No, you don't. It's working through the math problems that develops our intuition. Special relativity is something completely foreign to human experience.
You don't need the math? Then go ahead and draw the Minkowski space-time diagram for a stationary observer, complete with light cone. Draw a second light cone, to show the light-cone from the stationary observer's view of someone going .25, .5, and .75 c. Notice a pattern? The light cone tips over and gets narrower. Now, draw the light cone for an observer going c. It's a straight line - equivalent to the line of simultaneity in the stationary observer's view.
Now, draw the light cone for someone going 10c, 100c and 1000 c. The light cone now increasingly dips below the line of simultaneity and begins to widen out again. This means that the FTL observer can move into regions of the stationary observer's past and affect them. The light cone for someone going infinite c (instantaneously) is an upside-down light cone. From the stationary observer's view, the instantaneous travelers is no longer moving in space - he's moving backward in time.
Can you follow that without the math? I can, but that's because I've plotted enough Minkowski diagrams using the math. Even then, I have to stop and think about it. I'll admit that I had to look at the equations to figure out the slope of the world line for someone doing FTL.
Chris, if you want to go on believing that FTL is not the equivalent of time travel in Special or General Relativity (as currently formulated) then go ahead. It's fine with me.
Why should I care what mistaken beliefs you have?
Zooty