ELI5 How are the chinese languages mutually intelligible in writing only?

i speak 0 chinese languages, obviously

it baffles me that while cantonese, mandarin, shanghainese, etc are NOT mutually intelligible when spoken, they are in writing.

how can this be? i understand not all chinese characters are pictographs, like mountain, sun, or person, so i cannot imagine how, with non-pictographs like “bright”, meanings just… converge into the same meaning? or what goes on really?