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You almost correctly solved the problem of Space.

"Space" is three vectors dimension of space (ix +jy +kz) and one scalar dimension of space (r). Hamilton defined Quaternions in 1843. Einstein was correct in calling for a 4 dimesnional space, but Einstein's Spacetime is an incorrect 4 dimensional space both Physics-wise and mathematically.

Einstein and others considered time an imaginary (vector) dimension ( it) and space three real dimensions (x,y,z). This is opposite to reality where space is quaternion with one real scalar dimension (r) and three vector dimensions (ix +jy+ kz). The real dimension r is related to time by r=ct where c is the speed of light.

In summary Space is 4 dimensional and all dimensions are space one real space (r=ct) and three vector spaces (ix +jy +kz), just as you proposed,

why can't time be also a distance?

It can and it is called Quaternion Space.

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