"For him, as I understand his work, the ultimate synthesis of a design was never revealed in a flash; rather he approached it with infinite precautions, stalking it, as it were, now from one point of view, now from another, and always in fear lest a premature definition might deprive it of something of it's total complexity. For him the synthesis was an asymptote toward which he was forever approaching without ever quite reaching it; it was a reality incapable of complete realization."
Roger Fry... 'Cezanne, A Study of His Development,' page 3
In his book, 'A Theory of Semiotics.' Umberto Eco wrote: "The interpretant can assume different forms." So I have used the term, 'asymptote,' to convey to you how I think Cezanne's painting developed. An asymptote is a mathematical term that can also be used in a metaphorical way such as Roger Fry has shown. However, I use it in the sense of a visual pun to form a bridge between the different contexts... Signified you could say, by the viaduct in Cezanne's painting. In essence therefore, it circumscribes cultural units in an asymptotic fashion... Linking them together like the arches of the viaduct. Then again, because I cannot be absolutely certain that this is how Cezanne perceived the development, the synthesis is an asymptote. In which respect, this theory of mine is pure conjecture: having no basis in fact. Here now is Umberto Eco...
"Because it is such a broad category, the interpretant may turn out to be of no use at all and, since it is able to define any semiotic act, may in the last analysis become purely tautological Yet its vagueness is at the same time its force and the condition of its theoretical purity.
The very richness of this category makes it fertile since it shows us how signification (as well as communication), by means of continual shifting which refers a sign back to another sign or string of signs, circumscribes cultural units in an asymptotic fashion, without ever allowing one to touch them directly, though making them accessible through other units. Thus a cultural unit never obliges one to replace it by means of something which is not a semiotic entity, and never asks to be explained by some Platonic, psychic or objectal entity. Semiosis explains itself by itself, this continual circularity is the normal condition of signification and even allows communication to use signs in order to mention things. To call this condition a 'desperate,' one is to refuse the human way of signifying, a way that has proved fruitful insofar as only through it has cultural history developed."
Umberto Eco... 'A Theory of Semiotics,' page 71
You will note that I underlined the words, "Semiosis explains itself by itself," because Cezanne's painting is in itself, a semiotic entity. One that without any help from me; via this type of explanation or commentary, should be capable of doing the same.