This reminds me of the problem of designing digestive tracts for m-dimensional creatures in an n-dimensional ambient space. For example, if Pac-Man had had an anus, he would have split in two (without additional biology keeping him together).
This could apply to 1D too.
See Feynman’s video about why he’s not falling down through his armchair.
But note that we too are "split" into a myriad of pieces with nothing but empty space between them.