Theoretical Radiocarbon Discrepancies Document Actions * Print this page An attempt will be made to reconcile the calibrated radiocarbon dates from Akrotiri with the traditional archaeological chronology of the Aegean Bronze Age, supporting the archaeological date of c. 1550-1500 BC for the LM IA period. ** In the past decade a number of studies have led to the impression that the calibrated radiocarbon dates for the Aegean Late Bronze Age generally tend to be earlier than the archaeological dates. To explain the difference of 100-200 years between the archaeological dating of the Minoan eruption on Santorini (/c./ 1550-1500 BC) and the calibrated dates (/c./ 1700 BC) it has been proposed that the radiocarbon samples from Akrotiri were influenced by volcanic emanations, rendering them too early due to the photosynthesis of old CO_2 ^ deriving from fissures in the ground in the volcanic surroundings. On the other hand, on the basis of a reinterpretation of the archaeological evidence it has recently been argued that the archaeological correlations with the historical chronology of Egypt may well be consistent with the 'high' radiocarbon dating. My paper will take a closer look at the radiocarbon dates from the Aegean Late Bronze Age and from Egypt. Using the new high-precision ^14 C calibration curve, it will first be shown that in Egypt the historical chronology and the radiocarbon dates agree within margins of error judged to be 1-3 decades at the time of Dynasties XVIII-XX. This is demonstrated by sequencing the radiocarbon dates according to the known age of the Egyptian samples. When fixed to the calibration curve by Archaeological Wiggle Matching (AWM) the ^14 C dates are in perfect agreement with the historical chronology and, furthermore, show the expected fine variations in atmospheric ^14 C content. Using the same method, it will be judged that the radiocarbon dates from Akrotiri do not necessarily disagree with the traditional archaeological date for the Minoan eruption. The dates may well calibrate to /c./ 1550-1520, though not later than 1500 BC. However, the calibration reading is not unique and a date 100 years earlier, supporting recent tree-ring and ice-core studies, cannot be excluded. To find a unique ^14 C date for the Minoan eruption, an effort was made to develop an AWM sequence for all the radiocarbon dates of the Aegean Late Bronze Age, but here the interpretation of the radiocarbon dates is heavily dependent on the rather poor archaeological information available for the samples. The validity of the traditional chronology is, however, further supported by an analysis of the reasons why the Akrotiri dates appear to calibrate to 1700 BC, even though the samples may actually derive from /c./ 1520 BC. Calibration is essentially the task of transferring the ^14 C dating probability from the ^14 C time scale to the calendric time scale. Owing to the non-linear properties of this transformation, it is quite inevitable that the calibration readings are distorted. Model studies assuming precisely measured ^14 C dates for samples from 1550-1500 BC show that the mean value of the calibrated dates is necessarily /c./ 1650 BC, both for single dates and for larger date sets, irrespective of the actual age of the samples. This is because the calibration curve is essentially flat, with a few re-entry wiggles, from 1500-1700 BC A further implication of the non-linearity of calibration is that all archaeological ^14 C chronologies based on large numbers of dates are fixed to artificial regions of the calendric time scale and will be distorted quite generally. The problems of the calibrated ^14 C dates at the site of Akrotiri thus have to be generalized. Because the calibration readings of all ^14 C dates adhere to specific time intervals it appears appropriate to look at radiocarbon dates in the general terms of what I like to call ^14 C Quantum Chronology. *INTRODUCTION* When first published a decade ago there was some unrest about the radiocarbon dates from Akrotiri. Whereas the archaeological date for the destruction of the LM IA settlement was generally assumed to be about 1550-1500 hist BC (Marinatos 1939; Branigan 1973; Cadogan 1978; Hood 1978), the calibrated radiocarbon dates gave an age estimate of /c/. 