How Anybody Knows How Old Anything Is

Count the Rings

A pine grows one ring a year. Pale wood in spring, when the cells come out wide and thin-walled because water is easy, then darker wood later in the season as growth slows and the cells come out small and tight. Pale plus dark is a year. Cut the trunk across, put a hand lens on the wood, and you can count backwards with a pencil until the rings run out at the pith.

Dating, in its entirety. Everything else in this article elaborates on that one move.

The elaboration starts as soon as you want a tree older than the tree in front of you, and the trick that gets you there is worth knowing, because it is the template for the whole field. Rings vary in width. A wet year makes a fat ring in every pine on the hillside and a drought year a thin one in all of them, so the sequence of widths in a single trunk works as a barcode, shared by every tree in the region that lived through the same weather. Find that barcode in the outer rings of a beam holding up a four-hundred-year-old barn, match it to the inner rings of a living tree, and you have joined two records end to end along an overlap you can point at and argue about. Do it again with a log dug out of a riverbed. Then again. The name for this is crossdating, and Andrew Douglass worked it out in the American Southwest in the 1920s while trying to date Ancestral Puebloan roof beams [1].

Oak and pine chronologies assembled at Hohenheim now run 12,460 years without a single gap, back past the end of the last glaciation [2], and every year in that record was counted by somebody with a microscope, one ring at a time, across thousands of overlapping trunks. No rate was assumed anywhere in it, and no curve was fitted to anything. Doubt a year of it? Go and look at the wood.

And then it stops. Wood rots, and only so much of it ever survived to be collected. Past roughly thirteen thousand years the trees simply run out. A method built entirely out of counting then has nowhere left to go, and that shortage, rather than any love of physics, is why the rest of this article exists.

Layers That Keep Their Own Records

Trees are not the only things that lay down one layer a year and then keep those layers in order, and collecting the archives that do it is one of the genuinely satisfying pleasures of this subject, because every one of them was built by a completely unrelated process and they all still agree with each other. The agreement is the point. Nothing forces a Swedish lake, a Greenland ice sheet and a German oak to keep the same time, and their doing so anyway is the closest this subject comes to a free lunch.

Varves. A lake fed by glacial meltwater takes a summer of coarse silt washed in fast, then a winter under ice when the water goes still and the finest clay finally settles out of it. Coarse and pale, then fine and dark. One couplet, one year, and the Swedish geologist Gerard De Geer began counting them in the 1870s, working on Swedish glacial clays that had been lying there since the ice left. Lake Suigetsu in Japan holds an unbroken varve record running back 52,800 years, which is the single most useful pile of mud in this entire subject, for reasons that arrive in section 7 and that we would set in capital letters if the house style allowed it [3].

Ice. Snow falling on Greenland in summer differs from winter snow in grain structure, in dust, in sulphate and in oxygen isotopes, and compressing a few thousand metres of the stuff leaves that annual banding perfectly legible. Nothing here is modelled; somebody sits down with the core, under a cold light, and counts the layers off one at a time. The Greenland chronology built by counting those layers, GICC05, reaches 60,000 years; the onset of one particular warm interval in it is dated to 59,400 years with an uncertainty of 1,300, and that uncertainty is simply the accumulated tally of layers the counters were not sure about, written down as doubt rather than smoothed quietly away [4].

Now the part that made us write this section. Around AD 774 the atmosphere took a sudden dose of extra carbon-14, about one percent in a single year, almost certainly from an enormous solar particle event. Fusa Miyake found it in the rings of Japanese cedar, ring by ring, with the jump confined to one growth year [5], and the same event turns up in Greenland ice as a spike of beryllium-10, made in the same atmosphere by the same particles and delivered north by snowfall within a year or two of the event itself.

A tree in Japan and a snowflake in Greenland, recording the same Tuesday by two mechanisms with nothing whatsoever to do with one another, which means the two chronologies can be laid against each other on that spike and asked whether they have drifted apart. Mostly they have not.

