The Gold Standard of Archaeology | Calibration-Curve Plateaus, Multimodal Posteriors and False Chronological Precision

1. Calibration is a probability transformation, not a date conversion

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A radiocarbon determination reports a measured age and uncertainty in radiocarbon years. Calibration evaluates which calendar ages are compatible with that measurement under a selected curve. Because atmospheric radiocarbon has varied through time, the mapping is not a simple subtraction and the result need not be symmetric or continuous. The calibrated distribution can contain long tails, narrow peaks and separated islands of probability. Record the laboratory result, material, pretreatment, curve family and software version before interpreting the calendar range. A statement such as 950 BCE plus or minus 30 years can be seriously misleading if it treats the radiocarbon error as though it were calendar uncertainty. The shape of the curve is part of the evidence, not a graphical decoration added after the age has been calculated.

2. Recognise what a calibration plateau does to information

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On a plateau, many calendar years correspond to similar radiocarbon ages. Improving laboratory precision may then narrow the radiocarbon likelihood without distinguishing much more calendar time. A date can be analytically excellent and chronologically broad. Plateaus also interact with sample age, reservoir offsets and curve uncertainty. The correct response is not to select the centre of the broad interval or report the tallest local pixel. Show the probability distribution and state which research questions it can and cannot resolve. A plateau may still separate centuries from millennia or constrain ordering when combined with stratigraphy, but it may be unable to identify a generational transition. Precision should be judged against the archaeological question, not only the laboratory standard error.

3. Read multimodality as a real feature of the evidence

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A wiggling calibration curve can make one determination compatible with several separated calendar intervals. These modes are alternative age regions conditional on the measurement and curve, not repeated laboratory mistakes. Report all material modes and their probability mass using the software’s documented interval convention. A single weighted mean can fall in a calendar region with little or no posterior support, while the median can conceal a deep valley between modes. Before using another line of evidence to prefer one island, state that evidence independently. Typology, stratigraphy or historical association may legitimately redistribute probability, but the calibrated determination alone did not choose the preferred peak. Keeping the modes visible prevents external assumptions from being mistaken for information contained in the sample.

4. Separate the calibrated likelihood from the chronological model

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An unmodelled calibrated distribution shows what the measurement and curve imply before archaeological ordering is imposed. A Bayesian chronological model then adds information such as phase membership, stratigraphy, boundaries, offsets or deposition processes. Comparing the unmodelled and modelled distributions reveals how much precision comes from the radiocarbon result and how much comes from the prior structure. A narrow posterior is not suspicious by itself; sequence information can genuinely identify one curve intersection. But the interpretation is conditional on those constraints. Preserve both views and explain which link removed each alternative mode. If one contested stratigraphic relation causes the chronology to collapse from three possible centuries to one decade, that relation deserves more attention than the decimal places in the posterior.

5. Use sequence information without forcing the curve to confess

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Ordered short-lived samples can sometimes exploit the wiggles in the calibration curve, especially when their relative spacing is well supported. Yet sequence models can also manufacture confidence if residual material, intrusive samples, broad phases or uncertain ordering are treated as exact. Predefine which relations are observed, inferred or merely convenient. Test alternative memberships and orderings that field evidence permits. Inspect agreement and convergence diagnostics, but do not tune the model only until one mode remains. A strong chronological conclusion survives a small family of archaeologically defensible models. If several models select different islands, the honest result is model-dependent chronology. Additional well-chosen samples may help, but adding many dates of the same uninformative type on the same plateau can produce cost without resolution.

6. Worked example: short-lived seeds on a Hallstatt plateau

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A fictional storage pit contains three articulated layers of charred annual seeds. Each determination has a laboratory uncertainty near 25 radiocarbon years, yet the unmodelled calibrated distributions spread widely across the plateau and contain several local peaks. A model that treats all three as one unordered phase estimates a broad start. Adding the excavated order reduces some combinations but still leaves two plausible boundary regions. A later analyst reports only the narrower of those regions after excluding the lowest seed sample as an outlier. The field record provides no reason for exclusion. The gold-standard report retains the sample, shows both modes, compares ordered and partially ordered models and concludes that the event can be placed within a broad period but not assigned to the preferred historical generation. The worked example uses invented teaching data, not a claim about a real site.

