<nettime> Linkages Couplings

[Alan Sondheim <sondheim@panix.com>]

(I've been thinking about decompositions, things falling apart, Spencer
Brown, postmodernity and fragmentation, the 'way' protocols operate, pro-
gramming errors, the following brief description a node that might or
might not be of interest in this regard - Alan)
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Couplings and Linkages


Let:

L,M,N = linkages
C,D,E = couplings
a,b,c = elements

Then:

f(L(abcd),a') -> L(a'b'c'd')
f(C(abcd),a') -> C(a'bcd)

Think of linkages as joined elements, chain links for example, the Great
Chain of Being for another, cars in traffic for a third. Think of
couplings as adjacent or concatenated unrelated objects, glasses on a
shelf for example, people on a loosely-populated sidewalk for a second,
catastrophes for a third.

L(M,N) -> L'
C(D,E) -> C'
C(L,D) -> C'
C(D,L) -> C'
L(C,M) -> C'
L(M,C) -> C'
L(C,D) -> C'
C(L,M) -> C'

or: 

1*1*1 = 1; 0*0*0 = 0; 0*1*0 = 0; 0*0*1 = 0; 1*0*1 = 0; 1*1*0 = 0;
1*0*0 = 0; 0*1*1 = 0

A coupling of couplings is a coupling; a coupling of anything is a
coupling.

A linkage of linkages is a linkage; a linkage of anything with a coupling
is a coupling.

The 'principle of fragility of good things': The linkage is as strong
as its weakest links, and becomes increasingly improbable as the number
of elements is increased.

Nevertheless, we might consider action at a distance, such that:

f(R(stuv),s') -> R(st'uv) | R(st'u'v) | R(stu'v) | etc.: Consider this a
form of _chain negation._

Action at a distance combines linkages and couplings; there is an effect
'down the line,' but other terms are unmodified. Action at a distance may
also imply subsets of couplings which are linkages. A linkage within a
coupling remains a linkage, foreclosed, within the coupling.

One might put it this way; with a coupling and x to x', xy -> x'y.
And with a linkage, x to x', xy -> x'y'. In a linkage, both terms are
affected; in a linkage, only the catalyst term x.

A coupling always already absorbs; a linkage fastens, fetishizes. The
inverse of a linkage, however defined, is a linkage; the inverse of a
coupling, however defined, is a coupling.

The identity element as an _operation_ may be said to modify a linkage;
the identity element as an _operation_ has no effect on a coupling. But
these are metaphysical considerations.

The world-picture moves from linkages to couplings.


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