree-ring based measurements, we can go to a completely different part of the world and compare the C14 concentration of air bubbles in an ice core with the age of the ice-core, based on counting thaw-and-freeze layers in the ice. We get the same result (shown in red on the same plot)! We can see that the Carbon-dating age fluctuates with respect the tree ring age and it fluctuates the same way compared to ice cores [8]. This tells us that Carbon dating is the probably odd man out.


We have now shown that Carbon dating is not perfect, as we expected. However, we can quantify how imperfect it is: mostly within 10%. And, we can do this by directly comparing it against three completely different and complementary techniques (tree growth, ice formation, and sediment layers in lake beds). Now we have one more question: do we know why the C14 date is varying like this? Can we determine the cause?

Even here, we have independent data and methods we can use to test the various causes. Beryllium-10 is a radioactive isotope with a MUCH longer half-life than carbon (1.4 million years). This means that however much Be-10 there was in a sample a few thousand years ago, there is pretty much the same amount (because hardly any of it decayed). If rates of cosmic rays varied over time, they would change the concentration of C14 and cause these deviations in the C-14 age. They would also change the Be-10 concentrations in the atmosphere [9].  Since Be-10 has a very different and much slower lifetime, it provides a nice complementary measurement to compare with C14. In the plot below deviations between the C-14 age and tree rings are compared with deviations in Be-10 concentrations in layers of corresponding ice cores. Here we are essentially comparing two different radiometric techniques -C-14 and B-10 concentrations- against two independent chronologies from different parts of the world (tree and glaciers) and we see similar global cycles in the concentrations of radioisotopes.


It gets even better: We know that the earth’s magnetic field can change polarity (North pole flips with South pole). We know that this has happened in the past from looking at the magnetic polarity of layers of rock in the geological column. During the transition period from one polarity to the other, we expect low magnetic fields and therefore high rates of cosmic rays (since the earth’s magnetic field deflects cosmic rays). We would predict that, if this were the case, we would see a large deviation between carbon dating and varves or a large change in Be-10 concentrations in ice cores. Indeed, we see just this. The most recent such reversal is called the “Laschampe Geomagnetic Excursion” and it occurred around 41,000 years ago. Below are two plots from two different papers showing changes in radioisotope concentrations during this event. First, we see a paper specifically discussing the Lamschampe Excursion [10]. In this series of two plots, the bottom plot shows the orientation of the earth’s magnetic field and the top graph shows Be-10 concetrations measured in Greenland ice cores. We see spikes in the Be-10 concentrations following the “transition” periods when the orientation of the earths magnetic field flipped signs and cosmic rays would be at their highest rates.


Similarly, in a recent paper using varves taken from Lake Suigestu, a large deviation between the varve age and Carbon-dating age is observed at a little over 40,000 years before present [11].


Coherence is a much stronger proposition than mere repeatability. Repeatability of the same experiment or measurement is very important in science as a means for catching mistakes (or phony results). However, scientists are professional skeptics and we do not like to hang our hats on a proposition that relies on one single measurement technique. We demand coherence across a wide spectrum of different methods, each with non-overlapping assumptions. In this post we saw in Carbon dating some beautiful examples of how this coherence among many methods can be used to quantify and shine light on the limitations of each individual method. This is only the tip of a much deeper iceberg. Geological dating techniques, and radiometric dating, are approaching a century-old. There are literally hundreds of techniques and thousands of papers spanning the decades. These results have been reproduced again and again, under the careful scrutiny of thousands of scientists who gave these problems their undivided attention. I do want to come back to this subject. If I get good questions about this or other related concepts, I’m liable to write a follow-up post.


[1] For further reading, see:  (a) Carbon Dating   (b)   (c) Radiocarbon Calibration

[2] Refining the Radiocarbon Time Scale; Paula J. Reimer; Science 338, 337 (2012);

[3] For further reading, see:  (a) About tree rings   (c) Principles of Dendrochronology (d) NOAA slides on tree-rings

[4] For further reading, see:  (a)  Varves as natural calendars (b) Radiocarbon Dating of Varve Chronologies

[5] For further reading see: (a)  Ice Core 101  (b) Stratigraphic dating of ice cores (c) NOAA slideshow (d) Data from the Vostok ice core

[6] Dendrochronology and Radiocarbon Dating

[7] Lake Suigetsu and the 60,000 year varve chronology

[8] C-14 in ice cores and tree-rings

[9]  Influence of Atmospheric Processes on Be-10 atom concentrations; Y. Stozhkov;

[10] Dynamics of the Laschamp geomagnetic excursion from Black Sea sediments; N.R. Nowaczyk a,n, H.W. Arz, U. Frank, J. Kind, B. Plessen; Earth and Planetary Science Letters 351–352 (2012) 54–69

[11] A Complete Terrestrial Radiocarbon Record for 11.2 to 52.8 kyr B.P.; Christopher Bronk Ramsey et al.;  Science 338, 370 (2012);


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