Friday, July 21, 2006

Can there be more than one two-ity?

First, an excerpt from Jadran Mimica's Intimations of Infinity: The Mythopoeia of the Iqwaye Counting System and Number (Berg 1988, pp. 136-137):

In the Iqwaye case there is a binary mode of the ordering of elements, and there is an intrinsic rhythmicity which temporalises the entire structure of numeration and is the source of its dynamics. But in this scheme the digital progression is contained or, rather, closed in upon itself. The binary rhythm of succession reproduces the primordial rhythm (temporality) of the cosmic process of self-generation. Out of the one emerges two from which emerges one, and so on. This self-propogation, as we saw, is the pluralisation of the all inclusive oneness (the body) by means of the totalising particularisation of its composite parts (the digits). The totalised parts in turn fuse back into the original unity of the one which as such becomes an internally multiplied higher totality (201 --> 202 --> 203 ...). Understood thus in terms of the Iqwaye cosmology, we come to realise that in their arithmetical succession neither its logical form nor its inner temporality have an independent or ontological priority. Both are subsumed by the process of totalisation which relates counting to its cosmological foundations. We then have to accept that within the purview of the Iqwaye cosmology, our Western, intellectually seperated and idealised categories of intuition such as time, space, number, and so on, ultimately melt into the organismic unity of the body, consciousness and the world.

Organismic--hot stuff, two-ity. Anyhow, what I'm taking from my reading of Mimica is that two-ity is both irreducible and composite, and the thematicization of two-ity is not instantaneous but, rather, it unfolds. If flows. Is the intuition of two-ity also not realized in an instant? That would be a strange quality for an intuition to have, to be divorced from any single experiential moment. But perhaps much of our experience is like that, constituted in flows, rhythms, grooves.

A thinking person should have little trouble with Mimica's argument about the openness of the concept of number (albeit many people who work with numbers have a sedimentend, taken-for-granted conceptualization of number). But isn't there something paradoxical here? Can we have two-ity before number? And if we achieve an imagination of two-ity while number yet remains inchoate, should we really be calling it a two-ity? Might it not be some other kind of intuition, related to number perhaps, but not itself numerical, whatever the numerical will come to mean? Couldn't tell you. Just saying.

posted by Fido the Yak at 9:11 AM.


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