This technique produces no calendar years or absolute dates, it yields radiocarbon years, which are expressed as sets of statistical probabilities. To treat them as actual ages or to 'calibrate' them as such is therefore unsatisfactory (Muzzolini 1999b). Usually results are expressed with tolerances stated at one standard deviation, which means that under ideal conditions (which do not exist), the true 'age' of the sample should lie between the tolerance values in 68.26% of cases. But in the first instance, there are many problems with this assumption, and in the second, even if they did not exist, such a result is not a 'date' that one can simply compare with some other data, such as another 'date' (Bednarik 1994c). In comparing two such results, the probability that the deductions we are likely to make from them are all true is only 46.59%, or 31.80% for three dates, and so on. If we compare statistical probabilities we must not treat them as finite facts or figures, and when we compare sets of probabilities derived from two different methods (e.g. 14C and TL analyses) we are also bringing into correlation two sets of complex qualifications. We are truly comparing oranges and apples, and the logical underpinning becomes practically unmanageable.
But these simple qualifications refer to ideal conditions, which in any case do not exist in reality. We have already seen above that the technique relies on three false assumptions: that we know the atmospheric concentration of carbon isotopes in the distant past - we do not know it; that we know the isotope's true decay rate - we think we do but nevertheless use a wrong one; and that the decay process has not been influenced by factors other than the decay rate - we know this to be false. In considering just the first of these limiting factors in detail, we could examine just why the initial atmospheric concentrations of 14C and d13C are not known. There is, for example, an intricate relationship between atmospheric d13C, climate and vegetation: different plant communities facilitate specific carbon regimes. Shrub-dominated communities (C3 plants) provide values of between -12 p.mill. and -10 p.mill. d13C in respiratory CO2, grasses (C4 plants) -3 p.mill. to +1 p.mill. (Cole and Monger 1994). C4 plants, so called because of the four-carbon acids in which carbon dioxide is initially captured in their outer mesophyll cells, have a physiological advantage over C3 plants in low atmospheric carbon dioxide concentrations (Robinson 1994). The latter are directly related to world climate and were significantly lower during the Pleistocene glacials. This introduces yet another variable, the effect of which is an unknown factor and questions the utility of all Pleistocene radiocar-bon dates. Vulcanism would tilt the regime in favour of 12C, rendering atmospheric carbon balance apparently 'older'. Further, the effects of cosmic rays cannot be known for past periods.
These systematic problems may sound disconcerting, but they are only the tip of an iceberg. They and other variables affecting the result (e.g. the de Vries effect, isotopic fractionation, differences in laboratory treatment, laboratory error) represent reasonable risks because they are to some extent expected. Contamination is always possible, before, during and after sample collection (e.g. oil film on supposedly sterile aluminium foil). Hedges et al. (1998) have found that the standard acid treatment (acid-base-acid washes) of radiocarbon samples does not necessarily remove oxalates. A similar observation was made by Armitage et al. (1999), who observed that four results from a sample of Mayan charcoal paint averaged about 1440 BP, using oxygen-plasma treatment, while the same sample yielded a date of about 11 770 BP, using standard pre-treatment. Bearing in mind that most of the rock paint samples so far analysed, particularly those from European caves, received this standard pre-treatment, it is obvious that such results need to be consi-dered much more carefully than has been the case in the archaeological literature.
Just as serious is the plethora of general environmental variables that can significantly affect carbon isotopes. Among them is the hard water effect (the deposition of calcium and magnesium salts from aqueous solution in ground water), exchange with the atmosphere, humic acid, and especially the effect of the introduction of very old carbon from a variety of sources. Watchman (1998) has observed the occurrence of hydrocarbon aerosols derived from diesel exhausts, settling with airborne sand on a rock art site hundreds of metres from a road. Such deposits have the potential of significantly distorting the ratio of carbon isotopes in the surface deposit on an art panel. Just as a tree growing next to a busy motorway is likely to derive much of its carbon by assimilating exhaust fumes from vehicles burning ancient hydrocarbons, an animal or plant may contain high levels of carbon derived from a limestone environment. Thus the 14C level in the ivory of an elephant, related to its food source, may differ according to the geolo-gy of the live animal's environment. The gaseous emissions of volcanic eruptions may age a sample, major forest or grass fires may make it appear younger, and past variations in cosmogenic radiation may have either effect.
Finally there is the whole class of problems relating to the fact that rock surface layers are usually open carbon systems, which can be quite significantly affected by a variety of processes (see section above on inclusions in accretions).