1700 cal BC (Michael 1978). A review of the material evidence for the historical dating of the Aegean Late Bronze Age showed that a date as early as 1700 hist BC for the end of the LM IA period was not substantiated by the archaeological record (Betancourt and Weinstein 1976). The Pennsylvania laboratory ran a second series of ^14 C measurements and verified the results (Weinstein and Michael 1978). Because the majority of the ^14 C dates had been processed on selected short-lived plant materials such as grain and beans there was no reason to suppose that the age difference was due to the dating of 'old wood' materials. *COMPARISON OF CALIBRATION PROCEDURES* To begin with I will present a preliminary analysis of the Akrotiri dates, emphasizing that prior to interpreting calibrated dates it is useful to study the properties of the method used in their calibration. The dates have been assembled in Table 1 and are converted using the qualified high-precision curves of Pearson and Stuiver (1986) and Stuiver and Becker (1986). The various calibration methods now in use are reviewed by Aitchison /et al/. (1988). In the present paper the method used is 2-D Dispersion Calibration (Weninger 1986a, 1986b). This method assumes a Gaussian probability distribution for each date and transfers the total dating probability, by option either for single dates or for archaeological groups, from the ^14 C scale onto the calendric timescale. To avoid the ambiguities produced by multiple intersections of the dates with the calibration curve, the dates are calibrated from the viewpoint of the calendric timescale. Michczynska /et al/. (1988) support this approach and maintain it can be based on Bayesian probability theory. Robinson (1988) has proposed a calibration procedure in which the concept of an intersection is no longer implicit, an efficient and elegant integral approach. The method is available as a microcomputer program (CALSTS5) and the results are included in Table 1 for purposes of comparison. The methods give essentially identical results. Looking closer, some small, but systematic differences can be recognized. For the series as a whole (Table 1 a-d; N=33) the procedures used in 2-D Dispersion Calibration give a mean date which is younger by 12 ± 10 years than the mean date calculated by CALSTS5. A small and possibly systematic difference amounting to 3 years can also be recognized for the calculated SD. In the light of the complexity of the calibration algorithms such differences are not unexpected and it is satisfactory they do not turn out larger. *DISCREPANCIES AND INCONSISTENCIES OF THE DATES* Weinstein and Michael (1978) draw attention to a number of problems concerning some of the individual dates and also the series as a whole. A few examples of dates 'typical' for the series will illustrate the problem. First, a sample of seeds from a storage jar in Room 5 of the West House gives a date of 3340 ± 60 BP (P-2791). This date calibrates to 1622 ± 82 cal BC, a value which agrees within 95% error limits with the traditional archaeological date of /c./ 1550-1500 hist BC. Second, a grain sample from another jar in the same building dates to 3310 ± 60 BP (P-2565) which is equivalent to 1593 ± 79 cal BC. This is also an acceptable date. Third, a sample of beans from a further jar dates to 3340 ± 55 BP (K-3228) and calibrates to 1605 ± 88 cal BC (Table 1a). The date is, again, not problematic. A fourth radiocarbon determination on the young side of the interval 1550-1500 hist BC is P-2794: 3180 ± 50 BP or 1459 ± 53 cal BC. The date is not unacceptable. Judged individually, none of the 25 dates in Table 1 a-d would appear to be problematic. However, according to Weinstein and Michael (1978) the series as a whole calibrates earlier than expected. Today the alleged discrepancy is readily obvious, I judge, only for the two specific dates P-2560 and P-2561 which were processed on grain from jars M2 and M3 of Room 5 of the West House. The samples date to 3980 ± 70 BP (2491 ± 105 cal BC) and 3800 ± 50 BP (2235 ± 92 cal BC) respectively. It is quite curious why these samples, taken from two neighbouring storage jars on the ground floor of the West House, should date too old by at least 500 years. The grain samples from other storage jars of the same house give satisfactory dates. The radiocarbon determinations are similar to P-1893: 3990 ± 70 BP. This date was processed on charcoal found at a depth of 2 m below the floor level in Room 4. An age of 2507 ± 107 cal BC for this sample is not