A famous experiment was conducted in the late 1800s, in which a scientist wore glasses that showed him an upside down image of the world. After some time, he claimed he saw the world right side up. Scientists have been trying variations of this trick ever since.
Never let an experimental scientist give you glasses. They always have ulterior motives. The first documented case of optical experimental shenanigans was inflicted on the scientists himself. In 1897, George Stratton published 'Vision Without Inversion of the Retinal Image,' about his experiences with a pair of glasses which inverted the world.
The reason why it's called 'Without Inversion,' is, due to the quirks of optics, the image that hits the retina of the human eye is upside down. The brain automatically inverts it, so we see the world the way we do. The glasses made it so that Stratton, for the first time in his life, saw a right-side up image of the world. Not surprisingly, his brain turned it upside down again, and he blundered around and crashed in to things. After a few days, though, Stratton was able to adapt and work as normal. In his paper, he claimed that, by the end of the experiment, he actually saw the image through his glasses as right-side up.
Ever since then, scientists have tried to duplicate, or tweak, that experiment. Throughout the years, people have paid what must have been starving students with excellent headache medication to wear the glasses for long periods of time. The most recent study was conducted in 1999 and published in Perception.
As Stratton did, the subjects of the study all adjusted their actions to the upside down world. They did not, however, see the world as right side up. Mostly, they reported feeling as though they had been turned upside down in the regular world. Essentially, even though they knew it wasn't true, they felt like they were walking on the ceiling or the sky. But there was never any actual inversion.
Over the years, though, other people have had more luck. They found that practice with goggles which caused random but severe visual distortions let the wearers compensate for the distortions to the point where they didn't notice them. When the goggles were removed, the subjects saw the real world as distorted for some time. Minor distortions, like glasses which made objects directly in front of someone seem far to the right, could be worn for only a few minutes — subjects wore them to shoot basketballs — and left the person physically confused as to wear to aim the basketball for some time after the goggles were taken off.
So it looks like the mind adapts to a lot of different distortions. But actually turning the world upside down? It doesn't go that far.