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closeCalculation errors?
Posted by scholia on 25 Apr 2015 at 20:14 GMT
A recurring criticism, posted within a day of your article being published by PLOS One, is that your volumetric calculations in the following paragraph are flawed.
"Let us assume that the average volume of a piece of débitage is 7 cubic centimetres (5 x 3 x 1 cm). Taking the maximum figures, this yields 2.1 x 1020 cubic centimetres, or 2.1 x 1014 cubic metres of rock. This is the equivalent of 84 million Great Pyramids of Giza (which is 2.5 x 106 cubic metres [32]), or 42 million taking into account the uneven hominin occupation suggested above. To extend the comparison further, it would be the equivalent of finding between 1.3 and 2.7 Great Pyramids per square kilometre throughout Africa."
While recognizing these calcuations are estimates based on assumptions, using "maximum figures" (not the figures actually represented in the data), the conclusion presented is implausible in the extreme. Several commentators (one within a day of your article being published), have calculated that your figures would result in a volume of débitage sufficient to cover the surface of Africa to a depth of at least several meters. Additionally, it has been calculated that one Great Pyramid per km^2 with a pyramid volume of 2.5 million cu. m would require an average débitage volume of 2.5/5.0 cu. m. If this is correct, it is considerably larger than your estimate of 7 cu. cm, and is of course totally unrealistic.
Nevertheless, it is unclear why a surface area calculation of this kind is being made, if it is not merely a hypothetical for the purpose of illustration. It certainly does not reflect what would happen in reality. Over the course of one million years, débitage does not simply build up on the surface of the land, but is continually buried under an increasing number of layers. Since débitage can be found at depths of over eight meters, even up to twenty meters, and is also found piled on the surface of the land, it is meaningless to calculate the surface area of land which would be covered by one million years of lithic débitage, as if this has any relation to what would be discovered in reality.
Over the course of one million years, the débitage would not remain on the surface; most of it would be buried and the most recent débitage would pile up in high volume areas such as quarries. Consequently, distribution over the total surface of Africa would be very uneven, as indeed we find today.
Response to Scholia’s comment on ‘Lithic landscapes’.
RobertFoley replied to scholia on 07 May 2015 at 18:11 GMT
We thank Scholia for his comment suggesting a more modest number of ‘Giza pyramids’ per surface area to reflect the volume of prehistoric stone tool manufacture. Our paper estimates a volume parameter for the density models used to place the Messak observations into context. There was no particularly strong basis for selecting a particular value, given the variation from large Mode 1 to microlithic Mode 5 technologies, and a number of estimates were used in experimenting with the volume estimates, of which only one was presented. We used the minimum volume estimates (7 cm3 instead of 70 cm3 or 400 cm3), which are the medium and maximum estimates. The entries below provides a range of modelled volumes, for different industry types.
Macro Mode 1-3
Approximate volume of individual lithic = 400 cubic centimetres
Range of volumes per square kilometre = 4 x 10^8 - 4 x 10^11
Mixed model
Approximate volume of individual lithic = 70 cubic centimetres
Range of volumes per square kilometre = 4 x 10^7 - 4 x 10^10
Micro Mode 5
Approximate volume of individual lithic = 7 cubic centimetres
Range of volumes per square kilometre = 4 x 10^6 - 4 x 10^9
Assuming a large flake industry, such as we see in the Messak (Modes 2 and 3), where flakes are very large, with big original nodules, we might expect average flake volumes of at least 400 cm^3 . For microlithic Mode 5 technologies, an estimate of 7 cm^3, as reported, would be appropriate. For Africa we reported an order of magnitude of 10^20 cubic centimetres of rock used; for the full range of models here, this should be between 10^18 and 10^20. The key volumetric inference from the models is that hominin tool-making activity across prehistory would have resulted in between 400 and 400,000 cubic metres of debitage per square kilometre. The ranges of the estimates are large, but from the point of view of the utility of such estimates, they give some idea of the demand for raw material and the importance of being close to a source of stone - simple in some parts of Africa, less so in others (and the same would hold true of other parts of the world), and an insight into potential environmental impact. This was the primary point of estimating volumetric expectations.
We also tried to provide some comparison that would help visualise the scale of the stone tool-making activities of hominins. We took the Great Pyramid of Giza as an informal comparator. It had no other significance. On the figures presented here a better estimate would be that hominin stone tool production would have yielded between one ‘pyramid equivalent’ per 10 km^2 to 100 km^2, rather than the ~1 per km^2 reported. It should be stressed that this does not affect the rock volumes calculated, but only the informal comparator used to aid visualisation, and it does not affect the observed results of the Messak work, nor the expected artefact densities based on the models. It still remains the case that the quantity of raw material used on the landscape would be massive, as was the main point of the paper.
Scholia also questions the utility of a surface area calculation, given the scale of burial processes. This misunderstands the purpose of the model and the paper, which was not to predict the number of lithics we should be finding on the African landscape; we know that there are many taphonomical processes which will both destroy and render invisible any part of the archaeological record. Rather, the purpose was to provide some insights into how to interpret high density lithic scatters such as those we found on the Messak, as their meaning is entirely dependent upon assumptions we make about the processes of production. Our paper has highlighted the need for more empirically founded research into the scale of the record, to understand what sort of sample or fraction we are observing. To finish, we return to the main points of our paper, namely that the results on the Messak indicate the scale and impact of lithic production by hominins (~10^7 lithics per square kilometre), and the lithic density models (10^6 - 10^9 lithics per square kilometer) show clearly that such high levels of production are behaviourally realistic.