The definition of left is that when facing north, left points to the west. But if we were in deep space, how could we systematically devise left right coordinate systems?
I tried to solve this by using symmetry. Suppose our bodies were symmetrical in 3d (so we were spheres). There would be absolutely no way of making any reliable definition of left or right. Now, suppose our bodies had 3d asymmetry. We could ask everyone to align their fronts and ups. But there would still be no way of using this information to deduce what left is a priori. As far as i can tell, everybody's 3 asymmetries must be aligned for it to work. So I'm guessing in n dimensions, we can align n-1 orthogonal asymmetries without a problem, but a decision must be made on the direction of the nth asymmetry. (This is true given the rule that we must map an object from one point to another in an 'unbroken line', though I'm still not sure how to define this in euclidean terms).
For us on earth, this decision is made by the position of the west and north. But how do our bodies know whether to place the heart on the left or right? We surely don't have the position of north and west ingrained in our genetics? In general how 'made up' is left and right? Is it something that can be deduced at all?