While the obstacles to our appreciation of Chaldæann literature are of such a serious character, we are much more at home in our efforts to estimate the extent and depth of their scientific knowledge. They were as well versed as the Egyptians, but not more, in arithmetic and geometry in as far as these had an application to the affairs of everyday life: the difference between the two peoples consisted chiefly in their respective numerical systems--the Egyptians employing almost exclusively the decimal system of notation, while the Chaldæans combined its use with the duodecimal.
To express the units, they made use of so many vertical "nails" placed one after, or above, each other, thus [symbols] etc.; tens were represented by bent brackets [symbols], up to 60; beyond this figure they had the choice of two methods of notation: they could express the further tens by the continuous additions of brackets thus, [symbols] or they could represent 50 by a vertical "nail," and add for every additional ten a bracket to the right of it, thus: [symbols]. The notation of a hundred was represented by the vertical "nail" with a horizontal stroke to the right thus [symbols], and the number of hundreds by the symbols placed before this sign, thus [symbols], etc.: a thousand was written [symbols] i.e. ten times one hundred, and the series of thousands by the combination of different notations which served to express units, tens, and hundreds. They subdivided the unit, moreover, into sixty equal parts, and each of these parts into sixty further equal subdivisions, and this system of fractions was used in all kinds of quantitive measurements. The fathom, the foot and its square, talents and bushels, the complete system of Chaldæan weights and measures, were based on the intimate alliance and parallel use of the decimal and duodecimal systems of notation. The sixtieth was more frequently employed than the hundredth when large quantities were in question: it was called a "soss," and ten sosses were equal to a "ner," while sixty ners were equivalent to a "sar;" the series, sosses, ners, and sars, being employed in all estimations of values. Years and measures of length were reckoned in sosses, while talents and bushels were measured in sosses and sars. The fact that these subdivisions were all divisible by 10 or 12, rendered calculations by means of them easy to the merchant and workmen as well as to the mathematical expert. The glimpses that we have been able to obtain up to the present of Chaldaean scientific methods indicate that they were on a low level, but they were sufficiently advanced to furnish practical rules for application in everyday affairs: helps to memory of different kinds, lists of figures with their names phonetically rendered in Sumerian and Semitic speech, tables of squares and cubes, and rudimentary formulas and figures for land-surveying, furnished sufficient instructions to enable any one to make complicated calculations in a ready manner, and to work out in figures, with tolerable accuracy, the superficial area of irregularly shaped plots of land. The Chaldaeans could draw out, with a fair amount of exactness, plans of properties or of towns, and their ambition impelled them even to attempt to make maps of the world. The latter were, it is true, but rough sketches, in which mythological beliefs vitiated the information which merchants and soldiers had collected in their journeys. The earth was represented as a disk surrounded by the ocean stream: Chaldæa took up the greater part of it, and foreign countries did not appear in it at all, or held a position out in the cold at its extremities. Actual knowledge was woven in an extraordinary manner with mystic considerations, in which the virtues of numbers, their connections with the gods, and the application of geometrical diagrams to the prediction of the future, played an important part. We know what a brilliant fortune these speculations attained in after-years, and the firm hold they obtained for centuries over Western nations, as formerly over the Bast. It was not in arithmetic and geometry alone, moreover, that the Chaldaeans were led away by such deceits: each branch of science in its turn was vitiated by them, and, indeed, it could hardly be otherwise when we come to consider the Chaldæan outlook upon the universe. Its operations, in their eyes, were not carried on under impersonal and unswerving laws, but by voluntary and rational agents, swayed by an inexorable fate against which they dared not rebel, but still free enough and powerful enough to avert by magic the decrees of destiny, or at least to retard their execution.