Why does moving close to the speed of light cause time dilation???

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Hi anons! I'm someone who is extremely motivated to learn astrophysics and particle physics to the greatest degree. Anyway, I'm just getting started on learning spacetime, and something confuses me-why does moving close to the speed of light affect time and how you age? I understand that space and time can be one 4 dimensional plane, and that when you move close to the speed of light you are perceiving light slower than someone who is stationary in your frame of reference. But what I can't wrap my head around is why this slows your aging, since you're still moving slower than light. Can someone explain this to me?