The following clip from Chaplin's 1921 short film, "The Idle Class," one of his Mutual Series films, is for me both a clear example of the action-image as Deleuze discusses this in his Cinema books and it points to an important claim Mark Wilson makes in his book Wandering Significance.
With the time-image, however, the sensory-motor link is severed, or the connection between an action and a situation is wanting. For Deleuze Orson Welles’s Citizen Kane is, as he puts it, “the first great film of a cinema of time” (C2 99). And we can see why, beginning with the opening scene when Kane utters his dying word, "rosebud." What is the connection between this action and any situation from Kane's past? The rest of the film is then structured around this question as a reporter attempts to connect Kane's dying action to the relevant situation – it is assumed there is such a connection, whether to a former love, place, thing, etc.
I have discussed these issues elsewhere, but while reading Mark Wilson’s book Wandering Significance I was reminded of the importance of the sensory-motor link in tracking the relationship between actions and situations (or the behaviorist model). Although Wilson does not use terms such as a sensory-motor link, he does bring in numerous examples that highlight the difficulties of applied mathematics (and other disciplines) in tracking natural phenomena, or in maintaining the link between the model and the modeled. Take the efforts to model the formation of spray on the surface of a choppy sea. If we begin with a smooth surface, Wilson points out that the equations that track the formation of globules as they break free from the surface will never effectively break free. The “attached blob,” Wilson claims, “never relinquishes its absurdly elongated umbilical tie to the mother ocean” (210). The reason for this, Wilson explains, is that the “partial differential equations, left to their own devices, do not alter the topology of the situation they model.” This, however, is not how the droplets actually behave and so what applied mathematicians do is to adopt a two fluid approach that “run in parallel, one containing the still attached drop and the other describing a drop of similar shape detached from its ocean,” and these parallel approaches, it is then assumed, will merge at a critical boundary when the behavior will jump from one approach to the other. And it is this boundary, or transition region, that is critical, as Wilson illustrates in the following diagram:
The transition region in the third strip is the critical boundary where the two approaches merge, and in so doing establish a better model of the behaviors we actually observe.
What is interesting here is precisely what is going on at the boundaries. It is here where many of the difficulties emerge, or it is here, as I'd prefer to call it, where the axiomatic becomes problematized by intensive processes inseparable from the modeled actualities. If you watch the Chaplin clip again, knowing in advance the shift he makes from crying to shaking a cocktail, you can see the subtle (or perhaps not so subtle?) transition region. It is this region that is often overlooked, Wilson claims (and he makes this argument explicitly in an essay on Hume's scepticism regarding causation [here], where he claims the complexities associated with modeling and describing the impact of billiard balls was not only above the pay grade of Hume but remains, to this day, incompletely understood), or it is assumed to be neatly sewed up, without gaps, by a unifying theory, whether in traditional classical form or in what Wilson calls the hazy holism of Quine and others. Similarly for Deleuze the time-image is a consequence of the failure of the sensory-motor link, or a problematizing of the action-image, and it is in the resulting gap or intensive, problematic field where the interesting work of a cinema of time takes place (though I would argue that such problematic fields are present as well within action-image films). Wilson is adamant, however, in holding that although a single model may not successfully track natural phenomena through all scales and situations, such as boundary situations, this is not meant to undermine or discourage our ability or desire to track natural phenomena - what he sees as a poststructuralist skepticism. Far from it! If we abandon classicism, or what Wilson sees as the view which holds that there is a core attribute or property, or ghost property to use Wilson’s term, that will neatly enable a tightly sewed up axiomatic modeling of nature, and if we adopt instead a facades approach of loosely stitched and quilted methodologies (such as the diagram above illustrates), then we will actually have a more robust ability to track natural phenomena. This theory of facades that is neither a unitary approach nor a relativistic anarchy, is in large part right in line with a Deleuzian theory of concepts and Ideas as multiplicities, but that’s a whole other discussion (see here).