does not describe the physical conditions at this point. It is hoped that the solution to this paradox will be found with a consistent theory of quantum gravity, something which has thus far remained elusive. A consequence of this paradox is that the associated singularity that occurred at the supposed starting point of the universe (see Big Bang) is not adequately described by physics. Before a theoretical extrapolation of a singularity can occur, quantum mechanical effects become important during the Planck era. Without a consistent theory, there can be no meaningful statement about the physical conditions associated with the universe before this point. Another paradox due to mathematical idealization is D'Alembert's paradox of fluid mechanics. When the forces associated with two-dimensional, incompressible, irrotational, inviscid steady flow across a body are calculated, there is no drag. This is in contradiction with observations of such flows, but as it turns out a fluid that rigorously satisfies all the conditions is a physical impossibility. The mathematical model breaks down at the surface of the body, and new solutions involving boundary layers have to be considered to correctly model the drag effects. Quantum mechanical paradoxes A significant set of physical paradoxes are associated with the privileged position of the observer in quantum mechanics. Three of the most famous of these are: the double-slit experiment; the EPR paradox and the Schrödinger's cat paradox, all of them proposed as thought experiments relevant to the discussions of the correct interpretation of quantum mechanics. These thought experiments try to use principles derived from the Copenhagen interpretation of quantum mechanics to derive conclusions that are seemingly contradictory. In the case of Schrödinger's cat this takes the form of a seeming absurdity. A cat is placed in a box sealed off from observation with a quantum mechanical switch designed to kill the cat when appropriately deployed. While in the box, the cat is described as being in a quantum superposition of "dead" and "alive" states, though opening the box effectively collapses the cat's wave function to one of the two conditions. In the case of the EPR paradox, quantum entanglement appears to allow for the physical impossibility of information transmitted faster than the speed of light, violating special relativity. Related to the EPR paradox is the phenomenon of quantum pseudo-telepathy in which parties who are prevented from communicating do manage to accomplish tasks that seem to require direct contact. The