09.13 How Big is Infinity? Mathematical Surprises - by Roger House

Friday the 13th fell on a Thursday this month as Roger House dispatched the monster subject of infinity in a fashion that Harry Potter would have envied. Many people have avoided mathematics in their previous lives and therefore had not had the pleasure of such mind melding or mild melting thought processes as different "sizes" of infinity. Many such folk came away from Roger's disquisition feeling proud of themselves for having appreciated the aroma, nay, even the bouquet of mathematics, even if they did not fully taste the body, the sugars and tannins of the topic. Many were surprised that such thought has been given to the idea of infinity that whole bodies of technique and terminology have been developed.

Roger began by considering the problem of ordinary counting and thereby introduced the counting numbers, or natural numbers, and quickly convinced everyone that these critters march on and on forever, i.e., to infinity, beyond counting. He went on from there to discuss the rational numbers, formed from ratios, and they went to infinity. Then came the irrational numbers. These numbers cannot be formed from any ratio, the very essence of madness! Well, OK, you just had to be there. However, several in his audience said they did not grasp all the details but now have an appreciation of why mathematicians are the way they are. It has been said that the development of mathematics is like the development of enology. In the beginning there was just grapes. Nevertheless, after several centuries of being carried away, mathematicians and winemakers have developed a product that some cannot live without and some are glad it is there. Way over there.

Roger House at Science Buzz Cafe on September 13, 2007