Why the discrepancy? Well, it comes down to what counts in tie tying. Take, for example, a conventional standard: the knot must be covered by the cloth of the tie. In the film "The Matrix: Reloaded," a character (the Merovingian) sports a tie where the knot is exposed, and where the big end of the tie goes behind the small end. Also known as the Ediety knot, it's a tie knot that's possible (and even experienced some movie-inspired popularity) but wasn't accounted for in the previous math. Another metric changed in the Vejdemo-Johansson model was windings (where the tie is warped around another part of the tie), allowing for more windings and variable tie-length.