This is more mathematical than philosophical but through quantum mechanics, understanding that that higher dimensions are composed of higher amounts energy, and thus we invent a particle collider in order to create scenarios for evidence of these dimensions (subatomic black holes) I produced a argument:
Because of the particle liberty that complex 3D matter is exposed to in 4D space, the only true way of existing in a completely unified spectrum with another dimensional space is through the highly specialized and strengthened forces of gravity working at different intervals that would be so powerful it would not be able to differentiate matter...
In other words, I do believe that the concept of dimensionality exceeds beyond 3, but in a way that is not collectively held. Perhaps we might be able to create higher dimensions, but they quickly will supersede the presence of other particle forces through the sheer energy of and time lapse implied by electromagnetism at such conditions.
But to try to make this more philosophical...
When the universe does become static for a infinitesimal period of time (the point when expansion reverses) will higher dimensions supersede in that lapse of time.. essentially destroying everything it extends beyond. Or perhaps when it folds in on it self will we be exposed to more dimensions through the natural particle colliding of space in that effort.
Just wrestling around with our unitive desire for dimensions.
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