In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the unknot). While in common usage, knots can be tied in string and rope such that one or more strands are left open on either side of the knot, the mathematical theory of knots terms an object of this type a “braid” rather than a knot. To a mathematician, an object is a knot only if its free ends are attached in some way so that the resulting structure consists of a single looped strand.

However, give me any closed loop knot and an extra dimension and I will show you an unknot (i.e., there are no knotted 1-dimensional spheres (strings) in dimension 4. Zeeman took this further and stated that any n-dimensional sphere is an unknot in a space of dimension higher than (\frac{3}{2})(n+1)). Read the proof here.

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