The Alan Sondheim Mail Archive

August 14, 2009


give a number X, let's say it's reflexive with itself, and phenomenolog-
ically this constitutes identity.

not the signifier of identity, but identity per se.

let A + B = X, and let C + D = X. then clearly A + B = C + D - equivalence
is transitive. but now let us define a sign @ such that
A + B -@ C + D. in other words, let's say that the two additions are
fundamentally different processes, say for the subject carrying them out.
so that one might write X(@)A+B -= X(@)C+D - in other words, beneath or
within @, the additions are dissimilar. now we are dealing in a classical
realm within which history is preserved.

this is what I was working on as a child.

let's go further; we might abbreviate A + B as V and C + D as W. then V
and W have different histories, i.e. of abbreviation as well as symbol
content. we don't need X to say that if W = V then @W -= @V or equival-
ently, W -@ V. unpacking W or V again adds history: in fact, _every_
operation recontextualizes its objects. we are also dealing in a quantum
realm in which history is altered by the processes of perception.

this is all so simple.

it's a problem of notation.

if notation implies notating, notation is always an entanglement, always
entangles. notation builds up hierarchically, holarchically; every return
adds another layer.

one can think of this in terms of _immersive_ and _definable_ hierarchies
(something I thought about in my 20s, building on my child's work). a
definable hierarchy is such that if A + B = X = C + D then A + B = C + D
and if A + B = V and C + D = W then V = W = X and this is reversible of
course and we're working with traditional mathesis, propositional logic,
and the like. on the other hand an immersive hierarchy inhabits time (is
inhabited by time) and (perhaps) organism, intentionality, consciousness;
it's a different phenomenology altogether.

the difference is in the differance which lies in @. @ is an opening to
Lacan and Kristeva, for example, not Sokal: it is what _makes a mess of
things,_ mathematically and otherwise; on the level of the uncanny,
presence is involved.

this presence abjures notation, inasmuch as notation is employed. notation

in this sense one might even write @X -= @X or equally X -@ X - identity
is problematized. what of this? that @X -= @X involves a _split_ and
_nothing can be done with this split._ every mark is always already being
marked, and being marked is always already being marked otherwise.

(of course hierarchy and holarchy disappear as well.)

and of course there's more: it's always possible to construct formal
phenomenologies of immersion and @, phenomenologies of continuous organic
transformations. but the constructing per se is on the other of @ itself,
and substitutions have to stop somewhere, in order to avoid indefinite
regress: either way, mess appears. (and responsibility, since moving away
from definability means the preposterous strategy of taking organism

[note that -= is "not equals" and -@ is "not @".]

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