unexpected because it was stratified deeply below the Late Minoan deposit. This would also apply to the wood sample P-3046 dated to 2278 ± 334 cal BC. *VOLCANIC CARBON DIOXIDE* ** We will now reconsider the possibility that the dates have been influenced by emanations of volcanic carbon dioxide. The proposal that volcanic carbon dioxide, deficient in ^14 C, may have affected the plants growing during the LM IA period was first made by Michael (1978). Subsequently Bruns /et al/. (1980) demonstrated that modern plants on Thera actually do have pseudo-ages. This was shown to be the case for plants growing in the close vicinity of submarine CO_2 sources in the bay of Palaea Kameni. One plant at a distance of 5 m from the emanations had an apparent age of 1390 BP (H-5745). A second plant 10 m away from the same source gave a date of 1030 BP (H-5748). But then a third plant (H-5742) growing at a distance of 100 m had a 'modern' age and was apparently not assimilating 'old' CO_2 , In this way the pseudo-ages were strongly dependent on the distance of the plants from the CO_2 emanations, a natural phenomenon which can be explained by the quick admixture of the outflowing CO_2 with the atmospheric CO_2 . A further study on the influence of volcanic CO_2 void of ^14 C on the age of plant materials is available for the Eifel region, western Germany (Bruns /et al./ 1980). The authors show that the apparent ^14 C ages will generally depend both on the strength of the CO_2 ^ source and on the strength and direction of the prevailing winds. Plants growing near the Lake Maria Laach, for example, had apparent ages of 830 BP, 736 BP, 480 BP, and 460 BP at distances 1-20 m from the source. But again at a distance of 50-100 m 'modern' dates were obtained. Chatters /et al/. (1969) also report on local ^14 C deficiencies for volcanic fumaroles. The observation that the fossil CO_2 is locally confined is furthermore made for plants growing near to a heavily-travelled motorway and breathing in carbon dioxide from the automobile exhaust-gases. At a distance of 100 m to the highway the ^14 C contents of the plants was at a level of 98% of the natural, undisturbed ^14 C (Freundlich 1979). However, Sulerhitzky (1970) has reported on apparent ages of up to 2280 BP even 2 km away from the volcanoes on the Kunashir and Simushir Islands, Russia. Bruns /et al/. (1980) observe that, whereas the δ^13 C values of the emanations in the Eifel (δ^13 C = -4‰ to -5‰) are similar to clean air CO_2 (δ^13 C= -8‰, at Thera the fractionation of the carbon isotopes amounts to (δ^13 C ~ 0‰. There may thus exist a method by which to determine whether the LM IA samples have been influenced by volcanic CO_2 or not. δ^13 C measurements are available for the samples K-3227: 3400 ± 70 BP (charcoal, δ^13 C= -20.3‰) and K-3228: 3340 ± 55 BP, (beans, δ^13 C = -20.60‰) and the values do not appear unusual. But all we can safely say is that if ^14 C depressions have existed on Thera during the LM IA period, they are most likely to have been locally restricted. Plants growing at different positions on the island would have strongly varying ^14 C contents, depending on their distance from the source(s) of volcanic CO_2 and on the strength of the source. Thus, although it cannot be excluded that the dates P-2560 and P-2561 have been influenced by volcanic CO_2 , this appears unlikely for the other dates. I am tempted to speculate whether the two grain samples P-2560 and P-2561 could have derived from one crop and were mixed and homogenized in their ^14 C contents during the harvest. *UPDATING AND EXTENDING THE LATE MINOAN IA PERIOD * Let us return to the discussion of 1978. As Renfrew (1980) remarked, there were other and more apparent reasons that made it inadvisable to talk of an 'early trend' of the calibrated dates. First, it was unsatisfactory simply to give the calibrated dates the standard deviations of the conventional dates. By this the overall calibration errors were grossly underestimated. Second, although the mathematical procedures incorporated in the MASCA calibration scheme would smooth away the 'Suess' wiggles, it had not been checked whether the other calibration schemes (e.g. Suess 1970; Clarke 1975) supported the results. This means that until recently the discrepancy (excepting the dates in Table 1d) may well have been built on sand. Betancourt (1987) has recently evaluated the archaeological