Chomsky on “minimal structural distance” in language:
Take this sentence:
Eagles that fly swim.
Ok. And put an adverb in front of it:
Instinctively, eagles that fly swim.
“Instinctively” goes with a verb. Which verb? With “swim”? With “fly”? So, it’s “instinctively they swim” not “instinctively they fly.” Well, “fly” is the word that’s closest to “instinctively,” but you never use linear order, you never use closeness, to determine how things are understood. Or suppose you put “can” in front of it:
Can eagles that fly swim?
You’re asking a question about swimming, not flying, even though “swim” is farther away. And in fact there is a minimal-distance relation between “instinctively” or “can” and “swim,” but it’s a structural relation, and that requires looking into the nature of structure. Then you find that, yes, it’s a minimal distance, but a minimal structural distance, not a minimal linear distance.
Now, calculating linear distances is far simpler than calculating structural distances. If you look at the computational properties, calculating order is trivial. Calculating structure is quite difficult. Nevertheless, you just automatically, reflexively calculate structure.
Zizek on “minimal difference” in science/politics/love/art:
“In each truth-domain, anxiety signals the encounter with a minimal difference which hinders the absolute reduction or purification, that is, which is simultaneously the condition of possibility and the condition of impossibility (the immanent limit) of the domain in question: in science, ontological difference, which prevents the scientistic reduction of the object of knowledge to a positive entity (as in cognitivist brain sciences); in politics, class difference, which prevents the political project from fulfilling itself in a new non-antagonistic ‘harmonious society’; in love, sexual difference, which stands for the impossibility of the sexual relationship; and, in art, the minimal gap between art and daily life which condemns to failure all modernist attempts to unite the two. Each time the difference persists; however, each time, the point is not to ‘respect the limit’ but to push through to the end in order to encounter the minimal difference: to push through the cognitivist reduction of man to a brain machine to discover the “negativity” of the death drive; to push through the modernist unification of art and life to discover the ‘minimal difference’ between the two dimensions (Malevich, Duchamp); to push through love to confront the limit of sexual difference; likewise, one must push through a revolutionary process to the end in order to confront the insurmountable antagonism.” (Slavoj Zizek, Less Than Nothing, 2012)