Linear algebra is exactly where "dimension" gets its abstract but very limited definition as a property of spaces, best summarized as an axis or direction, rather than a kind of space itself, which is what you need for anything like an alternate universe. I know this because I have in fact taken a course in it. I'm not sure what point you think you're making at this point.
I had forget about this but at my first year and while the algebra professor was drawing 3D vectors to explain the lecture, I was thinking "that is a 2D surface, so there should be a linear transformation between the two worlds".
Later at home, I've found such space transformation and built a small 3D world that you can walk, using only vectors and plain triangles :)
I was really hoping for a continuous (rather than discrete) fourth dimension. The concept is cool and looks to be well executed, but it's not very different from other alternate reality implementations such as the Dark World in Legend of Zelda.
Ultimately the environments are 3D images being generated from a 2D dataset. How is it not 3D? A cube is a 2D square that's been extruded into another dimension. It's not 2D.
You certainly know Flatlands by Edwin Abbott. It's a spatially 2D world and already different. Four spatial dimensions would be something you could try out. But how to understand 5D when you don't understand 4D? That's the issue with higher dimensions. There are a lot of entertaining books by physicists about higher dimensions, could be inspiring for your work.
He has been working in 4D for more than a decade (first mentions of Miegakure was in 2009), if it is ever possible to get an intuitive feeling of a 4D world, that should do it.
The alternative is to just throw away intuition and just do the maths with one extra vector coordinate, but that would be unfortunate for a game that is all about thinking in 4D.
Our eyes could get 2-dimensional projections of any more-dimensional world, actually, if it was available. The light-sensitive outline of that little guy in the video could accept photons from any 4-direction, and not only photons floating in his current 2-plane.
Ofc it is abstraction, I know that physicists aren't happy with heterodimensional settings at human scale.
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