I've seen the statement repeated in many places that a stable knot comprising 1D curves cannot be created in 4D, since it's always possible to untie the knot by moving in the 4th dimension (whereas it is possible to create a stable knot in 4D using 2D surfaces). Can anyone point me to an authorative source for the proof of this statement (ideally available online)? Also, is anyone aware whether this statement remains true if the 4th dimension allows movement in only one direction (e.g. it represents time)? Intuitively I would guess that it wouldn't.