**Message-ID:** <Pine.NEB.4.40.0112032001510.5065-100000@panix2.panix.com>

**From:** Alan Sondheim <sondheim@panix.com>

**To:** CYBERMIND@LISTSERV.AOL.COM

**Subject:** The Ineffable Brought Back Below

**Date:** Mon, 3 Dec 2001 20:02:32 -0500

- The Ineffable Brought Back Below Simplices are generated in n-dimensional geometry by connecting the n-1 simplex to a point in the nth dimension (i.e. not co-n-1 with it). Begin with a point, then a line segment, triangle, tetrahedron, etc. For dim 0 and 1, the total number of elements are respectively 1 and 3. This is also true for the measure polytope, point, line segment, square, cube, etc. The latter is formed by sliding the entire n-1 measure polytope along an orthogonal n-flat. The total number of elements in a simplex is 2^(n+1)-1 which may be seen inductively; given an n-dimension simplex, the slide to n+1 creates 2(2^(n+1)-1)+1 elements - doubling through the 'smear,' the last 1 for the given point drawing the rest out, almost skein-like. This reduces to 2^(n+2)-2+1 = 2^(n+2)-1 elements for the n+1 simplex, i.e. 2^((n+1)+1)-1. Something also about binomial coefficients. For a measure polytope, the total elements are 3^n; this can also be shown inductively. For dim 0, the point, 3^0= 1 and 2^1-1 = 1; for dim 1, 3^1 = 3 and 2^2-1 = 3; dim 0 and dim 1 may be considered a phenomenological basis for these generations, identical for simplex and measure polytope. Note these two forms carry upward through the n-dimensional polytopes; this isn't true of the other platonic solids. Now consider n = -1; then the simplex is 2^0-1 = 0; this is the ineffable point, without elements or substance. The sim- plex below or beneath the series disappears, or might as well disappear. Elements and elementals. This is the ineffable point; we may read Derrida as subaltern extension: "(50) Calculability: question, apparently arithmetic, of two, or rather of n + One, through and beyond the demography of which we spoke above. Why should there always have to be _more than_ one source? There would not have to be two sources of religion. There would be faith and religion, faith or religion, because _there are at least two._ Because there are, for the best and for the worst, division and iterability of the source. This supplement introduces the incalculable at the heart of the calcula- ble. (Levinas: 'It is this being-two _<etre a deux>_ that is human, that is spiritual.') But the more than One _<plus d'Un>_ is at once more than two. There is no alliance of two, unless it is to signify in effect the pure madness of pure faith. The worst violence. The more than One is this n + One which introduces the order of faith or of trust in the address of the other, but also the mechanical, machine-like division (testimonial affirmation and reactivity, 'yes, yes', etc., answering machine and the possibility of _radical evil:_ perjury, lies, remote-control murder, ordered at a distance even when it rapes and kills with bare hands." ("Faith and Knowledge," in Derrida and Vattimo, Religion, trans. Weber.) It is Pythagorean in the sense of an empathetic harmony between number, numeracy, and the real, drawn out into neoplatonisms. It is desire manifest in an absolute that drops out at the bottom of the scale; in a very inert sense, nothing is below zero, neither negative nor imaginary, neither fraction nor transcendental, neither inaccessibly high finite, nor infinite. It stops there, as the nub or apex, the world under erasure, the world not yet declared. And it is a false derivation; a false transmission precisely within and by virtue of the scriptures, and the violence is there. It's the curlicue, the diacritical mark, to the effect that 0' -> 1, tends towards one; there is always a unique successor among the integers. One you start, there's no stopping; one an axiomatic system is laid out as in Euclid, or parameters declared, everything follows. Everything, but not necessarily _that_ One, which requires an extra effort, although it was always there by the self-performative of its own beginning; it's curious. _