Extra Dimensions: Real or Mathematical Constructs?

[DavidSnider]

When physicists talk about 4+ dimensional space are these real spatial/temporal/something dimensions or just mathematical constructs that are the only known way to accurately describe the observed behavior?

Take the flatland example... We live on a 2D Plane and see a 3D Object (say a sphere) descend through our plane and leave a weird pulsating circle that appears and disappears all over the place.

The flatlanders can easily come up with a 3D model that describes the behavior, but how do they know it's not just some really complex 2D behavior they don't understand?

 

[BruceW]

In your flatland example, yeah, I guess you could either say its a 3d object or a 2d object that changes with time. Both explanations seem consistent to me.
I guess that it is more likely to be a 3d object because the 3d object would be simpler, since it doesn't change with time.
Maybe a similar explanation gives a reason for why we think we live in a world with more than just 2 dimensions.

 

[khemist]

The 4D model of spacetime is not just a construct. If one were to give exact coordinates of an event, one would need 4 coordinates, 3 for space and 1 for time (x,y,z,t or $\theta$, $\phi$, $\rho$, t, or any other coordinate system).

From what I understand, even though one might be able to model a 3D object in terms of its projection, it is FAR easier to model it in 3D. And I would guess that often times the projection does not give all the information about whatever is being projected.