| (quoted from Robbins v. New York)
Hausdorff: The nub of the question is how the legilators intended us to measure distance. Did they intend the Euclidean metric, which measures distance in a straight line from point A to point B, oftend desribed as "how the crow flies", or were they intending the taxicab metric, also known as the Manhattan metric, which measures the total distance traveled as you walk from point A to point B if you are required to stay on the streets that meet at right angles and are not allowed to take the diagonal?
Justice Thomas: Couldn't they have intended some other metric all together?
Hausdorff: I'm sorry, your honor. I'm not sure what you mean.
Justice Thomas: For all we know, they intended the Weil-Peterson metric.
Justice Ginsburg: Clarence, I believe the Weil-Peterson metric only applies to Teichmueller space.
Justice Thomas: Okay then, how about the Hermitian Yang-Mills-Higgs metric?
Justice Breyer: That applies to complete Kahler manifolds. Can we stick to metrics for measuring distance in the plane?
|