I find it intriguing that chapter 14 of A Thousand Plateaus, Smooth and Striated, is organized in the form of a comparative analysis of a number of binaries. Each of the binaries presumably has roughly the same relationship between its members as the one in the Smooth and Striated pair. In their analysis, Deleuze and Guattari one by one examine the oppositions of felt and fabric, sea/desert/steppe and city, Eucledian and Riemann space, nomadic and sedentary lifestyle, optic and haptic vision, etc. The common and most important thing about all of these pairs is that their members are opposed to each other with respect to their structure, or their spatial and/or temporal organization: while one of the pair is amorphous the other is organized, while one is fixed and ordered the other is in a continuos flux, etc. As with other books by Deleuze and Guattari, A Thousand Plateaus is a complex text which invites many different interpretations and which perhaps provides more questions than answers. Naturally, I have my own set of questions. I wonder what motivates the authors to seek (and to find!) the smooth/striated dualities in different fields of human activity - from painting and music to mathematics and physics. How are such connections being made? Apparently, they are identified through analogy, or structural resemblance. But what would be the purpose of make such connections? It could be for the sake of creating a conceptual or cognitive metaphor, i.e., for facilitating understanding of a certain idea through other ideas from different conceptual domains, such as the scientific domain (so that the opposition of smooth/striated is explicated through the comparison with the opposition of Eucledian/Riemann).
However, in a different context Deleuze seems to insist that his use of scientific concepts is not for the sake of a metaphor: "Of course, we realize the dangers of citing scientific propositions outside their own sphere. It is the danger of arbitrary metaphor or of forced application. But perhaps these dangers are averted if we restrict ourselves to taking from scientific operators a particular conceptualizable character which itself refers to non-scientific areas, and converges with science without applying it or making it a metaphor" [Time-Image, 1989: 129].
It follows from the above that the purpose of comparing different binaries for Deleuze and Guattari is to extract from them certain idea or relationship that is operating in each singular case. If I understand Deleuze's project correctly, his overarching goal is to identify the constitutive forces that underlie the existing reality, or the plane of immanence. Different human activities, philosophy, sciences and arts, are brought into existence by these forces and at the same time reveal the forces through their respective tools: philosophical concepts, scientific "functions" and artistic percepts and affects (e.g., basic bodily forces, "the desire to sleep, to vomit, to turn over, to remain seated as long as possible" revealed in Bacon's paintings, or the "unheard-of force of a sunflower seed" exposed by Van Gogh).
If the meaning of the smooth/striated binaries in A Thousand Plateaus is to identify the smoothing/striating force, I wonder what is the Deleuze's (and Guattari's) onthological position with respect to such force(s). Do they exist in reality independent of human knowledge and understanding? Is this the nature of the universe? Or do such forces exist only in human perception and understanding? Are they mental constructs (just as concepts and scientific functions are) that we create in order to understand the reality, perhaps instinctively, responding to a biological need for producing thought similar to spider's need to produce a web? [Cf. Nietzshe On truth]. Finally, I am interested in the author's tendency to assign value to one or the other member of the opposition. Although it is rarely stated explicitely, the discussion seems to favor the smooth member in each pair (e.g., nomadic space vs. sedenatry space, etc.) in a certain complex balance of immanent ethics. The authors apparently lean toward the chaotic impulse of the smooth and nomadic, which overturns the striated and fixed space and produces new degrees of freedom and new possibilities of creation. But the new possibilities of creation lead to the new orders of striation as is the nature of rhythmic forces, and it seems pointless to favor only one part of the innately dual rhythm which is ever bound to transform into its opposite.