This is another one of those classic problems that Gibson (and James) attempted to solve by redefinition. Perception, said James, is extended in time:
The practically cognized present is no knife edge, but a saddle-back, with a certain breadth of it's own on which we sit perched, and from which we look in two directions into time (James, 1890)
As with many of James' radical claims, he lacked a clear mechanism, although he assumed it was rooted in the activity of the body. As usual, it's Gibson to the rescue, with ecological optics and the idea that information is contained in invariants that are revealed over time and activity. The present, by this account, has no fixed size, but it ebbs and flows with the event structure of what you are up to.
Heft offers the following example: imagine you are exploring a small cube by rotating it around in your hand. It takes a few seconds of exploration for the information about shape to unfold (because the information is what remains invariant over transformation). In this case, the 'present' of perception is a few seconds because it takes that long to apprehend anything resembling an 'object of perception', i.e invariant information.
Now imagine you are exploring a large object, like a statue, which you need to walk around in order for the required invariant information to reveal itself. What about navigating a city, where you might need hours for the structure to unfold? Is this still an act of perception? Surely, past a certain point, we must invoke memory; but when is that point? A few seconds? Minutes? An hour? On what principled basis can we distinguish between perception and memory?
Heft suggests (based on a proposal by Ed Reed) that time is the wrong dimension to distinguish these processes, because there is no obvious place to draw the line. Instead, he proposes that information is the key. In the case of exploring the cube, as the invariant structure unfolds you gain access to the whole of the thing, and thus now sit on a 'saddle-back' looking 'in two directions in time'; if you wish to recreate a perceptual experience there is information to guide that retrospective behaviour. and there is now also structure to guide prospective exploration, the search for additional information. Perception is the exploratory process in which there is the possibility of new information; memory is the exploratory process in which there is no such possibility (if, for example, the cube was no longer available).
In summary: Space and time are integral parts of the informational basis of perception and thus there is no mystery as to how they come to be in our experience. Perceptual experience is four dimensional because perceptual information actively supports all four dimensions. In the next section, Heft will apply this to the specific examples of navigation & the question of possible knowledge.
A note on all this: this account reflects the ecological hypothesis that stable actions and experience are never the result of educated guesses based on hints and inference - these things are actively maintained, and when the flow of information is cut off (if I flip off the lights, for instance) stable behaviour persists only for as long as the system can maintain it's hold on the event structure (by virtue of the dynamics of the device being used, for example; walking, for instance, can continue for a time without ongoing information because the inverted pendulum dynamic, once assembled, has structure and inertia).