synchronisms between the Aegean and Egypt a second time. Beyond abandoning the carbon dioxide hypothesis and asserting that a subset of the dates forms one of the most internally consistent groups of dates available, he now concludes that the archaeological evidence would allow an updating of the end of LM IA by about 100 years. Betancourt and Michael (1987) re-examine the Akrotiri series and reject all but nine of the 22 dates as having been processed on undersized samples or being deviant. The nine remaining dates are supposed to calibrate to 1619 ± 20 cal BC (1σ) on the bi-decade Pearson-Stuiver curve. Using the ten-year Stuiver-Becker curve they obtain a 1σ range of 1680-1600 cal BC and a 2σ range 1687-1575 cal BC, thus maintaining an early date for the Thera eruption. I venture to challenge these readings on grounds to be presented later. A correction of the late Aegean Bronze Age chronology had previously been conceived by Warren (1984), who considered it possible to raise the date for the beginning of LM IA by 50 years to /c./ 1600 hist BC, but not much higher. A review of the recent studies on the Akrotiri dates is by Aitken (1988) who shows that the 95%-confidence interval for the mean calibrated date on the short-lived samples is 1620-1525 cal BC (N=14). He criticizes the practice of rejecting dates for reasons not apparent. Warren (1988) remarks on the low precision of the date and notes that it covers both the 'early' and the 'late' chronology. The early date for the Thera eruption is possibly supported by research in dendrochronology. For bristlecone pines growing at high altitudes in the western US, frost damage has been observed for the tree rings of 1628-1626 dendro BC. This is the only serious frost damage observed in the second millennium dendro BC and it has been considered possible that the volcanic eruption on Thera could have emitted sufficient amounts of dust into the stratosphere to cause one or two abnormally cold winters (LaMarche and Hirschboeck 1984). A similar reduction in tree-ring growth has been observed in Irish peat oaks of the same age. Baillie and Munro (1988) have considered the question of tree-ring growth in some detail and they would not rule out a dramatic global effect of the volcanic dust veil. An early date is also supported by observations made on ice cores at Camp Century in Greenland. Distinct variations are noted in the acidity of the ice layers dating to 1644 ± 20 BC. The acid deposits could derive from aerosols emitted into the stratosphere during the volcanic eruption on Thera (Hammer /et al/. 1987). *ARCHAEOLOGICAL WIGGLE MATCHING* As a step towards a further understanding of the radiocarbon dates from Akrotiri we will now study the properties of a series of dates from Egypt. Single ^14 C dates are known to be of some limited value and in order to date an archaeological event reliably it is generally advised to make use of longer date series. In this case the method of comparing not only the BP values of ^14 C dates but also their time-derivates (i.e. their 'wiggles') with the calibration curve enables the precision of the calibration to be improved considerably, as was recognized by Ferguson, Huber, and Suess (1966). Curve-fitting techniques have since then found a wide range of applications in tree-ring studies (Clarke and Renfrew 1972; Clarke and Sowray 1973; Clarke and Morgan 1983; Pearson 1986). As was first demonstrated by Neustupny (1973) the wiggle matching technique can be adapted to ^14 C dates on archaeological samples. The basic idea in Archaeological Wiggle Matching (AWM) is to estimate the distance in calendric years between each of the samples of a series and then to fit the dates simultaneously to the calibration curve (Weninger 1986, 1987). The main difficulty is to estimate the errors of the sample sequence. Further studies have shown that the method of AWM can be supported herein by quantitative archaeological methods, for example, ceramic seriation (Weninger 1988). *RADIOCARBON DATING OF THE XVIIIth - XXth DYNASTIES IN EGYPT* For the XVIIIth-XXth Dynasties there are 75 dates with sufficient sample information to apply AWM. The dates are presented in Table 2 along with brief information on the dated plant materials and on the archaeological provenance of the samples. A large number of the dates are on short-lived reed samples (mostly /Desmostachya bipin/nata) built into