Saturday, May 7, 2011

Derrida & Binary Trees

Derrida in Dissemination speaks of the "double" and the "triplicity" of the concept, many times beginning with a dual opposition, and moving toward a dialectic transformation which con-fuses in an act of sublation, that Hegel refers to as abolishing and transcending.

In Of Grammatology this begins as a critique of Saussure's concept of the sign. The sign is a unity composed in opposition as a duality.

(sign) -> Signifier
-> Signified

To translate this concept of the concept, into computer terminology, you have in the signifier, a pointer which stands in the place of the reference to the value, which is the signified, the value itself.

The problem of such a methodology can be basically explained in terms of even the simplest expressions. Take for instance this utterance:

The tree is green.

The signifier is the raw text "The tree is green." The signified, the meaning, the value, of the utterance, means that there is a tree, and it is green.

The problem is that the green-ness of the tree, itself signifies (for instance) the season in which the tree exists, for winter trees are seldom green unless they're pines etc...

So in the discrete categorical logic of sign/signifier/signified, you have the reduplication of signifier/signified at the level of both the signifier and the signified.

That is to say, that a signified value can in fact, refer like a signifier to some extraneous meaning, that the categories in an of themselves, do not refer to some static relationship, but rather, are always codetermined by the relation of a signifier to a signified.

The effect of this is akin to the logic of a cause and an effect. If we imagine a row of dominoes toppling over, we can see that there is a first cause, which knocks over the first domino, and as an effect, it falls over. The next domino in the chain, will be knocked over on account of the domino which stands before it, which can now be seen as a cause.

So what we really end up describing is a state, and not a thing. The signifier itself is no-thing, it is merely the state of a relation between a label and a value. Furthermore, the operations which are the cause, necessity and desire for such a system, cannot be reduced to either relation, but rather must include both.

The structure of such a construction of the concept, would in all cases be identical to a binary tree. So let's say that you have 4 levels of bifurcation in a binary tree. How many references are there at the 4th level?

The answer to this question is our familiar binary logarithm of 2^N, ref:

0->1 & 2 (level 1) = 2^1
1-> 3 & 4, 2-> 5 & 6 (level 2) = 2^2
3-> 7 & 8, 4-> 9 & 10, 5-> 11 & 12, 6-> 13, 14 = (level 3) = 2^3 (8)


For those of you who are wondering what the hell I'm doing and why, I've been rereading through Dissemination and Of Grammatology, collecting and recollecting references to topics which relate to the thesis of the $This sentence is false$ essay.

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