Much evidence supports the idea that parietal cortex is involved in the simple maintenance of information, such as in object permanence paradigms (also here) and other tasks. This evidence is part of the justification for the "parietofrontal integration theory", which suggests that parietal areas work in concert with prefrontal regions of the brain to accomplish the maintenance and manipulation of information. Orthodoxy holds the prefrontal cortex is more involved than parietal cortex in information manipulation (eg).
However, some have suggested that the spatial transformations accomplished by parietal cortex might also be used for the manipulation or organization of nonspatial information - for example, in the subtraction and addition of magnitudes.
Merriam et al described another type of spatial transformation implemented by the parietal lobe - spatial updating of information based on saccades. The basic finding is that the human parietal cortex not only maintains information that is absent from the environment, but also that parietal cortex reflects dynamic reorganization of that information after changes in the direction of gaze. A parietal capacity for these spatial transformations indicates that its representations are not only maintained after the disappearance of the referent objects, but also that those representations can be dynamically rearranged.
Subsequent work by Medendorp et al has shown that this remapping can be triggered by task-set: when subjects are provided with an initial location in space, and then subsequent told to either saccade in that or the opposite direction, activity in the posterior parietal cortex (the reintotopic area of intraparietal sulcus) changed accordingly. The authors note their results do not indicate that parietal cortex is solely responsible for antisaccade performance, but instead suggest that it may receive "task set" information from prefrontal cortex.
Nyffeler et al refer to this remapping process as "visual vector inversion," and showed that this probably occurs within the first 500ms of the antisaccade cue: early disruption of activity in the right posterior parietal cortex (via TMS) will decrease antisaccade performance if that area was representing the initially cued location, whereas later disruption of activity in the same area decreases performance if that area is representing the target location for an antisaccade. MEG research on this topic is largely consistent with these results: intraparietal sulcus and frontal eye field areas show peak vector-inversion activity mostly around 230ms. A slightly longer estimate of 400ms is revealed by ERPs source localized to posterior parietal cortex.
In summary, it appears that "vector inversion" processes engaged by the antisaccade task occur first in the parietal cortex, and prefrontal areas other than the frontal eye fields are more crucial for maintained vigilance or "preparatory set" during the delay period and prior to target onset (perhaps because dlPFC is responsible for information maintenance over long delays).
What more abstract forms of information processing might rely on similar computations as visual vector inversion? One possibility is that any form of cue-to-goal mapping might rely on the same transformation: given preparatory biasing from prefrontal areas, parietal cortex might flexibly update a stimulus with a different response. "Vector inversion" might be detrimental when the precise spatial locations of information must be maintained; this would be consistent with improvements in visual binding seen after dirsuption of intraparietal sulcus activity (via TMS).
Fascinating. The mind is a hungry hunter.
Accurate pattern matching has to be paired with anticipatory "fictitious patterns" to provide the mind with a Darwinian power of selection. Quite a tangle to untease.