the mudbrick of pyramids at Dra Abu El-Naga (Olsson and El-Daoushy 1979). The samples are from the tombs of Tjanefer (1267-1168 hist BC), Roma-Roy (1244-1196 hist BC), Inhernakht (1290-1273 hist BC), Bekenkhons (1273-1223 hist BC) and Nebwenenef (1290-1273 hist BC), who were high officials during the reign of Rameses II. The dates given are based on the assumption that the reign of Rameses II began in 1290 hist BC (cf. Olsson and El-Daoushy 1979). Column (3) shows the results of calibrating the single dates by the method of 2-D Dispersion Calibration. The standard deviations (SD) of the calibrated dates range from σ = ± 53 cal BC (Q-2405) to σ = ± 338 cal BC (P-5). Beyond depending on the SD of the archaeological dates and on the calibration measurements, the SD of the calibrated dates are largely a function of the shape of the calibration curve. The estimated historical age of each sample is presented in column (6). The historical dates are based on Olsson and El-Daoushy (1979) and on Hayes (1980). Column (7) contains the calibrated mean date of the group, whereby the averaging was performed before calibration. The AWM sequence of the dates is given in columns (8) and (9) with D = time distance of each date to the following date, and S = sum of time distances. For example, the series covers an interval S =280 years. The sample U-5013 (group 11) is S = 55 years older than the youngest sample of the series P-1696 (group 1). The largest single time jump is D = 40 years between P-227 (group 22) and UCLA-1390 (group 21). Naturally, the AWM sequence rests on a number of interpolations. For example, the dates P-227 and P-5 of group 22 were processed on a piece of wood dated 'to the reign' of Seti I (1318-1304 hist BC). The dates were assigned to 1311 hist BC - i.e. the centre of the historical interval. When arranged in a fixed floating historical chronology in this manner, the dates can be calibrated simultaneously. It has been chosen, arbitrarily, to calibrate the series by dating the youngest event, group no. 1 of dates on reed samples from the grave of Tjanefer. The results are presented for the bi-decade calibration curve of Pearson and Stuiver (1986) in Fig. 1 and for the 10-year curve of Stuiver and Becker (1986) in Fig. 2. In both cases the AWM date of group no. 1 is 1175 cal BC. This result is in near perfect agreement with the historical date of 1168 hist BC. The statistical dating error is difficult to estimate but if is judged to be ± 30 cal BC (± 1σ) for the individual dates (N=78 dates) and 20 cal BC (± 1σ) for the averaged dates (N=34 groups). The error estimates are based on confidence intervals derived from chi-square statistics, but it should not be overlooked that a completely objective analysis of the dating accuracy is precluded due to the difficulties in estimating the errors in the sample sequence. We can conclude that there is excellent agreement between the radiocarbon dates and the Egyptian historical dates for the Dynasties XVIII to XX. *THE WIGGLE AT 1196 CAL BC* I would now like to draw attention to the scatter of the archaeological dates around the wiggles. A comparison of Fig. 1 and 2 shows that the scatter of the dates around the 20-year wiggles is considerably larger than for the 10-year wiggles. This may be an indication of 1-year variations of atmospheric ^14 C. Should this be the case, the 20-year calibration data would be smoothing the atmospheric ^14 C variations to such an extent as to produce artificial 'discrepancies' for the readings of some of the dates, notably on the short-lived samples of Roma-Roy. As can be recognized from Fig. 2 there is a strong wiggle at 1196 cal BC from which the reed samples (groups 6 and 7) may derive. The bi-decade calibration curve in Fig. 1 does not show this wiggle. Table 3 gives a close-up view of the relevant region of the calibration curves. The weighted mean average of the combined dates of group 6 and 7 is 3022 ± 22 BP (N=9). This date agrees well with the value of 2997 ± 24 BP of the 10-year calibration curve at 1196.5 cal BC. It supports the historical date to within an accuracy of 10 years. This is the width of the block of ten tree rings used in the calibration measurements. Unfortunately the date is not unique and an older reading cannot be excluded. *A 'DISCREPANCY' : THE DATE OF ROMA-ROY* Wiggles of such high-frequency and amplitude are easily over-looked and, as