At the time CAETS took to the Pacific, there was a perceived need to mathematicise the understanding of man among the social sciences, and thus propagate a more scientific anthropology, avoiding 'the not unkindly hesitancy on the part of men engaged in the precise operations of mathematics, physics, chemistry, biology, to admit that the problems of anthropology are amenable to scientific treatment' (Tylor 1889:245).
Sidney Ray, CAETS language specialist, adopts this system in Volume III of the Reports, where counting practices are divided into four categories: 1) quinary, or base number 5; 2) imperfect decimal, where base 10 is used following the use of quinary; 3) Decimal, with a straight base number 10 and; 4) Vigesimal, where quinary is used up to 20, upon which a primary base 20 takes over (Reports III [Ray] 1907:464).
Such was CAETS understanding of their own and Melanesian number systems; their presupposed ideas of the natural progression of mathematical knowledge resulting from their cosmological acceptance of abstract number, led them simply to document the insufficiencies of the Islanders in terms of bodily attribution, base system, and recording numbers.
We must therefore be extremely careful not to subject Melanesia to sweeping categorisation which would be tantamount to a similar classification to that used by CAETS and its contemporaries in the years of diffusionism.
By attempting to draw out certain common elements of Melanesian enumeration, this material is brought to bear on CAETS own interpretation of Torres Straits counting systems.
As discussed above, Codrington and CAETS note the practice of counting downwards on the body parts, effectively eliminating parts of the body as one counts upwards until the person is 'finished' or 'dead'.
5) This explains the ability of the Islanders to explicate words for their numbers when pressed, but appearing difficult for them to CAETS.
If we can now take Melanesian enumeration as materially constituted in a radically different way to European geometry, we are no longer looking for an understanding of 'advanced' abstractive geometrical laws as CAETS were when they tackled Torres Straits counting, but an expression of multiplicity and oneness coexisting within the properties of material objects as they are in persons.
Thus, as is noted by CAETS member Hingston-Quiggin: 'the distinctive character of each basket is most intimately bound up with its weaving pattern, which is, as it were, the expression of its maker's individuality, and the device of [his/]her peculiar skill' (Reports IV [Hingston-Quiggin] 1912:78).
We shall now search for analogy with this evaluation in the data brought back by CAETS psychometric tests.
The British anthropological scene at the time of CAETS was looking for differences between races at what they assumed to be a very deep level.
Richards (1998:138-139) in his analysis of the 'racist' underpinnings of the psychological aspect of CAETS, comments on the double-cross of this illusion; the more accurate and clever the natives ability to see through the illusion, the less intelligent the participant actually was at conceptualising advanced spatial perception, as they could not see the figure as a whole.