Calculating the distance between 2 straight lines in a 4d space?

The Euclidean method can be extended to 4 dimensions. If you mean 4 dimensions of space, then it's √(w^2 + x^2 + y^2 + z^2). If you mean 4-dimensional space-time, the distance is given by √(x^2 + y^2 + z^2 - t^2). Notice that t has a negative value, which makes time fundamentally different than space.

Problem with this is, between the 2 lines, the normal 3D-space rules do not apply. While in 3D space, there will always be at least a single 'closest' point between the lines that we can use to measure distance, in 4D space, the lines can be in any possible 3D 'dimension' within the 4D space. Therefore, even if we can calculate absolute distance through 4D space, that distance can behave unpredictably throughout the length of the lines if they do not occupy the same 3D dimension.

Hope that helps?

(BTW - Lodar's formula only measures the distance between points.)

sad