A new book by Alexandra Horowitz, "Inside of a Dog: What Dogs See, Smell and Know," gives humans a dog's eye view of the environment as seen - or rather, sniffed - by this most olfactory of creatures. She writes that dogs are "creatures of the nose" and that their gaze is actually a gesture accomplished via the nostril, and that the input is what shapes their world.
For squirrels, it is likely no different: A squirrel's world is populated by pinecones, nuts, predator urine and, of course, other squirrels, all striking a pose via the nose. A squirrel can sniff out a nut buried beneath a foot or so of snow, which probably would be the nasal equivalent of 70/20 vision. (Fitting the nose with eyeglasses, or noseglasses, would be a challenge however to any squirrels who are olfactorially challenged.)
See this for yourself: Throw a nut or some other goodie at a squirrel and the creature will probably continue to stare at you, even with the treat barely a half-foot away. But once the squirrel catches a whiff of what you've lobbed, all bets are off.
Clearly, this is why there is no U.S.Open tennis championship for squirrels: Tennis balls don't have any distinguishing odors to make them worth pursuing.
The same for competitive diving: Swimming pools smell only of chlorine, a scent unknown to squirrels, and so squirrels also eschew competitions such as Olympic diving (although flying squirrels would likely do quite well).
Likewise, squirrels also don't play soccer or football because, unless the object of the team's pursuit is a giant hazelnut, what's the point?
And squirrels would make awful commercial pilots. Clouds don't smell, and neither do runways. Air-traffic controllers would have a hard time guiding them in to the runway without incident.
But squirrels have better insight than they do foresight or even hindsight and for them, the environment looks so much better when it's viewed nasally. It's no surprise, then that from their own treetop worlds, they're looking down their noses at us!