Perhaps i am operating under a different (wrong?) understanding or definition of “dimension”, but this layperson was lost as early as “ The only possible one-dimensional surfaces are an open string, where there are two separate, unattached ends, or a closed string, where the two ends are attached to form a loop”. A sur”face” requires two dimensions. The only one-dimensional objects are (straight) lines, of which “strings” are one variety. If they are not straight they will require two dimensions as curvature will break out of this one dimension, unless the one dimension “housing” it is “curved” (in relation to what?) itself. Therefore a “closed” string that can only extend within one dimension would have to have an extension of l=0 in order to remain closed and be equal to a point, thus requiring no dimension at all. What am i missing ?