I would like to regard an intrinsically flat 2-torus. This is usually sketched as a square with the left and right edge identified and the upper and lower edge identified, respectively. The four corners of the square represent the same point. Now I connect this point to itself via a loop on the torus, which shall be a straight line, and there shall be only one winding. There are only two possibilities: Either along one of the edges, which is the short distance; or along one of the diagonals, which is the long distance. Does this mean that there are preferred directions on the torus or is this only an artefact of an inappropriate graphic representation? Sorry, if this is a dumb question and thanks for any answers.