The greatest difficulty, however, is misinterpretation of results by archaeologists. A fragment of charcoal is not of the radiocarbon age derived from it (it is younger), and the soil from which it was excavated is not necessarily of the same age as the piece of charcoal (taphonomy sees to that). Archaeologists have introduced their inductive reasoning into rock art dating in several ways, especially through their favoured technique of carbon isotope analysis. Accordingly it has been assumed that charcoal pigment found in rock paintings must be of the same age as the picture. There is clearly no connection between the two, except that the picture should be more recent than the date secured from the charcoal, but the difference may be tens of millennia. When a motif yielded two different dates it was seen by various authors as proving that repainting had occurred, when in fact there are several alternatives possible:
a. The true age lies outside stated tolerances, of one or both samples;
b. Charcoal fragments of different ages were used at the same time;
c. The picture was retouched at a later time;
d. One or both samples are contaminated;
e. One or both samples provided erroneous results;
f. There were differences in laboratory procedures;
g. Or there could be any combination of some of the above factors.
Thus archaeological deductions drawn from charcoal paint dates may be essentially valid, or they may quite easily be false. Bearing in mind that as a rule these data were acquired by AMS analysis from exceedingly small samples, measuring only in the order of milligrams of carbon, the kinds of interpretations of these results we have already seen proliferate in the literature are certainly unwarranted.
Having said all this, it is timely to remember that, in the final analysis, radiocarbon dating remains one of the most reliable, most precise and most widely used techniques of estimating the age of rock art. This provides a fair measure of the very real complexity of dating issues, and of the qualifications concerning other, sometimes more experimental methods. Clearly this is a matter of judicious and careful assessment, without which rock art dating would soon be back in the wilderness from which it emerged only a few years ago. If this field of rock art science were to be judged on the basis of the distorted and uninformed interpretations archaeologists have made about it, direct dating would not be worth-while. Fortunately the outlook is not that bleak, provided we can persuade archaeologists to take a greater interest in rock art science before they attempt interpreting such data.
Determination of cation leaching
This technique serves as a classical example of the pitfalls in rock art dating. Hailed as the miracle cure for rock art dating blues for about a decade, it has now been abandoned by all and sundry, particularly after its inventor and advocate effectively disowned it by rejecting his own method of calibration.
Cation-ratio dating (CR) provides results that must be expected to be highly variable depending on sampling site. This method seeks to calibrate the rate of leaching of the more soluble cations of rock varnish (potassium and calcium) relative to the supposedly more stable titanium content (Dorn 1983, 1986). After it was developed during the 1980s, its reliability and accuracy were seriously challenged (cf. Nobbs and Dorn 1988 and comments; see also Bednarik 1991; Bierman et al. 1991; Watchman 1992). Dorn has conceded that it is an inferior method (1990) and that it is susceptible to an excessively high number of variables (1994).
One of the numerous flaws of this technique is the great variability of the crucial indices, the cation ratios. For instance, sedimentary rocks have great variations in Ti on a millimetre scale, e.g. due to a single layer of heavy minerals, or spotting effects of low-grade metamorphism. Such differences of cation ratios in the host rock may be reflected in those of the varnish over the motif area. Anomalies can occur not only in Ti, but also in Ca and K. In addition, numerous other factors affect the CR of rock varnishes: the proximity of soil, oxalate, amorphous silica or organic matter; lichens, fungi, pH, water run-off; and of course relative exposure to leaching or weathering. Moreover, the ratio will differ laterally, depending on how the varnish spreads out from initial colonisation sites. Structurally, rock varnishes are as a rule highly variable, again on a millimetre scale, which is precisely why I abandoned the idea of using them for dating in the 1970s (Bednarik 1979). The extent of erosion episodes or of cation scavenging by micro-organisms, which certainly invalidate CR dates, is well demon-strated by SEM photographs of varnish stratigra-phies. This applies also to episodes of micro-colonial fungus attack or lichen activity. Even the fundamental proposition that cations are uniformly soluble is open to question. After all, they do not occur as pure elements and it would seem to be the solubility of the minerals they occur in that determines the relative leaching rates. The solubility of diverse Ti-minerals relative to different Ca-minerals varies considerably. Some minerals, such as titanite, in fact contain both cations, which means that their removal will not affect the ratio at all. All of the factors determining the cation ratio of a weathered rock varnish are locally variable, besides distorting that ratio, and this probably explains the significantly discordant results of Watchman's (1992) re-sampling program.