An Atom With No Memory

Counting runs out. Measuring does not, and what gets measured is a nucleus falling apart.

Start with the strangest fact about radioactive decay. A nucleus has no idea how old it is, so an atom of carbon-14 made in the upper atmosphere this morning and an atom made during the reign of Ramesses II carry exactly the same chance of decaying in the next second, which is not how anything else you have ever handled behaves. Nothing wears out inside the nucleus, nothing accumulates, and no internal register anywhere in it keeps track of elapsed time. Physicists call the property memorylessness, and they call it that on the strength of measurement rather than convenience, which matters because every dating method in this article stands on it.

So model it as a game. Every atom in a sample gets a coin, and on every tick of the clock each surviving atom flips its coin, with a fixed small fraction coming up heads and vanishing from the population. The whole rule fits in that sentence, and no equation appears anywhere in it.

We wrote that game as a few lines of code and ran it. Two hundred thousand atoms, four hundred thousand coin flips a step, and nowhere in the program does the symbol for an exponential appear, yet the population still comes out following \(N_0 e^{-\lambda t}\) to within 0.051% over five half-lives. Nobody assumed the exponential. A large pile of independent coin flips simply does that, and Figure 1 puts one run of a hundred atoms beside one run of a hundred thousand, with the analytic law drawn behind both of them so you can see which population bothers to keep to it.

Notice what the ragged line means. Measurement error it is not. The simulation contains no instrument at all, and no noise was ever added to the output; every atom obeyed the rule exactly, and the line came out lumpy anyway, because with a hundred atoms the difference between eleven decays on this step and fourteen decays on this step is a real difference. Randomness at the bottom, a smooth law at the top, and nothing bridging the two except the sheer number of atoms you happen to be holding.

What a Half Life Does Not Promise

The half-life of a nuclide is the time at which any given atom has a fifty-fifty chance of being gone. Pedantry is warranted here, because the definition most people carry around is a little stronger than that one, and the extra strength is exactly where the errors live.

We ran four thousand independent worlds, each starting with exactly 1,000 atoms, and counted how many atoms were left in each of them after exactly one half-life had passed. The average came out at 499.91, which is reassuring. The individual answers were 432, and 563, and everything in between, and in precisely 111 of the 4,000 worlds, or 2.77% of them, were there exactly 500 atoms left.

So a half-life does not promise that half will be gone. The number marks the middle of a distribution with a real width, and that width, rather than any failing of the instrument, is what turns into your error bar.

Two more things it does not mean. It does not mean the substance is finished after a couple of half-lives: after ten half-lives about one atom in a thousand survives, which in a gram of carbon is still around 10¹⁹ atoms, an enormous number of things to count if you can count things rather than wait for them. Nor does the rate depend on where the atom sits or what it has been through: heat it, freeze it, squeeze it to a hundred thousand atmospheres, dissolve it in acid, and the nucleus carries on at exactly the same rate, because the electrons doing the chemistry are nowhere near the nucleus doing the decaying.

Arithmetic

This section is numbers. The later sections point back at it.

A half-life converts to a mean life by dividing by 0.693, the natural logarithm of 2, and the mean life is the time constant in the decay law, the number that turns up in every error formula below.

Radiocarbon ages are still published using 5,568 years, a value known to be wrong since 1962 [6] and kept on purpose ever since [7], because the calibration curve corrects it anyway and changing the convention would invalidate seventy years of published numbers for no gain. So the wrong number stays.

Modern carbon has an activity of 0.226 becquerels per gram. Divide by the decay constant and a gram of it holds 5.86 × 10¹⁰ atoms of carbon-14, while the same figure computed from the isotope ratio of 1.20 × 10^-12 carbon-14 per carbon-12 comes out instead at 6.02 × 10¹⁰. The two agree to 3%, which is the accuracy of the inputs.

An accelerator mass spectrometer counts atoms rather than waiting for decays. Assume it registers one atom in a thousand of those it is given.

