More importantly, the concept of speed itself is confusing when you try treating time as just another dimension. Traditionally, speed means how many units of sp

More importantly, the concept of speed itself is confusing when you try treating time as just another dimension. Traditionally, speed means how many units of space do you move in a unit of time. Asking about your speed through the x dimension is as simple as asking for dx/dt. Asking about your speed in the time dimension is even simpler, it is just dt/dt, which probably isn't what you where actually interested in. You can ask for your overall speed in all spatial dimensions with dX/dt where dZ^2 = dy^2 + dx^2 + dz^2. By analogy, you could say that your speed through all of spacetime is dS/dt, where dS = dx^2 + dy^2 + dz^2 - dt^2. You could then say that your speed through time us dT/dt, where dT=1-dS. Although this quanity is really measuring the difference between proper time and coordinate time, which is just time dilation. An equivalent derivation works for length contraction as well. Importantly, all of these qualities are dependent on your choice of reference frames. Only dS and dT are frame independent, so (in some sense) they are the only true quantities. Both of them also rely on merging time and space to a single quantity. Of course all of what I wrote applies to special relativity (flat spacetime). Once you get to curved spacetime, your metric gets more complicated, but the general ideas still apply. Really, I don't see how you can make sense of general relativity as anything other than a 4 dimensional geometry with a really weird metric.