CR analysis has not provided any accepted results, its methodology is fundamentally flawed and it does not offer a valid method of estimating the ages of rock art or geomorphic exposures. Following its demise, Dorn has focused on the possibility of using the nano-stratigraphy of rock varnish to estimate the ages of distinctive strata. These micro-laminations are viewed in ultra-thin sections (<5 microns), using a transmission light microscope (Liu and Dorn 1996; Dorn 2001). Dorn claims to recognise distinctive layers in samples from petroglyphs, layers he has observed and dated elsewhere. Sequences of such laminae have reportedly been dated by radiocarbon and uranium series analysis, spanning many tens of millennia. Dorn's own outspoken rejection of the carbon isotope analysis of accretionary deposits of this kind inspire no confidence in the precision he suggests for his results from such deposits. Moreover, rock varnish laminae are notoriously heterogeneous, because of their irregular deposition patterns, scavenging and recycling of cations by micro-organisms, and highly variable weathering patterns. Nevertheless, the possibility of nano-stratigraphic dating of varnish layers does need to be pursued, if only to test Dorn's claims.
Cosmogenic radiation nuclides
Another analytical method strongly supported by Dorn since at least 1990 is the determination of maximum rock exposure ages supposedly attainable from measuring the presence of cosmic ray-caused radiation products in rock. This can never provide actual age estimations of rock art, and even the claims that it can offer mere exposure ages need to be carefully qualified. The nuclides available for measurement by this method are 3He, 10Be, 14C, 21Ne, 26Al, 36Cl and 41Ca, using accelerator mass spectrometry and noble gas mass spectrometry. Among the key qualifications are the need to be certain the sample comes from a closed system, and the production rates of the various nuclides need to be better calibrated than they are at present. There is a preference for using more than one radionuclide in tandem, and in particular the pair 10Be and 26Al is thought to give good results from quartz (Nishiizumi et al. 1989). Their half-lives are suitable for Quaternary deposits (1.5 Ma and 725 ka respectively), contamination can be dealt with effectively (Brown et al. 1991), and their production ratio of about six is not thought to be much affected by altitude and latitude. Another pair used is 3He and 21Ne, which is suitable for older surfaces, but helium data from radiocarbon-dated Hawaiian lava flows imply very coarse precision (Kurz et al. 1990; Rubin et al. 1987).
The production rates of the radionuclides in the substrate that result from cosmogenic radiation are variable according to topographic exposure, altitude, latitude, oscillations in radiation, overburden and time. Even past fluctuations in the earth's magnetic field may effect variations (Kurz et al. 1990). It is of concern that the method, which is almost as old as radiocarbon dating (Davis and Schaeffer 1955; Lal et al. 1958; Lal and Peters 1967), remains poorly calibrated. Its only two applications in archaeology, at Stonehenge (Williams-Thorpe et al. 1995) and Coa valley (Phillips et al. 1997) produced apparently false results (Bednarik 1998c). Estimates of production rates (Lal 1991; Yokoyama et al. 1977) remain severely hampered by the lack of appropriate reaction cross-sections for neutron-induced spallation. It has been difficult securing data from polished rock surfaces of known ages (Cerling 1990; Kurz et al. 1990; Nishiizumi et al. 1989; Phillips et al. 1986; Zreda et al. 1991). The well-established ages of lava flows are generally very young, usually of the Holocene (Poreda and Cerling 1992), which permits only the three nuclides with the shortest half-lives to be considered.
Cosmogenic radiation analysis has been applied at one rock art site, Penascosa in the Coa valley, northern Portugal (Phillips et al. 1997). Using the less attractive 36Cl nuclide, geologically and historically unacceptable results were obtained, and the analysts made several crucial errors in their interpretation of their data. Most importantly, they ignored the high solubility and mobility of chlorides, and the susceptibility of subterranean strata to the nuclide conversion process, even though both factors were implied by their own data (Bednarik 1998c). Moreover, their method necessitates the assumption of a rate of erosion retreat (Phillips et al. 1990), while at the same time any surface retreat over tens of millennia would effectively exclude the survival of the petroglyphs they were trying to date. These several self-contradictions render the specific dating attempt of Phillips et al. (1997) refuted, but this does not imply that the method itself is discredited. Its use in estimating the age of geomorphic exposures is certainly valid, particularly in cases where exposure occurred on a massive scale, such as by meteor impact, major tectonic adjustment or quarrying operations. In such circumstances background radiation products would be either absent, or hopefully negligible. However, such conditions rarely apply in rock art dating, for which the determination of cosmogenic radiation nuclides therefore has little if any relevance.