User:Jules/dissymmetry

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About symmetry in things

While digging into the notion of entropy I bumped into texts referring to Roger Caillois. I became very interested in one particular writing from 1973 entitled “la dissymmétrie” from the book “Cohérences aventureuses”. Unfortunately, I wasn't lucky enough for a proper first hand reading of the whole text. Therefore, I based some of the following observations on some material I found across the Internet (hopefully I will fix that one day). I tried to cross it with other readings and allowed myself a total freedom to establish analogies as they came up to me.

First of all, symmetry comes from the Greek and is formed of syn for with, together, and metria for measure. Symmetry concerns a set of things sharing a common measure. Therefore, the part and the whole are in a relationship of harmonious proportions, or at least this was the way the notion was perceived during the antiquity. This perception led to the establishment of conventional systems for representation in Art for instance as with Leon Battista Alberti's Della Pittura which marks the reintroduction of linear perspective at the beginning of the Renaissance. Symmetry became the doctrine that established canons of beauty that would prevail for a long time. The idea of a system for common measurement (enabling proportional distribution) can be identified in other activities such as Maths, Geometry or even Music.

What is interesting within the ideas I could get from what I read about Caillois is that the notion of symmetry becomes applicable to various domains of human activity by the symbolic fields it opens up. Moreover, symmetry is rooted within chemistry, physics, life, art, almost like a transdisciplinary philosophical concept (and ironically a transposable system for apprehending the world). Symmetry is also due to renegotiation, through dissymmetry, the title of the work on which I want to focus my attention here.

At first it was all magma

Caillois had a passion for mineralogy which helped support his argumentation. His developments on symmetry would start with the example of the magma, which would represent a limited form of existence, describing it as some homogeneous “environment of matter”:

«J’afirme qu’il est cohérent de la tenir pour dénuée de toute symétrie et pour douée d’une symétrie infinie, puisque tout point pris au hasard dans le magma indistinct peut y être considéré comme centre, toute droite comme axe, toute coupe comme plan de symétrie. Pareil chaos n’est peut-être que théorique.»
(Very bad translation : I state that it is coherent to regard it as exempt of symmetry but also gifted with infinite symmetry, as all point chosen randomly within the undistinguished magma can be taken for centre, any line as an axis, any cut as symmetrical plane. Such chaos can only be theoretical)

Then, by becoming crystal, magma experiences its very first moment of dissymmetry, which is a rupture with the previous ruling symmetrical condition gives birth to property. Determined symmetrical axis appear and eliminate other ones, which will remain unaccomplished. Every stage marked by the advent of dissymmetry leads to evolution and liberation. Matter gets organised to a higher degree of complexity. Therefore, a high quantity of symmetrical axis notable within an organism means that this organism is at an early stage of development/evolution. This is not merely speculative as molecular dissymmetry was also very important to Louis Pasteur after his discoveries on molecular chirality, which I will come back to later on. The reach of any state of symmetry means the achievement of a temporary equilibrium which might be subject to renegociation through the event of dissymmetry.

It becomes important to differenciate asymmetry from dissymmetry. Asymmetry is not a lack of symmetry but absence of determination. The magma before the establishment of some arbitrary order. This order will follow the apparition of a few selected symmetrical axis, points or planes. According to Caillois, asymmetry is both null and infinite symmetry. Asymmetry is perhaps a state of agnosis. Dissymmetry is a rupture within the order that will complexify the equilibrium. It will enrich the structure within which it appears, leading to a higher level of organisation.

The conquest of polarity

Mirror reflection and sagittal symmetry.
My right and left hands are anatomically identical (in principle) but not superimposable. This opens up the symbolic field for human thinking.
Font/back, top/bottom, left/right, north/south

CO2 + H2O = CH2O3
Smooth space – striated space
Mimesis – Plato
Rubenists – Pussinists
Time – Hours
Much (indenombrable) – Many (denombrable)
Site - Non-site

Robert Smithson non-site theory comes back here


The Universe is a sphere

One can easily perceive the influence of Luis Borges' work. It actually appears that Roger Caillois helped a lot popularising his writing in France (he translated some works as he was working for Gallimard). It is especially striking when reviewing extracts from the Library of Babel with this approach to symmetry in mind.

"The universe (which others call the Library) is composed of an indefinite and perhaps infinite number of hexagonal galleries, with vast air shafts between, surrounded by very low railings. From any of the hexagons one can see, interminably, the upper and lower floors. The distribution of the galleries is invariable."

"In the hallway there is a mirror which faithfully duplicates all appearances. Men usually infer from this mirror that the Library is not infinite (if it were, why this illusory duplication?); I prefer to dream that its polished surfaces represent and promise the infinite ... Light is provided by some spherical fruit which bear the name of lamps. There are two, transversally placed, in each hexagon. The light they emit is insufficient, incessant. "

"The Library is a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible."

"... the Library is total and that its shelves register all the possible combinations of the twenty-odd orthographical symbols (a number which, though extremely vast, is not infinite)"

The Babel Library is somehow very close to the magma described by Caillois. It is made of shapes still holding a very rudimentary symmetry (lack of polarity), and therefore without a very complex orientation. It is full of everything that it could potentially contain. Therefore, its exclusion criteria are proportionally as simple as the symmetrical principles applying to it. Although the Library of Babel may appear like a very complex object, it seems paradoxically to embodies a very simple definition.

Dissymmetry is life at work

An object is said to have reflection symmetry if it is superimposable on its mirror image. Elements not showing this behaviour are called dissymmetrical or chiral. To Pasteur dissymmetry is the only way to draw a line between the living and the inert, the barrier between life and non-life.

“Life is dominated by dissymmetric actions of whose enveloping and cosmic existence we have some indication. I can even foresee that all living species are primordially, in their structure, in their external forms, functions of cosmic dissymmetry”.

Dissymmetry liberates energy to move forward

“to walk you need to throw off the equilibrium, you have to let yourself go into a fall, then you cut it off and regain the balance. You move forward by playing with the constraints, not avoiding them”
- Brian Massumi, navigating movements
(NB - Caillois and the development of polarity for organic life under the influence of gravity)