2.11: Expandability Through Nested and Conjoinable Design

From something hanging, one can hang something else. To something tied, one can tie some- thing else. Khipu design uses these two physical facts to enable (in principle) the indefinite formal extension and proliferation of any given data frame. To put the same thing another way, canonical Inka khipu design and some vernacular versions are recursive, like the syntax of natural languages: into a relative clause one may insert another relative clause, etc.

Nestedness

With few exceptions (markers and other metasigns) any given cord structure may be part of a larger cord structure of the same design, or may conversely bear subordinate members of like design. A pendant bears subsidiaries but subsidiaries bear sub-subsidiaries. Subsidiary structures up to 12 levels deep have been found. Even a whole khipu, i.e. main cord plus pendants, may be a part of a larger khipu. Conklin observed that already in Middle Horizon khipus, “string groups... are virtually little quipus in themselves, containing up to three more hierarchies of dependency” (Conklin 1982: 277). Urton found more pervasive examples of this principle in the khipus from Laguna de los Cóndores. Two examples are visible in the lower left part of Figure 23. He calls the small sub-khipus slung from the main cord ‘loop pendants’ (Urton 2007: 25). One main cord held 24 loop pendants, each related to a corresponding but separate first-order pendant.

Nestedness pervades fiber structures. Nestedness greatly interested Inka designers, even to the point of designing tunics whose surface consisted of emblems (tukapu) of other whole tunics. Nested structures are congenially congruent to many hierarchies in which small structures combine to make large ones of the same form: for example, ayllus, or decimal brackets in Inka administration.

Conjointness

There is another way for a khipu to form a part of a larger khipu: instead of nesting, main cords are attached directly to each other (Figure 23). In practice it is hard to tell which junctures imply horizontal combination of two corpora, and which ones imply hierarchical subordination, but horizontal combinations certainly exist. In one case, they are joined to make a ring of main cords (Figure 24). Conjointness is congruent to relations among peer units, like allied polities, neighboring villages, or sibling-ayllus. It is important to notice that such relations do not necessarily imply equality or interchangeability, because peer segments are often seriated; in Andean ritual they stand in relations of ritual precedence, which imply rank among fellows.

Urton has studied numerical and categorical relations among khipus of less and more aggregated nature within a single Inka-era khipu archive, developing from the phenomenon of nesting a model of khipu ‘intertextuality’. Numerical patterns in lower-level detailed khipus were extracted and summarized in more aggregated high-level ones. This practice in effect extends the phenomena of nestedness and conjointness upward and outward, regardless of whether the parts are physically tied together.