Cathleen Schine, in a New York Times review of Alexandra Horowitz's Inside of a Dog: What Dogs See, Smell, and Know (Scribner, 2009), suggests that
A human being experiences a rose as a lovely, familiar shape, a bright, beautiful color and a sublime scent. That is the very definition of a rose. But to a dog? Beauty has nothing to do with it; the color is irrelevant, barely visible, the flowery scent ignored. Only when it is adorned with some other important perfume — a recent spray of urine, perhaps — does the rose come alive for a dog. How about a more practical object? Say, a hammer? "To a dog", Horowitz points out, "a hammer doesn't exist. A dog doesn't act with or on a hammer, and so it has no significance to a dog. At least, not unless it overlaps with some other, meaningful object: it is wielded by a loved person; it is urinated on by the cute dog down the street; its dense wooden handle can be chewed like a stick." Dogs, it seems, are Aristotelians, but with their own doggy teleology. Their goals are not only radically different from ours; they are often invisible to us.She goes on to comment that
Dogs do not just detect odors better than we can. This sniffing "gaze" also gives them a very different experience of the world than our visual one gives us. One of Horowitz’s most startling insights, for me, was how even a dog's sense of time differs from ours. For dogs, "smell tells time", she writes. "Perspective, scale and distance are, after a fashion, in olfaction — but olfaction is fleeting. ... Odors are less strong over time, so strength indicates newness; weakness, age. The future is smelled on the breeze that brings air from the place you're headed." While we mainly look at the present, the dog's "olfactory window" onto the present is wider than our visual window, "including not just the scene currently happening, but also a snatch of the just-happened and the up-ahead. The present has a shadow of the past and a ring of the future about it."I may have to spend some time looking at Jakob von Uexküll's notion of the Umwelt.
A dog's vision affects its sense of time, too. Dogs have a higher "flicker fusion" rate than we do, which is the rate at which retinal cells can process incoming light, or "the number of snapshots of the world that the eye takes in every second." This is one of the reasons dogs respond so well to subtle human facial reactions: "They pay attention to the slivers of time between our blinks.") It also helps explain those eerily accurate balletic leaps after tennis balls and Frisbees, but Horowitz lets us see the implications beyond our human-centric fascination with our pets. This is more than a game of fetch; it is a profound, existential realization: "One could say that dogs see the world faster than we do, but what they really do is see just a bit more world in every second."
On time there's a broadly positive review of Shaping the Day: A History of Timekeeping in England and Wales, 1300-1800 (Oxford University Press, 2009) by Paul Glennie and Nigel Thrift.