![]() If represents 1, and is 10, then the third column would be the numbers 49, 50,51,…, 58, 59, and then 1, for a reason that is not yet clear. The third, especially, changes in so regular a way that it is fair to infer that this is a column of successive numbers, constructed on a principle like that of the Egyptian hieroglyphic numbers. It seems to consist of four columns, of which the second and fourth do not change, but the first and third do. Look at the illustration and see if you can identify some of its main features, then come back to the description here. This discovery was due, once again, to Henry Rawlinson, who in 1855 was studying a tablet from the ancient city of Larsa. The earliest understanding to emerge was that of the Babylonians' remarkable numeration system. The results of studying these emerged in the 1920s and 1930s, and led to a considerable re-evaluation of the Babylonians, who within a decade changed from being a bare footnote to biblical studies (as in the Tower of Babel), to being a culture whose mathematical attainments put those of the Greeks of 1200 years later into a fresh perspective. It is only a small proportion of these that have been shown to have mathematical content, perhaps five hundred or so, compared with the several hundred thousand extant tablets. ![]() These have sometimes been unearthed in vast quantities, with the result that there are now many more tablets available, in museums and universities throughout the world, than have been translated or even catalogued. Shortly thereafter, the burgeoning science of archaeology resulted in excavations of cuneiform tablets from ancient sites in Mesopotamia. It was the British Consul in Baghdad, Henry Rawlinson, who rediscovered this inscription and between 18 copied it (at the risk to his life that any amateur mountaineer faces 300 feet up a precipice) and began to decipher both the script and the languages. Their equivalent of the Rosetta Stone-a trilingual inscription for which one of the languages could be partially understood-was a sheer rock-face at Behistun in south-western Iran into which a text was carved in three languages, Old Persian, Elamite and Babylonian, proclaiming the victories of Darius the Great (520 BC). ![]() ![]() Now, how did historical study reach the stage where Neugebauer and Sachs could pick up a tablet in a library and translate it so as to provide a fair degree of understanding? As with Egyptian hieroglyphs, cuneiform studies date from the last century. This makes for a slightly more complicated calculation than most of the otherwise similar Rhind Papyrus problems that exist from this period in Egypt. So it is the stone less its seventh, plus the eleventh of that, and so on. The fractions in the question are not all parts of the original stone, but are parts of whatever the previous step has been. There is one further point that we should mention, in case you tried to work out the problem but could not obtain his answer. It could also have been a question of how to handle these unit fractions-notice that they are all awkward ones in that they do not divide into the weights (one-seventh of a ma-na does not come out as a whole number of gin or of se). Just what was being taught is unclear, however, as several possibilities spring to mind: it could have been the method of solving problems like this it could have been the learning of units of weight (for the solution comes out only if these are understood correctly). The facts that there are so many similar problems on the tablet and that no working is shown, both suggest that it may have been for teaching purposes in an oral teaching situation where the method was explained verbally. So, on the evidence of this tablet at least, similar things seem to have been taking place mathematically in Egypt and Babylon, at much the same time. You probably noticed that it was formulated in terms of unit fractions. It is clear this is not a practical problem-he would have done better to have weighed the stone when he found it, if he were really interested directly in its weight!
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