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If simulation is possible, we could upgrade reality to 4D
(sh.itjust.works)
A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. A showerthought should offer a unique perspective on an ordinary part of life.
I'd recommend checking out 4d Toys - I believe it is compatible with VR so you could sort of do what you're describing.
You are correct that 4d toys (and other games) already simulate 4 spatial dimensions. But those games all display the 4th dimensional space from a 3 dimensional projection. I think what OP is suggesting is creating a game that displays an actual 4 spatial dimensions. I have argued in another comment that I don't think this is possible in a way that our brains could ever percieve or process due to the limitations of a brain evolved in 3 spatial dimensions.
The subject of how humans might perceive four dimensional space is covered in a later book of three body novels (Remembrance of earth's past series). The author describes is as being able to see into sealed three-dimensional objects as if they had an open top. As such you could easily traverse into sealed rooms etc from such a perspective.
I thought it was quite an interesting idea.
I've read it. Recently actually. It is really cool. It kind of supports my point though. It's hard for those to both comprehend and describe that have been in higher dimensional spaces and much of what they do describe is in 3 dimensional terms, (enclosed spaces being visible as if by an open top being a good example of trying to comprehend a thing that would be uncomprehendable in 4d through a 3d mindset). Of course, it's also written by an author that hasn't actually experienced such things and is also trying to imagine what it would be like to experience his interpretation of the phenomenon, so... not exactly conclusive either way.
Also later in the story
When they describe how 3 dimensional space is dropped into 2 dimensions, I think it also illustrates how hard it would be to comprehend 4 dimensions from our 3 dimensional mindset because every bit of 3 dimensional spaces that drops into 2d space would unfold and expand infinitely because there's no way to fit 3 dimensional data completely in 2 dimensions. So trying to comprehend 4 dimensions from a 3 dimensional perspective will likewise always leave gaps