7. Report intervals and modes without creating a false centre

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State the probability level and whether the interval is highest posterior density, equal-tailed or produced by another documented rule. For multimodal distributions, list disjoint ranges rather than joining them into one apparently continuous span. Give probability mass for each material range when the software supports it. Avoid converting the result into a midpoint plus or minus half the span. Graphs should retain the curve and distribution at readable scale, with modelled and unmodelled results distinguishable. When summarising many dates, tables can include mode count, dominant ranges and sensitivity to model variants. A concise narrative is possible without erasing shape: name the broad conclusion first, then state the alternatives that remain and the assumption that would distinguish them.

8. Changed-context transfer check: wiggle matching a timber sequence

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A timber sequence with known ring spacing can use that spacing to align several radiocarbon measurements against calibration-curve structure. The transferable principle is to distinguish information in the measurements from information in the sequence. The changed context provides exact or near-exact internal gaps, which can make curve wiggles highly informative. Yet the result dates the sampled growth sequence, not automatically felling, construction or final use. Missing sapwood, reused timber and unidentified offsets can move the archaeological event. The fit may also have alternative alignments. Report competing placements and the assumptions linking the dated rings to the event. Wiggle matching can earn precision, but only through a documented temporal pattern and a defensible event association.

9. Know the limits and common misconceptions

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A narrower laboratory error does not guarantee a narrower calendar range. A calibration plateau is not a software failure, and multiple modes are not uncertainty that can be averaged away. The tallest mode is not automatically the correct mode. Stratigraphy can sharpen chronology but cannot repair an incorrect sample association. Agreement indices do not prove the field model, and a posterior interval remains conditional on curve, priors, offsets and data. Curve updates can move ranges, particularly where evidence is sparse or uncertainty structure changes. Reservoir and old-wood effects require separate treatment. Calendar-age probability is not uniformly distributed inside a reported range. When the archaeological question demands resolution the data cannot supply, the proper answer is to redesign sampling or accept a coarser conclusion.

10. Audit the determination-to-calendar chain

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Archive sample identifiers, material and life span, context, pretreatment, laboratory reports, conventional ages, covariance where applicable, reservoir or offset choices, calibration curve and version, software and version, model code, ordering evidence, boundary assumptions, outlier settings, random seeds where relevant and convergence diagnostics. Export unmodelled and modelled distributions. Record every material mode before and after constraints, then explain which evidence altered it. Refit the chronology under plausible curve, association, ordering and boundary variants. Preserve rejected models and the reason they were rejected. An independent reader should be able to identify whether an apparently precise historical placement came from the measurement, the curve, the stratigraphy or an analyst’s decision.

11. Frequently asked questions

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Why can one radiocarbon date produce two calendar ranges? The calibration curve can pass through compatible radiocarbon values more than once. Should the two ranges be averaged? No; the average may lie where little probability exists. Does a plateau mean the date is useless? No; it can still constrain broad periods and contribute to a sequence. Can more samples solve the problem? Sometimes, especially when they add ordering or span informative curve structure, but repeated equivalent samples may not. Which curve should be used? Use the appropriate current curve for the material and region, documenting version and special corrections. Can a Bayesian model choose one mode? Yes, when defensible archaeological information supports it; report that dependence.

12. The gold standard preserves the shape of chronological knowledge

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Radiocarbon chronology becomes trustworthy when calibration is treated as an evidence-bearing transformation rather than a machine that prints one year. Plateaus reveal where calendar resolution is weak, multimodal posteriors preserve real alternatives and sequence models show exactly which archaeological relationships earn additional precision. The gold standard reports the whole shape, tests fragile constraints and lets the research question determine whether the remaining uncertainty is acceptable. A broad honest chronology is better archaeology than a narrow date created by hiding the curve.