Schrödinger's Cat

The subject of an experiment conducted by mad crazy quatum physics man named Schrödinger. Here is the kicker of the experiment: Most believe that Schrödinger was attempting to prove that the cat was both dead and alive at a single point in time. This is not quite true. The fellow was merely attempting to prove that the rules regarding microscopic objects (such as particles that can be in "dual states" so to speak) are in no way governed by the established laws for macroscopic objects (a cat). You see, it is well established that a cat is either A. Dead or B. Alive. Schrödinger put his cat in a solid lead box with a vial of gaseous hydrocyanic acid (HCN(g)) and a radioactive isotope with an established half life of about one hour. Because a single particle was used, the chance of it decaying was 50/50. The vial would be broken when the particle decayed, and the cat, being rather allergic to hydrocyanic acid, would die. The problem arises here. After an hour, the single radioactive particle, speaking on quatum terms, was in a dual state of decay and, eh, not decay. The laws of quatum physics say that all items in a closed system can be related with well known and well tested equations. Using these equations, the cat is in a dual state of being dead and alive. Not possible. Therefore, there can be no assumptions made regarding the relations of macroscopic objects and microscopic objects. However, I believe the cat was just a clear cut zombie cat.