in the case of the ^14 C oscillation at 1196 cal BC, there is the real danger that a radiocarbon date, though well measured, may be a 'near miss' to a strong wiggle. The age estimate may then turn out considerably too old. For similar reasons it is difficult to develop a calibration method which gives precise, unbiased results for all sample ages. With the method of 2-D Dispersion Calibration, for example, the dates of group 6 (N=9: 3009 ± 29 BP) calibrate to 1275 ± 66 cal BC. The results of CALSTS5 are quite similar: 1278 ± 65 cal BC. The date is /c./ 80 years too old in both cases. The dates of group 7 (N=3: 3062 ± 33 BP) have an age 1353 ± 55 cal BC (CALSTS5: 1349 ± 52 cal BC) and here the deviation from the historical date amounts to 150 years. *A 'DISCREPANCY' : THE DATE OF SESOSTRIS III* ** Although the Egyptian radiocarbon dates have repeatedly been shown to be in good agreement with the historical chronology (e.g. Quitta 1972; Clarke 1978) in recent studies Hassan and Robinson (1987) have noted that unexplainable discrepancies still exist for a few of the Egyptian dates, even though they are calibrated on the high-precision curve. Notable discrepancies are for six dates processed on a beam of cedar wood from the funerary boat of Sesostris III. The dates are of some interest because the 7th year of the reign of Sesostris III (reign /c./ 1878-1843) coincides with an astronomical observation of the rising of the star Sirius which gives the date of /c./ 1872 BC (Smith 1964).The radiocarbon determinations are UCLA-900: 3640 ± 80 BP, C-81: 3621 ± 180 BP, BM-22: 3530 ± 150 BP, GrN-1157: 3550 ± 55 BP, GrN-1178: 3610 ± 50 BP and P-1821: 3600 ± 70, an internally consistent series. The weighted average of the dates is 3593 ± 29 BP which calibrates to 1955 ± 55 cal BC (Hassan and Robinson 1987, 125, 133). To explain the deviation of 120 years between the historical-astronomical date and the calibrated age estimate, it was considered that the sample could represent 'old wood'. This is indeed likely but we can offer the alternative explanation that the date represents a 'near miss' to the unusually strong ^14 C fluctuation at 1836.5 cal BC: This wiggle is dated to 3541 ± 27 BP (Stuiver and Becker 1986, 879), a value which agrees within 95% error limits with all six single dates. Both neighbouring tree-ring decades have lower dates of 3475 ± 27 BP (1826.5 cal BC) and 3471 ± 27 BP (1846.5 cal BC). However, the reliability of the pooled mean date on the cedar beam is difficult to judge and the calculated low-limit standard deviation of ± 29 BP may be unrealistic. *ESTIMATING RADIOCARBON DISCREPANCIES* The high frequency and amplitude of the atmospheric ^14 C variations makes it quite difficult to conceive calibration calculations which avoid such discrepancies. Our case studies demonstrate that even precise radiocarbon determinations may appear 'too old' by up to 150 years simply due to the fact that the sample derived from a strong wiggle. Now, we can readily expect the calibration deviations to be a function of quite a large number of parameters such as the SD of the dates, the SD of the calibration measurements, the shape of the calibration curve, the time-width of the dated sample and of the calibration samples, whether or not the calibration curve has been smoothed, notably the frequency and amplitude of the wiggles, and finally the sample age. In order to obtain a quantitative estimate of theoretical discrepancies we will make use of a probabilistic model based on the Trondheim high-precision calibration data (Radiocarbon 28, 1986). The basic idea is to take an ideal sample of known calendric age, date the sample as precisely as possible, calibrate the date as accurately as possible and finally compare the result with the known sample age. The theoretical discrepancies can then be calculated as the numeric difference between the given sample age and the derived calibrated radiocarbon age. However, as Robinson (1986, 1988) has noted, experimental calculations show that for most regions of the high-precision calibration curve the output ages actually compare well with the input ages. I have performed similar calculations and have found similar results. For the presently available routine dates on archaeological samples, having standard deviations of ± 50 BP upwards, the deviations are usually safely covered by the standard deviations of the calibrated