There is no cognition without memory, that is, without the redintegration of events. In Semantic Cognition (Rogers & McClelland Reference Rogers and McClelland2004), the depth and breadth of thought by the authors on semantics is impressive, but I fear the claim that their model dwells in the perceptual/ecological sphere ignores the realities of this sphere, resulting in an inadequate theory of redintegration.

Consider an event: stirring coffee in a cup, using a spoon. The event has a time-extended invariance structure, here defined as the transformations and invariants specifying an event and rendering it a virtual action. The swirling coffee surface is a radial flow field. The constant size of the cup, should it move forward or backward, is specified, over time, by a constant ratio of height to the occluded texture units of the table surface gradient. The tau ratio defined over this flow field supports modulating the hand for grasping the cup (Savelsbergh et al. Reference Savelsbergh, Whiting and Bootsma1991). Were the cup cubical, its edges and vertices are sharp discontinuities in the velocity flows of its sides as the eyes saccade, where these flows specify the form of the cup (cf. Robbins Reference Robbins2004; Reference Robbins2007). The periodic motion of the spoon is a haptic flow field that carries an adiabatic invariance – a constant ratio of energy of oscillation to frequency of oscillation (Kugler & Turvey Reference Kugler and Turvey1987). The action of wielding the spoon is defined by an inertial tensor describing the moments of force (Turvey & Carello Reference Turvey, Carello, Epstein and Rogers1995). It is this entire informational structure and far more that must be supported, globally, over time, by a neural network – by the resonant feedback among visual, motor, auditory, even prefrontal areas. To define the “summary sketch” or compressed format, stored in the hippocampus, of this dynamic, ever changing, global pattern (McClelland et al. Reference McClelland, McNaughton and O'Reilly1995) would be interesting.

In Rogers & McClelland's (R&M's) formulation, I present an occurrence, SPOON, in the context, CAN, and the network is trained, via weight adjustments, to respond with STIR. In the causal version, the network is trained to predict the sequelae – the “circular motion of the coffee liquid,” the clinking sound, and so forth. What sense is this? This is a remnant of the supremely non-ecological verbal learning tradition, its roots in the semantics-eradication program of Ebbinghaus, which ultimately bifurcated events arbitrarily into components (now feature vectors), for example, SPOON and COFFEE, then asked: How do we learn these components as a paired-associate pair? This is the paired-associate (PA) learning framework of the older cousin-model (McClelland et al. Reference McClelland, McNaughton and O'Reilly1995). Paivio's (Reference Paivio1971) introduction of imagery, later the elaboration techniques, where SPOON and COFFEE are imagined in a dynamic event, were the first near-ecological cracks in this brute force, syntactic learning framework. Coherent covariation is essentially a low-order, syntactic invariance, insufficient to carry the form of invariance structure described above.

In reality, we are perceiving the spoon as an integral part of a stirring event, with all the event's ongoing invariance structure. Where is the “error?” We need no weight adjustments to “link” the event “components.” A spoon scooping and lifting oatmeal is yet another event with an integral and complex set of forces and auditory/visual patterning. A spoon stirring pancake batter is yet a different complex invariance structure. A spoon digging into and cutting grapefruit is yet another. A spoon balancing on the edge of the coffee cup another. Now we have the set: SPOON CAN: [stir, balance, scoop, cut]. If I re-present SPOON, which event will it redintegrate? Presenting SPOON is roughly equivalent to a static event, a resting spoon. There is little structure to this cue-event; it is underspecified, yet common to all. It is like sending an imprecise reconstructive wave with little coherence through a hologram – we reconstruct a composite image of multiple recorded wave fronts, in this case, spoon-related events. It is the classic interference of McGeoch (Reference McGeoch1942). The brain's neural network does not require error-training to specify this set.

But we can retrieve specific events. The cue must bear the same invariance structure or a sufficient subset. For the coffee stirring, we re-present an abstract rendering of the coffee's radial flow field, or simulate the inertial tensor of the wielding. We are creating, globally throughout the brain, a more constrained, more coherent “reconstructive wave.” To reconstruct the batter-stirring event as opposed to the coffee-stirring, we must constrain our wielding cue differently to capture the larger amplitude of the stirring motion and/or the greater resistance of the batter. In essence, we are discussing a “paired associate” paradigm, call it A-B/C/D, that is impossible in the verbal learning realm, for every cue is in effect SPOON, yet with the appropriate ecological, dynamic constraints on a cue event involving a spoon, we can reconstruct each separate event (Robbins Reference Robbins and Fallio2006a; Reference Robbins2006b). But we also understand, “A SPOON can CATAPULT (a pea),” for the spoon, we know, can be inserted in, and supports the forces/invariance structure of, catapulting. This is precisely the realm of French's (Reference French1990; cf. Robbins Reference Robbins2002) devastating critique regarding the Turing Test – we would need to train for all possible object pairs – and the network proposed is no better equipped for these emergent analogies; it is simply not capturing the source of the semantics. It might be held that some analogy program such as Structure Mapping Engine (SME) (Gentner Reference Gentner1983) must now take over, but these must now define, ad hoc, the relevant “features” of catapult and spoon which are then merely algorithmically related (French Reference French, Riegler, Peshl and von Stein1999; Robbins Reference Robbins2002), again precisely because these systems ignore the ecological invariance defining events.

Ecological invariance forces an entirely different principle of retrieval for events and higher-order invariance (classes) across events. Discovering invariance laws, it is heavily argued (Kugler & Turvey Reference Kugler and Turvey1987; Wigner Reference Wigner1970; Woit Reference Woit2006; Woodward Reference Woodward2000; Reference Woodward2001), is scientific explanation. This subsumes the “causal” explanations of theory-theory. In this, science models itself after the brain in perception, and in this sense R&M, in holding, contra theory-theory, that there is no special mechanism, are perceptively right. But the neural dynamics required for the transformations and invariance noted here is beyond the coherent covariation detection of the model; the lesson of invariance in the ecological sphere has yet to be engaged by either side.