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Arguably all of these domains have the same "dimension", which is the intrinsic dimensionality of the human mind.
(I'm expecting pedantic, braindead replies about how mathematics is not a product of the human mind 
)
I don't know how probability of those group being wrong differs from those claiming it is.
Talk more about the dimensionality of the latent manifold. Obviously anything that can be encoded is one dimensional in that sense. Encoded is a representation through which we perceive a manifold with dimension irreducible in what sense?
Braindead if math is really out there 
Is there really one true latent manifold? I mean, you could stretch your way to 1D 
I remember seeing some work that tried to assign a VC dimension to the human brain.
Mathematics is product of human mind. What about the underlying patterns and principles it describes?
It is and linear algebra is how exactly the human thinks, yet it can become AI
Is it also brain-dead to ask how different cultures that used very different number systems, theories etc, ended up with the same mathematics? This leads to a fun question as to whether mathematics is invented or discovered, or both?
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