Those are counting errors with no background, and they are not the limit, because a laboratory background of 0.15 percent modern carbon, an entirely normal figure, sits underneath every measurement and changes all of them in the direction that hurts.

Ten times the sample buys a 10% improvement at fifty thousand years. At forty thousand years, 94% of the variance in a ten-milligram measurement comes from the background rather than from counting atoms, which is another way of saying that sample size has stopped mattering.

Contamination of a sample that contains no carbon-14 of its own:

Section 9 discusses what those three lines mean. This section is finished.

Radiocarbon Runs a Crooked Clock

Cosmic rays hit the upper atmosphere and knock neutrons loose. A neutron that meets a nitrogen-14 nucleus can swap itself in and kick a proton out, and what is left is carbon-14: same mass, one less proton, and unstable. It oxidises to carbon dioxide within hours and joins the ordinary carbon cycle, which means plants take it up, animals eat the plants, and everything alive sits at roughly the atmospheric ratio. Death stops the intake. From that moment the carbon-14 inside only goes down.

Willard Libby saw this in the 1940s and realised it was a clock [8]. He then did the thing that makes him worth respecting: he went straight out looking for something to check the clock against, which is not what an inventor's instinct usually tells him to do. Wood from the tombs of the Egyptian kings Zoser and Sneferu, dated by dynastic records to 2625 BC give or take 75 years, came out of his counters at 2800 BC give or take 250 [9]. Agreement to a quarter of a combined standard deviation, on the first serious try. The chronology it was checked against had been assembled entirely out of king-lists.

Now the crookedness. The clock assumes the atmosphere always held the same proportion of carbon-14, and the atmosphere did no such thing, because production depends on how many cosmic rays get through, which depends in turn on the Sun's magnetic field and on the Earth's, both of which wander. Uptake depends on the ocean, which holds fifty times more carbon than the air and gives some of it back on a schedule of its own. So the concentration in the atmosphere has drifted up and down by several percent over the last fifty thousand years, and an object that died during a high-carbon-14 century looks younger than it really is, by a margin nobody could have guessed from first principles.

Two human-made distortions sit on top of that, and both are useful.

Hans Suess noticed in 1955 that wood grown in the twentieth century held less carbon-14 than wood grown in the nineteenth [10], and the reason is that coal and oil are hundreds of millions of years old, carry no carbon-14 whatsoever, and dilute the whole atmosphere measurably when a civilisation burns them at scale. By 1950 the dilution was already a couple of percent. It shows up in the calibration curve as the odd fact that a sample from exactly AD 1950 has a conventional radiocarbon age of 199 years rather than zero.

Then, between 1955 and 1963, atmospheric weapons testing nearly doubled the carbon-14 over the northern hemisphere, the test ban stopped the production, and the excess has been draining into the oceans and biosphere ever since, leaving a curve so steep and so well measured that a scrap of organic material grown in the last seventy years can often be dated to within a year or two [11]. A nuisance for archaeology. A gift for forensics, and for anybody wanting to know when a whale was born.

The Calibration Curve

Now the object this whole article was written to show you, plotted in Figure 2.

Take a tree ring whose calendar age you know because somebody counted the rings. Measure its radiocarbon age. The two numbers disagree. Write the pair down. Do it again with the next ring, and the next, and the next, for twelve thousand years of wood, and then keep going with varve-counted lake sediments and uranium-dated cave formations and corals out to fifty-five thousand years, which is roughly where the carbon gives out. What you end up holding is a map of exactly how wrong the radiocarbon clock runs at every point in the past, century by century, and the current version of that map is IntCal20 [12].

The thing to appreciate is that nobody had to assume anything to build it. The calendar axis came from counting and the radiocarbon axis came from measuring, and the two axes were assembled by different people, in different laboratories, for different reasons. The disagreement between them is the data, and it was collected by people who mostly did not know in advance what shape it would be.

