special relativity - Calculating speed in four dimensions

If you are moving at $c$ in 3D space and $c$ in time axis too, What would be your total speed?

Edit: Since question has been voted to be closed, I shall make an Edit. In 4D world all objects move with speed $c$. This implies there should be a relation to compare speeds in two realms space and time.

Answer

The spacetime interval is a relativistic invariant, and is proportional to the travelers proper time. So in a since you are traveling one second per second, per your own wrist-watch. Every other measurement would be the speed of some other inertial reference system, measured with your clock.

Let $s^2 = x^2 + y^2 +z^2- (ct)^2$, where $x$, $y$, $z$ are coordinates in some inertial reference frame, and $t$ is the clock from that same frame. Then $s$ is the spacetime interval for the object that began at location $(0,0,0,0)$, and is now located at $(x,y,z,t)$. Perhaps you set off a firecracker at the beginning, and again at the end: two spacetime events. While different inertial observers will observe different coordinates and times, based on their relative velocity, they will all agree on $s^2$ for the spacetime interval between the two events.

You, the person setting off the firecrackers, can also measure $s^2$. Perhaps you are standing still -- then $s^2 = (ct)^2$ according to your wristwatch. Now calculate your speed: $ds/dt = c$, and in units where $c=1$, it is just one tick per tock.