Language is elegance in form: an algorithm without advance knowledge of a problem or containing any actions that a problem necessitates
[1]. And yet a solution is attained, through selection and recursion; adaptation. Saussure
[2] :
"In French, the accent always falls on the last syllable unless this syllable contains a mute e. This is a synchronic fact, a relation between the whole set of French words and accent. What is its source? A previous state. Latin had a different and more complicated system of accentuation : the accent was on the penultimate syllable when the latter was long; when short, the accent fell back on the antepenult (cf. Amícus, ánima). The Latin law suggests relations that are in no way analogous to the French law. Doubtless the accent is the same in the sense that it remained in the same position; in French words it always falls on the syllable that had it in Latin : amícum - amí, ánimum - âme. But the two formulas are different for the two moments because the forms of the words changed. We know that everything after the accent either disappeared or was reduced to mute e. As a result of the alteration of the word, the position of the accent with respect to the whole was no longer the same; subsequently speakers, conscious of the new relation, instinctively put the accent on the last syllable, even in borrowed words introduced in their written forms (facile, consul, ticket, burgrave, etc.). Speakers obviously did not try to change systems, to apply a new formula, since in words like amícum - amí the accent always remained on the same syllable; but a diachronic fact was interposed: speakers changed the position of the accent without having a hand in it. A law of accentuation, like everything that pertains to the linguistic system, is an arrangement of terms, a fortuitous and involuntary result of evolution."
A program, a system with states that change from one state to the next, through this process ( recursion ) language is able to adapt. Saussure frames the story of the French accent in the context of Latin so the juxtaposition ( Latin and French ) yields difference
( an act of anthropology, the difference is read. ) Saussure relates the evolution of phonetic changes throughout his
Cours de Linguistique Générale, but does not allow for drastic evolutions syntactically. Fifty years later, Chomsky proposes a theory of a
Generative Grammar.
To define, Chomsky
[3] :
The syntactic component specifies an infinite set of abstract formal objects, each of which incorporates all information relevant to a single interpretation of a particular sentence. Chomsky clarifies the notion of a sentence as a string of formatives that specify a string of phones. Further, let a deep structure (composed of Phrase-Markers) be specified by the syntactic component to determine semantic interpretation.
Chomsky's illustration is phrase-marker S, "sincerity may frighten the boy," which is composed of formatives (sincerity, boy) and abstracted as categories: sentence, Noun Phrase, Verb, etc.
To pierce; a heart of the matter is generating phrase-markers. To do this Chomsky uses a series of rewriting rules in the format
[4]
A -> Z / X - Y
where
X and
Y are strings of symbols,
A is a category symbol, and
Z is a non-null string of symbols;
A is realized as
Z when it is in the environment consisting of
X to the left and and
Y to the right:
XAY yields
XZY.
Rewriting rules to generate the phrase-marker earlier would be
(I)
a. S -> NP + Aux +VP
b. VP -> V + NP
c. NP -> Det + N
d. Det -> the
e. Aux -> M
(II)
a. M -> may
b. N -> sincerity
c. N -> boy
d. V -> frighten
A string of formatives is generated after rewriting rules are applied recursively. The state of language is determined by the grammar that composes it; these grammars are composed of their own internal states. The rules used to generate the formatives are a set of instructions ( genotype ) that is embodied in physical manifestation ( phenotype ) as phones. A phenotype is derived from a genotype, and is situated in a feedback loop so that the genotype is affected by the phenotype.
Saussure's example of evolving phones, it is through the act of language that language adapts.
The shifting position of accents in French could not have occurred if the language had not been actually used ( phenotype, actualized ). There is no reason for the shift in the underlying structure.
Ah-MAY, AH-nee: these sounds were activated by the French people; they embodied the language ( which applied an involuntary process of recursive selection and altered the underlying rules of grammar. ) The adaptation of a system shifting between states: the physical manifestation of the phenotype - as formatives and phones - alter the underlying structures. Without the actualization of a phenotype, the genotype cannot evolve;
without a trajectory, there can be no mark.
Imagine the evolution of a generative grammar to be plotted as a phase-portrait
[5]
( a series trajectories ) in a differential vector field . This vector field
[6] is defined by Chomsky's rewriting rules and is plotted as a topological state-space.
In this, singularities form; vectors converge; language unfolds.