Look closely at the curve and it wobbles. Those wobbles are the Sun and the ocean, recorded in wood, and they are the reason calibration turns out to be more interesting than a subtraction. Where the curve climbs steeply, a small change in radiocarbon age means a small change in calendar age and your date comes out sharp; where the curve goes flat, several centuries of calendar time share one radiocarbon age and a single measurement cannot tell them apart. The flat stretches are called plateaus, and no single fact about radiocarbon dating is more underappreciated by the people commissioning dates.

So we quantified it. Taking every radiocarbon age from 200 to 12,000 BP in ten-year steps, with a laboratory error of ±25 years, and calibrating each one against IntCal20, the median calendar range you get back is 143 years wide. The worst comes back 419 years wide, at 10,360 radiocarbon BP, and arrives in four disconnected blocks, while the best comes back 33 years wide, at 10,780 radiocarbon BP.

Those two numbers sit 420 radiocarbon years apart and differ by a factor of twelve in what they tell you about the object in your hand. Nothing about the sample changed. Nothing about the laboratory changed. The atmosphere was simply behaving differently across the two periods. The trees wrote it down.

Bench Notes: One Date, Start to Finish

We gave ourselves a measurement to work with: 2450 ± 30 radiocarbon years BP, which is an utterly ordinary number for an Iron Age sample and the sort of thing a real laboratory report contains.

First attempt took about forty seconds. BP means before 1950. 1950 minus 2450 is minus 500. So, 500 BC. Somebody wrote it on the board. Somebody else asked why we had downloaded a calibration curve.

Because 500 BC is wrong, is why. Calibrating properly means asking a different question altogether, namely for which calendar years the curve predicts a radiocarbon age anywhere near 2450, so you take the curve, you take your measurement with its error bar, you compute how well every candidate calendar year matches, and you keep the best 95.4% of the resulting probability.

What comes back is not one range. Three come back, and Figure 3 shows why.

Before believing any of that we tested the machinery two ways. First against an analytic case: feed it a fake calibration curve where radiocarbon age equals calendar age exactly, with no curve uncertainty, and the answer must collapse to the textbook Gaussian interval. Feeding it 3000 ± 30 returns 2940 to 3059, against an analytic 2940 to 3060. One year out, from the one-year grid we are working on.

Second, a coverage test, which is the one that actually matters. Pick 4,000 calendar years at random between 100 and 13,900 years ago, read the true radiocarbon age off the curve, add realistic noise, calibrate, and count how often the 95.4% interval contains the year we started from. It should be 95.4% of the time. We got 95.6%, 3,823 hits out of 4,000. The intervals are honest.

Our estimate of a half-life from a single simulated run was supposed to improve as one over the square root of the population, and it does, right up until it stops. At ten atoms the scatter is 45% of the answer; at a thousand atoms it is 4.5%; at a hundred thousand atoms it should be 0.3% and instead it sits at 1.2%. We spent a while confused before noticing that the simulation only samples the population every 0.025 half-lives, so past about ten thousand atoms we are measuring the coarseness of our own time grid rather than anything about decay. The floor is ours, not nature's. We left it in the output rather than hiding it, because finding out that your error bar is really a property of your own code is an extremely common experience and nobody writes it down.

Contamination, and Other Ways to Be Confidently Wrong

Every method described so far has a way of producing a number that is wrong and looks perfectly fine. Here we go through them one at a time, because a method you cannot break is a method you do not understand, and Figure 4 shows where radiocarbon's own limit actually sits, which is not where people usually put it.

Start with the worst one. Take a sample that is genuinely ancient, old enough that every atom of its original carbon-14 has already gone, leaving a sample with no clock left in it at all. Now let one percent of its carbon, by mass, come from somewhere modern: a root that grew through it, a fingerprint, a preservative applied by a museum in 1930, a trace of the solvent used to clean it. The measured radiocarbon fraction is now 1%, and the laboratory will report an age of 36,993 BP with an error bar of a few hundred years. No warning accompanies it, and nothing in the measurement itself looks wrong to the person holding the printout. A date comes back for an object that could be a million years old. The failure is quiet, which is exactly what makes it dangerous: a contaminated ancient sample does not return flagged or noisy or suspiciously wide, it returns looking like a clean measurement of something forty thousand years old.

