A stubborn knot in three-dimensional space is not stubborn at all from the vantage point of a fourth dimension. What looks absolutely locked is only constrained because every strand must dodge every other strand inside a tight three-dimensional corridor where paths collide instead of pass through.
Mathematicians capture that constraint with ambient isotopy and fundamental group, insisting that in three-dimensional Euclidean space a closed loop cannot change its knot type without cutting. The missing move is simple yet banned there: letting one arc of the loop pass straight through another, an operation that would require matter to overlap in three dimensions but becomes a generic motion once a new coordinate is available.
Grant a loop access to four-dimensional Euclidean space and the judgment flips. The extra spatial axis opens a direction in which one strand can lift out of the way, travel around what used to be an obstruction, then drop back without any cutting or self-intersection in that higher space. Rigorous results in topology show that any knot in three dimensions becomes unknotted by such deformations when considered inside four-dimensional space, not because the loop changed, but because the ambient geometry stopped caring about its former entanglement.
