Interesting way to phrase the question, the answer is... depends on relative motion. The notion of simultaneity which is the technical term for what you describ

Interesting way to phrase the question, the answer is... depends on relative motion. The notion of simultaneity which is the technical term for what you describe as "being flat" in the time-direction is not an absolute thing in relativity. With respect to your own reference system you are essentially "flat" in the time direction [1], but with respect to someone that moves at a certain speed with respect to you you have certain size in the time direction. The best way to picture it is via Minkowski diagrams, you can find some neat visualizations in the wikipedia article: https://en.wikipedia.org/wiki/Relativity_of_simultaneity https://en.wikipedia.org/wiki/Relativity_of_simultaneity Simply picture an extended object in the x direction, Lorentz transformations are going to rotate it slightly in the time direction causing it to become extended in the time direction. [1] If you take it to the extreme you may consider that different parts of your body move with respect to each other and thus they are not in the same reference frame. In which case, not even with respect to yourself are totally "flat" in the time direction.