In English language we understand qualities of spatiotemporal entities as constituting the basis of “unitizing” the material world prior to quantifying. If spatiotemporal entities have numerosity, then that is the quality we use, and we say we “count.” With spatiotemporal entities that cannot be understood as having the property of numerosity, other qualities (length, mass, and so on) can be used to constitute temporary units understood as analogous to things, and we measure.
For Yoruba speakers, with a world already categorized on what English speakers understand as a qualitative basis, the modes in which these sortal particulars manifest, with varying degrees of dividedness, constitute the basis of quantification. The sets of unitizing material practices incorporated into kà and wòn might resemble the sets of unitizing practices built into counting and measuring, but because the categories taken to constitute the world differ, the sets of practices hold together in different ways.
Constituting a recursion of names is the third set of practices that contribute to the assemblage of “natural number.” The role of fingers and toes in both the Western and the Yoruba assemblages is implicit. In both cases seriation in words is patterned on the scale of finger-toes, but there are significant differences. The contemporary numeral recursion that has developed with English has ten as its base — “ten” is the point in the series of words that marks the end of the basic set. As each ten is reached, the basic series is started again in a systematically modified form. The rule by which the series continues is addition of single units. Yoruba numerals are a multibase recursion. The most important base is twenty (ogún). Ten (èwà) and five (àrùútin) provide points at which the twenties are broken up. The rules for working the recursion make little use of addition; the processes of multiplication and subtraction are more important. We can explain the difference between English and Yoruba in the practices of numeral recursion by going back to the primary categories in the language. When the entities talked of are spatiotemporal objects, the linguistic code explicitly differentiates fingers from one another. When the primary entities talked of are sortal particulars, a linguistic code to report the position on the finger-toe scale must necessarily be more complex. With the primary categorical distinction of Yoruba, the fact that finger-toe matter ordinarily manifests in sets of twenty with inherent divisions into collections of ten and five is relevant—a sortal particular—and a person coincides with the manifestation of fingertoe matter in this way.
Thus a cross-cultural tension enables us to see number and quantification as the “clotted assemblage” of three quite heterogeneous sets of practices: linguistic practices of designating, material practices of unitizing matter, and practices of tallying units through linguistic analogy to fingers and toes. In the past, in communities speaking Indo-European languages and in those speaking West African languages, number and quantification have resulted from efforts of people to produce meaning. But this has been forgotten as we just go on using number as a standardized form of knowledge that has become so “clotted” as to now be considered part of our grammar.
We can [..] understand quantification as just another robust, clotted form of knowledge that originated in particular situations and enterprises. Par excellence, it displays both plasticity and coherence. Through number, other accomplishments are possible; it is “a technology.” Understanding number as contrived in past work by people is likely to be a rather startling idea for some, yet it is a useful way to understand number as a social phenomenon.
//Helen Watson – Verran and David Turnbull, 1995, Handbook of Science and Technology Studies: Science and Other Indigenous Knowledge Systems
For Yoruba speakers, with a world already categorized on what English speakers understand as a qualitative basis, the modes in which these sortal particulars manifest, with varying degrees of dividedness, constitute the basis of quantification. The sets of unitizing material practices incorporated into kà and wòn might resemble the sets of unitizing practices built into counting and measuring, but because the categories taken to constitute the world differ, the sets of practices hold together in different ways.
Constituting a recursion of names is the third set of practices that contribute to the assemblage of “natural number.” The role of fingers and toes in both the Western and the Yoruba assemblages is implicit. In both cases seriation in words is patterned on the scale of finger-toes, but there are significant differences. The contemporary numeral recursion that has developed with English has ten as its base — “ten” is the point in the series of words that marks the end of the basic set. As each ten is reached, the basic series is started again in a systematically modified form. The rule by which the series continues is addition of single units. Yoruba numerals are a multibase recursion. The most important base is twenty (ogún). Ten (èwà) and five (àrùútin) provide points at which the twenties are broken up. The rules for working the recursion make little use of addition; the processes of multiplication and subtraction are more important. We can explain the difference between English and Yoruba in the practices of numeral recursion by going back to the primary categories in the language. When the entities talked of are spatiotemporal objects, the linguistic code explicitly differentiates fingers from one another. When the primary entities talked of are sortal particulars, a linguistic code to report the position on the finger-toe scale must necessarily be more complex. With the primary categorical distinction of Yoruba, the fact that finger-toe matter ordinarily manifests in sets of twenty with inherent divisions into collections of ten and five is relevant—a sortal particular—and a person coincides with the manifestation of fingertoe matter in this way.
Thus a cross-cultural tension enables us to see number and quantification as the “clotted assemblage” of three quite heterogeneous sets of practices: linguistic practices of designating, material practices of unitizing matter, and practices of tallying units through linguistic analogy to fingers and toes. In the past, in communities speaking Indo-European languages and in those speaking West African languages, number and quantification have resulted from efforts of people to produce meaning. But this has been forgotten as we just go on using number as a standardized form of knowledge that has become so “clotted” as to now be considered part of our grammar.
We can [..] understand quantification as just another robust, clotted form of knowledge that originated in particular situations and enterprises. Par excellence, it displays both plasticity and coherence. Through number, other accomplishments are possible; it is “a technology.” Understanding number as contrived in past work by people is likely to be a rather startling idea for some, yet it is a useful way to understand number as a social phenomenon.
//Helen Watson – Verran and David Turnbull, 1995, Handbook of Science and Technology Studies: Science and Other Indigenous Knowledge Systems
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