Is there an effective difference between distances in 3d space and higher dimensional space

Note before I begin: I am aware that this might be a Math-heavy question that might be better suited for the math.se

Goal: I'd like to use n-dimensional geometry as a method for effectively travelling/sending information with FTL speeds without technically violating the lightspeed limit in 4D Spacetime.

Assumptions

1. The technology to manipulate space to works
2. The necessary power can be generated on board of space vessels
3. You can transfer mass into a higher and from a higher into a lower dimension

Question

How would perceived distances change in higher dimensional spaces? Can you reduce the perceived distances by using a dimensional transformation between our 3D-Space/4D Spacetime to higher dimensional space and back? If not, is there another (mathematically) feasible solution that would reduce the distances using some kind of transformation?

How would the dimensionality of the hyperspace affect the ability to shrink distances in normal space when shifting dimensions?

Notes

I prefer solutions that allow for a more or less physically different "hyperspace".

I am aware of only some spacial properties like geometrical transformation of appearance of objects that change from 4D-Space to 3D-Space to 2D-Space only by what little I can remember of geometry classes and the novels from Xishin Liu The Three-Body Problem

It is explicitly encouraged to provide the Maths for me to understand the principles, or to provide geometrical explanations.

posted over 7 years ago

Doomed Mind‭

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