154 Are the Androids Dreaming Yet? thing we thought true must be false and the opposite is true. This is a somewhat circuitous route to prove things, but it is often the only prac- tical way. Two paradoxes we are taught as children are the liar’s paradox and Zenoss paradox — also known as the story of the tortoise and hare. The first is a real paradox but the second is a false paradox. The liar’s paradox is just the simple statement: “This sentence is false.” It is a paradox because of the internal inconsistency: We cannot determine if it is a true or false. First assume it is true, but it says it is false, so it is not true. Then try it the other way around. Assume it is false but the sentence states it is false, so it must be true. If that were so it must be false by the first argument and so on ad infinitum. Either way around, the sentence contradicts itself. A paradox. Zenos Paradox, on the other hand, is a false paradox. Here is the story. Once upon a time there was a hare. He was a very arrogant hare and believed he could outrun any animal. A tortoise was walking along the way and the hare jumped out in front of him. “You are so slow, said the hare. The tortoise replied, “You may be the fastest hare in the kingdom but I am the most persuasive tortoise. I bet I can persuade you of anything, including that I am faster than you.” “T don't believe you,” said the hare. “OK, said the tortoise, “let me show you. Give me 100 meters head start since you are so fast. Then, we'll both start to run. After 10 seconds you will have run 100 meters and arrived where I used to be, but I will now be ten meters ahead. After another second you will be where I am now, but I will be 1 meter ahead again. So you can never catch me.” The hare pondered for a while but, being a hare of little brain, could not make out the true answer. It is a false paradox. The time intervals are getting shorter. The question for a mathematician is, does the problem converge to a solution. T