Even a fetus has stimulus. Sound, pressure, movement, touch. Without stimulus and the ability to react you would develop no intelligence, your brain networks cannot be trained. Life would be a fuzzy haze until you die.
Interesting thought experiment.
Your ability to rotate in place is redundant. Your vestibular apparatus is located in your ears, which don't exist in this space, meaning that you are wholly incapable of proprioception.
Hence, the only input you're getting is the colour white. However, since you have nothing to compare it to, I would expect that any and all circuits designed for perceiving lines, edges, shapes and other colours would fail to develop. The same goes for circuits related to sensory input that is non-visual.
Connections between neurons that go unused are pruned, and it seems that all connections that originate and terminate in the brain go unused in this thought experiment. My guess would be that you would end up with a brain full of disconnected neurons, though I'd hesitate to even call that a brain.
To me it seems intuitive that you wouldn't be able to form cogent thoughts, especially not in language. An interesting question to me is what would happen if you did receive stimulus of some kind. Say, a small red die appears in the bottom of the sphere. How much "random" stimulus of this variety would it take to stimulus consciousness? Would the stimulus have to be nonrandom in order to provoke any patterns of thinking?
Three data points from which to infer a possible result for this thought experiment:
AFAIK, feral children rescued after the age for developing language passed have extreme difficulty learning words and abstract concepts. Their vocabulary ends up limited to about 400 words, all about simple, concrete things, and they don't develop past that. This despite them having had several years of sensory stimulation.
Some people who go into coma and remain conscious while unable to provide any feedback. Eventually their despair ends, and their minds settle into a dreamlike state that may last for years, during which they construct fantastical worlds, sometimes partially awakening due to some perceived external stimulus, followed by falling asleep again. Once they get out of the coma and back into a proper awakened state their memories of those imaginary events becomes fuzzy and fades.
The human visual cortex requires movement as much as color for visual processing to function or even, I suspect, to develop. You may try this yourself: fix your sight on a single point devoid of any mobile stimulation, while managing to not move your eyes at all, and it'll shutdown, your field of vision filling with something akin to grayness irrespective of whatever it is your eyes are fixed on.
Your thought experiment seems to be a combination of all three. Such a mind would be incredibly crippled from a cognitive standpoint, and even if it managed to somehow developed something at all in that department (maybe the whiteness is imperfect so it caught on the smallish of variations?), it'd be in a permanent state of dreaming about the raw sensory input of "noise" (which is what pure whiteness is, maybe the closest to "nothing at all"), without any possibility of any abstractive mental counterpart to that one single sole raw sensory reference, as there's nothing to compare it to to draw distinctions.
Then, once you put it into any other environment it'd develop somehow, but by that point most of his neural pathways would have atrophied, so whatever this mind developed would be orders of magnitude simpler than a feral children could do. I imagine it'd be mostly in a vegetative state, simply empty.
Seems that meditation is largely about looking in and one of the main obstacles is that looking out is so enticing that the motivaton to looking in is not apparent.
I would think that as a environemnt oriented brain the expectation of what the experience would be like would be largely different than what would actually be experienced.
Part of the problem with the setup is that normal human eyes need the visual cortext to be calibrated before vision even works. So do you get a miscalibrated or uncalibrated brain? If you get a "healthy" brain then part of the functional requirements would be all kinds of capacity for thought.
Imagine an existence where the only perspective for your entire life (40 years) has been from the inside of a white sphere. In this white sphere, you have no physical body, and there is nothing else in the white sphere with you. You only exist in this white sphere as a brain with perfectly working eyes attached. The gravity inside creates a perfect equilibrium which forces you to float in a single spot, but you can rotate in any direction. You can't see your own brain, or what is powering your brain. Your brain sleeps for 8 hours a day, and it's capable of dreaming. What do you think or dream about inside this white sphere?
I can't imagine you would be able to think about anything at all. You can't imagine, "What is this place?", because you don't know those words and what they mean. Any language happening in your conscious would be impossible. You've never seen an object or angle, so your concept of reality is confined within the white sphere, which, as far as you know, is infinite in every direction. My assumption would be that you'd have the cognitive ability of fetus and nothing more. On the other hand, could it be possible that evolutionary biology would force concepts in your conscious, provoking thought? If so, what would those concepts be? Would they be profound enough to make your conscious question its existence?
Besides sight, could it ever be possible to achieve sentience in this white sphere? And, if not, is it subjectivity that creates the sentience that drives us?