The attached notebook shows that interpolation can only work on scalar data in up to 3 dimensions (that are not structured over a grid). The following code runs:
(*interpolation works with 4D data*)
d = RandomReal[{0, 10}, {1000, 4}];
f = Interpolation[d, InterpolationOrder -> 1]
f[5, 5, 5]
But it doesn't work with higher dimensional unstructured data. The following code fails:
(*interpolation fails with 5D data*)
d = RandomReal[{0, 10}, {1000, 5}];
f = Interpolation[d, InterpolationOrder -> 1]
f[5, 5, 5, 5]
Any idea why? And is there an easy fix?