dates. This may seem satisfactory, but two points can be made. First, the non-linearity of the calibration curve in many cases does lead to systematic distortions of the calibrated dates which are larger than the SD, albeit noticeable for specific dates, for longer date series, or for dates of higher accuracy. Second, the calculation of weighted averages of calibrated dates will, in general, not be justified. The calibration deviations define a lower limit to the SD of pooled dates and the limit is independent of whether the pooling is performed before or after calibration. If the dates are pooled before calibration, as is usually proposed (in order to achieve 'more accurate' results), the results are more apt to underrun the limit. The SD of ± 20 cal BC proposed for the nine pooled Akrotiri dates by Betancourt and Michael (1987) underruns the limit and is unrealistic. Our approach to analysing such final limits to calibration is illustrated in Fig. 3. The probability distributions presented here are based on a constant sample distribution and utilize 800 dates interpolated at steps of ten calendar years from the high-precision calibration data (Radiocarbon 28, 1986). The series thus covers 8000 calendar years and we are making the assumption that the sampling probability is not a function of the age of the sample. Each of the 800 dates is assumed to accord to Gaussian statistics and to have a standard deviation of ± 50 BP. The dates were added to a histogram of the total dating probability (Geyh 1969). The histogram was then transferred back to the calendar time scale by the method of 2-D Dispersion Calibration. The calculations were run to an accuracy of 1 year and the SD of the calibration measurements were taken to be ± 20 BP from 0 to 7000 BP. The 'Gauss-over-Gauss' calculations necessary to include both the SD of the dates and of the calibration measurements were in each case truncated at ± 3σ. Fig. 3 shows (a) the dating probability on the ^14 C scale and (b) the reading probability for this histogram as viewed from the calendric time scale. The shape of the ^14 C histogram can be understood as representing the constant sample distribution viewed from the direction of the ^14 C scale. The conspicuous peak on the ^14 C scale at 2480 BP, for example, lies directly opposite to the flat region of the calibration curve from 800-400 cal BC now commonly known as 'Pearson's Peril'. The 2480 BP peak contains 40 dates interpolated for 40 samples of 800-400 cal BC. Other regions of the ^14 C scale with enhanced dating probability are 4100 BP, 4500 BP, and 6100 BP. The shape of the probability distribution on the calendric timescale is the result of the fact that ^14 C dates reading onto flat regions of the calibration have a larger number of crossing points than dates reading onto steep regions with few re-entry wiggles. In our example, wherein the dates have σ = ± 50 BP, the readings between 800 and 400 cal BC are enhanced by a factor three. The artificial reading probability is also high at 1800 cal AD (100 BP), 600 cal BC (2480 BP), 3200 cal BC (4500 BP), and 5100 cal BC (6100 BP), and further local maxima are situated at 1600 and 1850 cal BC. A local minimum is at 1450 cal BC. The physical background to Fig. 3 is best understood again in the particular case of the flat regions of the calibration curve. For the period 800-400 cal BC the atmospheric carbon-14 level has decreased exponentially at almost exactly the same rate as the natural radioactive decay of carbon-14. Thus for the time span of 400 calendar years following 800 cal BC all plants, when measured with reference to AD 1950, have ^14 C contents of 2480 BP. We assumed earlier that the sampling probability was not a function of the sample age; however, as a result of the non-linearity of the calibration curve, both the dating and the reading probability turn out to be a strong function of the sampling age. *QUANTITAZATION OF RADIOCARBON CHRONOLOGY* This comes to the following. Radiocarbon dates on archaeological samples have preferences on the ^14 C scale and their readings have preferences on the calendric timescale. With such a behaviour radiocarbon chronology is a function of time, a quite disturbing vision. This is illustrated in more detail in Fig. 4 where five Gaussian dates with values running from 4520 BP to 4360 BP are set at equal intervals on the ^14 C scale and given SD of ± 45 BP. There is a real chance that all five dates were processed on the same sample. How old is this sample? We notice first that the calibrated probability distributions are not Gaussian but rather have peaks at Φ_1 = 3300 cal BC, Φ_2 =3400 cal BC, and Φ_3 = 3000 cal BC. With this, each of the five dates can be expanded to some degree of accuracy in a series of time states with varying probability and will satisfy the equation: Age estimate (cal BC) =a_1 Φ_1 + a_2 Φ_2 + a_3 Φ_3 Each calibrated date is now represented in a coordinate system of three orthogonal functions Φ_1-3 and is specified in this system by its three alternative ('either/or') coefficients a_1-3 . The amplitude a_1 of the time state at 3300 cal BC, for example, diminishes from left to right in Fig. 4. But because the sample has one and only one age, it is possible (though not necessary) that two of the three coefficients are equal to 0. If we choose a_2 = a_3 = 0, then a_1 = 1 and the true age of the sample is 3300 cal BC. Unfortunately, having no knowledge of the true sample age, we must allow for finite a_1 , a_2 , and a_3 . What is important is that the readings at Φ_1-3 appear enhanced for all five calibrated dates. As can be seen in Fig. 3, there are not more than a few dozen such time states that are basic to radiocarbon chronology. The strength and position of the states depends partly on the assumed standard deviation of the date to be calibrated. *THE AKROTIRI DATES* The results of calibrating the Akrotiri series by the method of 2-D Dispersion Calibration are shown in Fig. 5. The ^14 C histogram has a strong peak at /c/. 3350 BP with a width (Full Width Half Maximum) of 200 BP. The peak is of Gaussian shape with a pronounced step on its younger side. I have no explanation for this step. However, the dates read onto the wiggles of the calibration curve a number of times at /c./ 1600 cal BC and once only onto the small irregularity of atmospheric ^14 C at /c./ 1520 cal BC. Because the readings at 1600 cal BC and 1850 cal BC are enhanced, the distribution is distorted and its median value is artificially displaced /c./ 150 calendar years beyond the traditional archaeological date of 1550-1500 cal BC. *CONCLUSION* Theoretical studies give reason to suppose that radiocarbon chronology will show artificial time states on the ^14 C scale and on the calendar timescale. The concept offers an explanation, quite tentatively, for the difficulties encountered in earlier interpretations of the Akrotiri dates. -------------------------------------- /For figures and tables please refer to book/. *Figures and tables mentioned in this paper:* *Fig. 1:* Archaeological Wiggle Matching for 75 radiocarbon dates of Dynasties XVIII-XX. 20-year calibration (Pearson and Stuiver 1986). *Fig. 2:* Archaeological Wiggle Matching for 75 radiocarbon dates of Dynasties XVIII-XX. 10-year calibration (Pearson and Stuiver 1986; Stuiver and Becker 1986). *Fig. 3:* Probability distributions assuming 800 Gaussian dates with σ= 50 BP and a time constant sample sequence. *Fig. 4:* 2-D dispersion calibration of dates 4520-4360 BP. *Fig. 5:* 2-D disperstion calibration of the Akrotiri dates. *Table 1:* Akrotiri, short-lived samples LM IA. *Table 2:* AWM Egypt, XVIII-XIX dynasty. *Table 3:* Comparison of the ^14 C date of Roma-Roy with the calibration data. ----------------------------------------- *Source:* *"Thera and the Aegean World III"* *Volume Three: "Chronology"* Proceedings of the Third International Congress, Santorini, Greece, 3-9 September 1989. *Pages:* pp. 216 - 231 *Written by:* B. Weninger lnstitut für Vor- und Frühgeschichte. D-7400 Tübingen, Germany *Book information:* ©The Thera Foundation *ISBN:* 0 9506133 6 3 ISBN (Vol 1-3) 0 9506133 7 1 *Published by:* The Thera Foundation, 105-109 Bishopsgate, London EC2M 3UQ, England *Editor:* D.A. Hardy with A.C. Renfrew To order the 3 vol. book from amazon.co.uk: http://www.amazon.co.uk/exec/obidos/ASIN/0950613371/qid%3D1142955023/202-1072334-5731058 Created by pmnae Last modified 2006-03-26 16:13 Search Upcoming Events 2009-09-22 3rd Greece – Japan Workshop: Seismic Design, Observation and Retrofit of Foundations Petros M. Nomikos Conference Centre, ------------------------------------------------------------------------ ------------------------------------------------------------------------ therafoundation disclaimer | privacy policy | donations