01NoteBook or 122Desings (in Metaphysics). 2012-2013. Paper.Ink. 20x29cm (c) Maria Methimaki
I am seeking to a potential process of theoretical and artistic practices which I shall coin the prosthetic method. The characteristics of this method arise from the mathematical operation of prosthesis (addition).
The prosthetic method, as a creative phenomenon, originates in the moment of replacing mathematical symbols-variables with theoretical and artistic elements. The abstract equation a + b = c is converted into a prosthetic relationship of rational and material entities. For example: a + b = c ⇔ Logos + b = Matter ⇔ words + b = ink, e.t.c.
Prosthesis, as a mathematical operation, combines two
numbers (addenda) and produces an equal number (a sum),
while the repetition of adding the number one is
the most fundamental type of enumeration:
The manner in which the addenda are combined in relation to the sum gives rise to the main qualities of the operation. This combination reveals the qualitative nature of this operation, which can ultimately be transformed – by transposing thought - from a mere mathematical operation into a work of art and research.
The commutative property (the order of the addenda may be changed: a + b = b + a), the associative property (addenda may be replaced by their sum or broken down: a + (b + c) = (a + b) + c) and the fact that 0 is a neutral element (when 0 is added to a natural number it does not change: a+0=0+a) are the properties of addition. From observing these properties, it can be derived that addition is of a qualitative nature. Thus, it is possible for addition to be interpreted as a convention of potential balance among elements of the same nature.
It is a potential balance because each element can be converted into two equivalent sums, thus revealing an internal trend towards the breaking down of the element.
a + b = b + a ⇔
⇔a1+a2 + b = b + a, when a=a2+a1⇔
⇔a3+a4 + a2 + b = b + a, when a=a2+a4+a3⇔
⇔a5+a6+ a4 + a2 + b = b + a, when a=a2+a4+a6+a5⇔
⇔∞+……+ a6+ a4 + a2 + b = b + a, when a=a2+a4+a6+………+∞⇔
⇔a=a2+a4+a6+………+a100+………+a1000+………+a∞ ⇔ lim f(a),a→∞
Also, each element can be infinitely added to and the subsequent sums reveal a linear trend towards maximization.
a + (b + c) = (a + b) + c⇔
⇔a1+a2 + (b + c) = (a + b) + c1+c2⇔
⇔a3+a4+a2 + (b + c) = (a + b) + c1+c3+c4⇔
⇔a5+a6+a4+a2 + (b + c) = (a + b) + c1+c3+c5+c6⇔
⇔∞+……+a6+a4+a2 + (b + c) = (a + b) + c1+c3+c5+………+∞⇔
⇔lim f(a)+ (b + c) ⇒ (a + b) +lim f(c), (a,c)→∞
The same nature of the elements is obvious in both operations. A natural element can be broken down and added to, without being changed. A natural element remains unaffected by zero and independent of the position of the elements.
The prosthetic method is based on this balance. The prosthetic method to be a method of research and artistic activity is based also on transforming logos matter as addenda of the same nature, into a relation of syn-ousia.
The main addenda are logos and matter. Logos and matter are constantly being subjected to addition and breaking down of elements of the same nature. Logos is treated as a material phenomenon, without being divested of its original meaning. Matter is treated as a narrative without being divested of its spatial dimension. In this manner, the syn-ousia of elements is achieved. They become entities of the same nature which may be subjected to addition and breaking down, without disturbing the balance of the procedure.
Logos is broken down. It becomes a meaning, a cause, an analogy, a text. It becomes a word, a phrase, a metre, a formation. It is further broken down. New forms of alphabetic letters are created. Spaces and punctuation are eradicated. Each letter becomes autonomous. It is not a merely element of words and phrases, but become a visual phenomenon. Text size changes and acquires various dimensions of reading. Inscriptions which are not easily discernable, but can always be understood and cease to be only meaning.
Matter is broken down. It becomes space, quality, an image, a text. It is further broken down. It becomes flat, a point, a metre, a formation. It is further broken down. All materials are presented in multiple stages of processing, so that it is easy to distinguish the narrative nature of its formation. For example, plaster is presented in its solid form, in its liquid form, at high temperatures and back again to its solid form. A narrative is formed upon the space of the material. They just cease to be only matter.
At the same time, each element is in a constant prosthetic relationship with the whole. No texts are eradicated, no materials are torn away. Each piece of information is displayed and each point is determined. Completeness envelopes the void in such a way that zero is the neutral element of the prosthesis. In this manner, the continuous prosthesis of elements leads to a dense depiction of phenomena. To a great extent, approach their composite nature.
The prosthetic method seems to create the conditions for a free dense depiction of phenomena. It maintains the balance of the attempt and activates the theoretical and artistic practice.
A mathematical representation of syn-ousia can be:
lim f(L),L→M ⇔ lim f(M),M→L, (L=Logos, M=Matter)