[quote=Morric]
But the dimensionality of an object cannot exceed the number of dimensions of the space it is embedded into. Physical “connections” have material properties only in the directions not tangent to the point. From the point of view of the internal observer “connections” will not have material properties. They will define a metric on the surface as it was explained in the multidimensional elastic geometry. Ultimately, physical “connections” in one dimensional existence can have non material properties in another.
[/quote]

You're misunderstanding. There are simply three spacial dimensions under normal circumstances. There is also time, but that is disputed. Another could possibly be multidimensional creatures, but those are few and far between.