Religion
In reply to the discussion: Challenge To Theists [View all]and you don't get to decide that THE point is YOUR point.
But your point is also interesting. The question about direction of 1D-line presupposes an embedding space of higher or same number of dimensions where coordinates can be assigned, otherwise the question is meaningless. In the embedding space of infinite real line a subspace of finite length could have e.g. coordinates -1 and 1, but the question of "direction" wouldn't mean much. If we add another dimension, the "second" dimension to construct a plane, it is by definition orthogonal to the first dimension, in terms of complex numbers the real part remaining the same and the imaginary part as variable covering all the values of real numbers. Adding 3rd and 4th dimensions to the number theoretically non-trivial construction leads to quaternions:
http://en.wikipedia.org/wiki/Quaternion
The point: from the point of view of number theoretical structure of space geometry assigning ordinals to the construction of dimensions is not trivial, but goes hand in hand with the set theoretical hierarchy real numbers - complex numbers - quaternions - octonions (etc.).