Contamination damages old samples and young samples in wildly unequal measure, which is the thing to carry away, and a table shows it better than a sentence can. Read across a row to see how little a young sample cares. Read down a column to watch the identical laboratory slip turn into a catastrophe.

One percent of modern carbon costs a thousand-year-old sample eleven years. It costs a fifty-thousand-year-old sample 14,445, and the error in the laboratory was identical in the two cases.

Carbon can also come in from the wrong direction. A young sample diluted with dead carbon reads too old, and 5% of dead carbon adds 412 years to anything at all, regardless of its real age. Not hypothetical, either. Shellfish build their shells partly from dissolved carbonate that has been out of contact with the atmosphere for centuries, which makes marine material read several hundred years too old before you start, and the correction for it is regional, imperfectly known, and argued about at every conference on the subject. A hedge beside a 1970s motorway breathed exhaust from Carboniferous carbon.

The answer to all of this is not cleverer statistics. Chemistry, rather. Modern laboratories destroy the contaminated fractions before measuring anything: bone gets its collagen extracted and then ultrafiltered to keep only the large molecules that could not have come from the burial environment, charcoal gets an acid-base-acid wash, and where these treatments were introduced, published dates moved, sometimes by thousands of years and always in the older direction [13]. Some of the redating of Neanderthal sites is exactly this story. The older dates were not fraudulent and the people producing them were not careless; the pretreatment of the 1970s simply could not remove what the pretreatment of the 2010s can.

The Long Clocks

Past fifty thousand years carbon is finished, and the methods that take over run on exactly the same physics with nuclides that are simply slower about it.

Potassium-40 is the workhorse. It sits in feldspars and micas, minerals that turn up in most volcanic rocks anywhere on Earth, and it decays with a total half-life of 1.2491 billion years. The complication that makes it interesting is that potassium-40 decays two ways. Roughly nine atoms in ten emit an electron and become calcium-40, which is useless as a clock because ordinary calcium is everywhere and you could never tell the new atoms from the old, while the other 10.37% capture one of their own electrons and become argon-40, a noble gas that was not in the rock to start with. So the measurable branch is a tenth of the decay, and the branching ratio itself had to be measured separately before any potassium-argon age meant anything at all [15].

Argon being a gas is both the method's gift and its catch. Gift, because a freshly crystallised mineral contains essentially none. Catch, because a hot mineral leaks argon, so the clock does not start when the rock forms but when it cools below a temperature at which argon stops escaping. Geochronologists call that the closure temperature, and it means a potassium-argon age is answering the question "when did this cool" rather than "when did this exist", which is a different question, occasionally the wrong one, and worth checking before you quote the number at anybody.

Uranium-lead is the other long clock, and it carries a feature that nothing else in this article can match: two independent clocks running inside one crystal. Uranium-238 decays through a chain to lead-206 with a half-life of 4.4683 billion years, and uranium-235 decays through a different chain to lead-207 with a half-life of 0.7038 billion years [17]. Both parents are uranium. They sit in the same mineral in a fixed and known ratio, and both run at once, one of them 6.35 times faster than the other.

So a single zircon crystal hands you two independent ages, and they have to match. If uranium leached out, or lead leached out, or the crystal was heated, the two clocks are thrown off by different amounts and the disagreement shows up plainly on a plot. Agreement is called concordance. Nobody designed it, and it audits every single date for free. Zircon helps further by chemically refusing to take lead into its structure as it grows, so almost all the lead now sitting inside a zircon got there by decay and by nothing else at all.

Clair Patterson used lead isotopes in meteorites in 1956 to put the age of the Earth at 4.55 billion years, give or take 70 million [18]. The current best figure for the oldest solids in the Solar System, from lead-lead dating of calcium-aluminium inclusions in a meteorite, is 4,567.30 million years with an uncertainty of 0.16 million [19]. Patterson's answer sits a quarter of one standard deviation from that figure. Fifty-six years, and instruments he would not have recognised, separate the two.

