The Alan Sondheim Mail Archive


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.


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