ealth warning! The man who discovered infinity had a mental so This subject may tax your brain. Georg Cantor didn’t really ‘discover’ infinity but he was the first mathematician to put it on a firm theoretical footing. In the late 19" century, most mathematicians thought infinity was a curious idea with no proper place in mathematics. They treated Cantor's attempts to make it into a real mathematical object with contempt. This affected Cantor’s morale and caused him to suffer several bouts of deep depression, retreating to a sanatorium from time to time. Infinity is a difficult idea to grasp but it is vital to our study of information. It behaves counter-intuitively but is not impossible to grasp. The reason it is important is that information can always be translated into numbers and numbers go on to infinity. If you want to know all about information, you must understand infinite numbers. History Indian scholars began studying infinity in the 4 Century BC. It turns up naturally in all manner of places. In geometry, parallel lines extend forever in either direction without ever meeting. To define a parallel line you must contemplate infinity. In arithmetic, even if you pick the largest number you can imagine, there is always a larger one; just add one. In the physical world if you look up at the night sky it appears to go on forever. Again you have infinity. Historically there were two interpretations of infinity. The first, favored by Plato, was a journey. When you embark upon a journey, you can always take another step. Infinity is the idea of ‘one more’ or never- ending. It can never be reached. The second definition is more radical. Infinity is a thing, a number so bigyou could not imagine anything bigger, but it is one number. Plato thought this second definition tantamount to madness. Today we embrace this madness and go a whole lot further. Let me show you how. Ifinfinity were a number, you should be able to perform mathematics with it; add it, multipl