What People Get Wrong, and Why the Wrong Version Is Nicer

Five things come up over and over. We have said some of them ourselves.

"Carbon dating says the rock is two hundred million years old"

Radiocarbon cannot see anything past about fifty-five thousand years and does not work on rock at all, because rock generally does not contain carbon that was ever alive. Dinosaurs are dated by potassium-argon or by uranium-lead, applied not to the bone but to the volcanic ash layers lying above and below the fossil itself. The appeal of the wrong version is simple and forgivable: radiocarbon is the only dating method most people are ever taught by name, so it becomes the name for the whole activity.

"Half life means the sample is half gone at that date"

Section 4 has the numbers. A half-life marks the middle of a distribution, and in four thousand simulated samples of a thousand atoms, exactly half were left in 2.77% of them. The wrong version appeals because it converts a statistical statement into a mechanical one, and mechanical statements are far easier to hold in your head than distributions are. In practice it is nearly harmless, because real samples contain enough atoms to make the distribution extremely narrow. Believing it does not usually hurt you. It just stops you understanding where error bars come from.

"You have to assume the decay rate has always been constant"

The strongest-sounding objection of the five, and the one most worth taking apart slowly, because it is half right. Yes, the calculation assumes a constant decay constant. No, that assumption is not untested. Decay rates have been measured directly in the laboratory for over a century, they are predicted by nuclear theory from parameters fixed by completely different experiments, and their constancy is checked by the geological record itself: the Oklo natural reactors in Gabon ran two billion years ago and left isotope ratios that would look different if nuclear parameters had shifted even slightly since. The wrong version appeals because it reframes a measured physical constant as an unexamined guess, and spotting an unexamined guess feels like insight. It would be insight, if the guess were unexamined.

"One wrong date proves the method does not work"

Wrong dates are produced constantly, and this article has explained several of the ways. A shell that fed on old carbonate, a bone with modern glue on it, a mineral that leaked argon, a sample taken from the middle of a plateau. What makes a method trustworthy is not that it never fails but that its failure modes are known, predictable from first principles, and testable in advance. The wrong version is appealing because in most of life a single counterexample really does kill a rule, and it takes some getting used to that a measurement technique is graded on its error distribution rather than on its worst case, the way a rule would be.

"Calibration means adjusting the answer until it fits"

The misconception we care about most, because the word itself invites it. Calibration here means comparing a measured quantity against a counted one and writing down the difference between them, year by year, for as long as anybody has the patience. The calendar axis of IntCal20 came from people counting rings and varves. None of them had a stake in what radiocarbon would eventually say. And if calibration were a way of getting convenient answers, it is doing a spectacularly bad job: a clean measurement of 2450 ± 30 goes in and three disconnected stretches of the Iron Age come out, with the most probable single year sitting in a block that holds only a quarter of the probability. Nobody invents a fudge factor that makes their own result worse.

What all five have in common is that the wrong version needs fewer moving parts: one method instead of eight, one rule where there is really a distribution. Fewer parts, easier to hold. And holding things is genuinely what a mind is for, which is why the wrong versions survive as well as they do, though this particular subject does not fit in one hand.

The Case Against This Article, and Why We Still Think We Are Right

Our claim throughout has been that the reason to believe any of these methods is that independent methods agree. What follows is the best version of the argument that the claim is weaker than it sounds, and we think it is a good argument, and we are not going to pretend otherwise. We would rather publish the objection and lose the argument than publish the conclusion and have somebody else find the objection a year later.

Start with the word "independent", which is doing a great deal of work. IntCal is not radiocarbon checked against something else, because radiocarbon measurements go into the building of it in the first place. The people who make calibration curves, the people who run accelerator laboratories, and the people who date zircons all attend the same conferences, use the same reference standards, and know perfectly well what number the field expects. A network of scientists who share expectations can converge on a wrong answer honestly.

