Introduction (Draft 2)
(Rewritten Feb 20, Mar 3, 2004)
I want you to think about tips. I want to you look at tips, notice their abundance and their variety and their ubiquity. The crocket at the top of a building, a dragon's tail and tongue, the pointed _________ of a seed pod, the taper of a decorative scroll and the sharp point of a canine tooth are all tips. If I were to ask you to point to the tip of each item in this diverse collection you could easily point to the tip, but more difficult is to define the word "tip". What comes to mind most readily is that a tip is the end of an object. This is clear enough, until scrutinised. Where exactly does an object end? If you begin to think about it, an object ends everywhere its surface meets the space around it. Why, then, does a tip feel like the end of an object? Not an easy question to answer, nor perhaps one this is frutifully pursued. For the time being let us simply agree that some areas of an object feel more like the end than other areas.