A generative grammar is a kind of evolutionary algorithm. One that searches this space, shifting from state to state along trajectories actualized. Holland developed another. He saw that through adaptation natural forms navigated a morphological space. Forms are generated as variations of singularities in this morpho-space. ( D'Arcy Thompson, all fish are one fish distorted, folded, deformed
[7]. ) Holland's Genetic Algorithm is an attempt to analogize morphology with the state-space of a computer program. Holland:
"The result was the classifier system, consisting of a set of rules, each of which performs particular actions every time its conditions are satisfied by some piece of information. The conditions and actions are represented by strings of bits corresponding to the presence or absence of specific characteristics in the rules' input and output. For each characteristic that was present, the string would contain a
1 in the appropriate position and for each that was absent, it would contain a
0.
[8]"
Begin with noise, static: all forms. A pool is tested and adeptness - even nominal - is duplicated and bred. Slowly, through repeated mutation, cross-breeding, testing, a GA navigates the vast n-dimensional design-space, narrowing its search field until a match is found within the pre-specified threshold; an elegant and efficient way of searching an infinite. But, its implemented form is must be finite. State-spaces become limited and constrain possible outcomes: traditionally, the GA has been programmed into a digital computer. When the GA is isolated within the space of the computer it is limited to a virtuality. In addition, the implementation of a GA in software requires a meta-program in which to be run. Here again: limitations are imposed upon the search-space. Now, the GA can only search within a "safe" quasi-virtual space inside a program where it is removed from our physical world and the fundamental world of the computer's operating system. The GA's abilities are now severely limited as is its search-space and realm for 'actualization'.
Any agency inherent in evolution is removed; any innovation in design is eliminated.
Three tenets as hypotheses: Adrian Thompson's aim was the expanded actualization of Genetic Algorithms
[9] :
Hypothesis 1 - Conventional design methods can only work within constrained regions of design space. Most of the whole design space is never considered.
Hypothesis 2 - Evolutionary algorithms can explore some of the regions in design space that are beyond the scope of conventional methods. In principle, this raises the possibility that designs can be found that are in some sense better.
Hypothesis 3 - Evolutionary algorithms in practice can produce designs that are beyond the scope of conventional methods and are, in some sense, better.
A digital circuit as a network of logic controllers: binary gates switching currents according to an on-board clock. The benefits of digital circuits: the modularity of the individual components; the large threshold of error for signal noise. Yet, the innate modularity of components promotes a 'top-down' approach to circuit design: large abstracts with functions made up of smaller blocks with more and more specific functions. There is often heat due to their excessive numbers.
Thompson used a fully reconfigurable PC with a 10 x 10 array of cells on which to form a circuit: each array consisted of a logic gate that was controlled by a multiplexer reading from the computer's RAM, as well as four I/O. The card ran independently of the computer once configured. The GA
( 1800 bit genotype, population size: 50, crossover probability: 0.7, per-bit mutation as 2.7 per genotype ) programmed in the computer controlled the multiplexers that configured the logic gates. The circuit was then tested independently of the computer, its fitness rating being fed back into the PC after each test. The goal was the discrimination of two tones: 1khz & 10khz without an on-board clock which it achieved perfectly in 4,100 generations.
The finalized circuit used only 32 of 100 cells and the exact methods of discrimination are unknown as the circuit resists all known types of testing. A diagram of the arrays suggests a delay loop was created: several cells were knotted together, causing the silicon underneath to conduct more heat and somehow affected the behavior of the remaining arrays. Efforts to rebuild the evolved circuit on an identical programmable array failed, the circuit somehow used characteristics unique to the card it was evolved upon. Thompson concludes by questioning the ability of any human designer to design a chip of comparable size without components.
The successful evolution of Thompson's circuit, Chomsky's generative grammar: both are actualized algorithms. Both contain genotypes and phenotypes. They both consist of phase-portraits in vector fields, they exist in an ontology defined by Deleuze as the virtual, the intensive, and the actual
[10] . The vector-space upon which a trajectory lies is the
virtual. Transient qualities are those that are manifested through the process of actualization, or the
intensive. And the calculable individuals of a vector-space, such as phones and unknown circuits are the
actual. Evolutionary algorithms such as Thompson's circuits and Saussure's phones exist in all three. However, algorithmic systems which are solidly delineated and defined ( such as cellular automata ) cannot be new, they have no actualization and exhibit no intensive properties. They are sequestered from
being. It is in these ontological dimensions that a system such as language can exist. And it is here that language manifests its own agency and undoubtedly, its own wonder.