Then the deepest part of the radiocarbon curve, which leans on other isotopic methods. Past about fourteen thousand years there are no trees. The curve out to fifty-five thousand rests on varve counts, on corals and cave formations dated by uranium-thorium, and on marine sediments, and uranium-thorium is an isotopic method with its own assumptions about initial thorium and about whether the carbonate stayed closed to exchange. So the oldest radiocarbon is checked against something that is not really an outsider.

Some decay constants rest on very few experiments. The half-lives of uranium-238 and uranium-235 that essentially all of uranium-lead geochronology depends on come substantially from a single careful study published in 1971 [17], and from nothing else of comparable weight. The internal concordance check we praised in section 10 cannot catch an error in those constants, because a wrong constant shifts both clocks in a correlated way. A genuine single point of failure, and the field says so out loud.

The network has also been wrong before, and took decades to notice. Until 2008 argon-argon ages and astronomically tuned ages disagreed by about 0.64%, because the age assigned to the Fish Canyon sanidine standard was off by rather more than anybody had expected [20]. Nothing internal to argon-argon dating revealed the problem, and it took a comparison against orbital mechanics to drag it into the open. If one systematic error of that size survived for that long, asking how many others are still in there is a fair question rather than a rhetorical one.

Last, agreement is sometimes enforced by judgement. When a date comes out discordant, somebody decides whether it is a real result or a contaminated sample, and "this one is contaminated" is a judgement call made by a person who knows what the other dates said. Do that enough times and you can manufacture consistency out of scatter.

Those objections are real, and two of them are not fully answerable. Figure 5 collects the evidence for what we think survives anyway.

Shared expectations, the first objection, would show up as suspicious agreement. What the record actually shows is constant small disagreement: laboratories argue about reservoir corrections, about pretreatment protocols, about which varve count is right, about whether a particular zircon is concordant. Constant small disagreement is the texture of independent measurement. Collusion looks tidier than this.

The second we concede, with a boundary drawn in the right place. Radiocarbon below fourteen thousand years is checked against counting and nothing else. That covers most of archaeology. Above it the check genuinely involves other isotopic methods, and the honest statement is that the oldest part of the calibration curve is better than nothing and worse than the tree-ring part, which is exactly what the published uncertainties on it say: the curve's own quoted error at fifty-five thousand years is about a thousand radiocarbon years, against ten to twenty in the Holocene.

Thin evidence for the decay constants is the best objection of the five, and we do not think it has a full answer inside uranium-lead. It has an answer outside it. Astronomical tuning dates sediments by matching their cyclic layering to the calculated wobbles of Earth's orbit, a calculation built out of orbital mechanics and containing no decay constants, no laboratory standards and no geochemistry of any kind. When argon-argon was tied to that, it moved by 0.64%; when uranium-lead has been compared against the same tuned sections, it has held its ground without adjustment. Only an external check can catch a common-mode error, and one exists.

Fish Canyon answers itself. We present it here as evidence for the network, because the network is what caught it, after the field had spent years reporting a discrepancy it could not explain rather than quietly splitting the difference.

Judgement calls need watching permanently, and always will, and the defences against them are the ones any field has. Rejection criteria get published before the data come in, measurement is done blind, as the three Shroud laboratories did it, and the chi-squared gets printed even when it comes to 6.4 on 2 degrees of freedom and is slightly embarrassing to the people printing it.

The summary comes out narrower than the one we started with. We like it better. Tree rings, varves and ice layers count years, and they can be checked against each other and against written history; radiocarbon is corrected by counted years wherever counted years exist, which is the last fourteen thousand of them, and corrected more loosely beyond that. The long isotopic clocks are checked against each other, against history at the young end, and against orbital mechanics in the middle, and one of those checks has already caught a real error that nothing internal could see.

None of that makes any single date certain. A date is a measurement, and measurements have distributions. What it does make is a structure in which a wrong number has somewhere to show up, which is a smaller claim than certainty and a far more useful one, and more than most accounts of the past can manage.

References