In this essay, I intend to give a non-deistic definition of an Artwork. However, some certain mechanisms of it are mysterious enough to possibly still require a "divine light" to act. At the moment, my definition is still hazy to me, and this essay is only a sketch of a potentially deeper theory yet to unfold.
As mentioned in my other essay, once the concept of an "Artwork" is defined, "Art" is simply the set of all Artworks, and an "Artist" is someone capable of making an "Artwork".
Here we will assume the pre-existence of an "inspiration" or primary impulse producing a "vision" which the rest of the creation process follows in an approximate manner. The end result may in fact significantly deviate from the preconcieved vision. (Note that I prefer unaided artistic visions.)
To begin the definition, first we will define "Taste". Let Taste be a finite set of contractive transformations (mathematical functions in the sense of Iterated Function Systems), which each transform a perceivable object into another, in one step. Define an "impulse" as a specific contractive transformation of Taste.
Note that here "perception" is that of any conscious being (whatever consciousness means), not necessarily a Human, and the object may be visual, written, auditory, or other. What "contractive" means, is unclear to me at this point, but it certainly means that in an abstract space (not mere 3D), a certain mathematical measure (abstract volume) of the Artwork gets smaller due to the transformation. This abstract measure could be beauty, ugliness, dynamism, etc. depending on the impulse's given function in the abstract space. Let that abstract space be called (Collective Human) Imagination, and let the transformations of Taste (impulses) be operators over that space.
The impulses likely have two main classes: creative and corrective. Creative impulses bring new elements into the object, while corrective impulses merely modify the object, or its certain part(s). The new elements could be the overall composition, color and tone patches, new note in a musical score, etc.
A crucial question is how impulses act in time. Do they act one after the other, or in a parallel manner? In the second case, which is implied by Human brains being parallel processors, the impulses create a multilayered flow of creation, which nevertheless has a finite number of layers, as many as the impulses. Since for instance if there are ten acting impulses, each of them act sequentially by themselves, creating an individual sequence. So ten parallel sequences will make up the flow of creation. In the first case, there is only one sequence of impulses, where each sequence element is due to one random impulse.
How do impulses acting in parallel create a new object as a whole? Each individually produces a result, but how do the results get combined? Possibly via a weighted average of the individual results, or by a simple set union, or there may be one additional complex "master impulse" directing their combination.
What is the nature of the transformations? Are they genetically ingrained, learned over time, or inspired by a divine light? Possibly their biology have components due to each. This is the mysterious, potentially deistic point in my new definition. Impulses certainly have an evaluating element of the object under transformation, and they produce a result based on the evaluation.
Impulses may not be deterministic, due to the fact that the Human brain is non-deterministic to an extent. In practice this means that Humans have "opinions" that may change - in other words for the same input, the brain produces a different output at a later time. The actions of impulses may vary similarly to some extent, based on probabilistic factors due to hormonal, emotional, etc. changes in brain chemistry, or for other reasons, at any moment.
We have now arrived at defining an Artwork. The initial object which is acted upon by the impulses, could be anything. Visually it may be a blank canvas or a heap of trash. Define an "iteration" to be one acting step - when the impulses act in parallel to transform the object into a new stage (some impulses may skip acting in an iteration), while combined via a master impulse.
Thus the impulses transform the object iteration by iteration, acting upon the previous result in a recursive manner. Since impulses were defined as contractive in the abstract space of Imagination, we thus have a contractive Iterated Function System (IFS) which by the Banach fixed point theorem has one unique fixed point, as the iterations tend to infinity. Let this fixed point / attractor be called an "Artwork".
Continued in Part 2/3: Artworks as Attractors in Practice.