7/04/2006 08:15:00 PM
We study the categorical structure of balloons and the container behaviour they get when blown. This structure implies some simple observations, which however haven't been explored yet as far as we know: ballons can be nested in several ways. See below the representation of
f(g,h)and the triple nesting
f(g(h))-- a spectacular performance by Dr. Simon.
Then we point out that the notion of blowing a balloon is self-dual, as demonstrated on the picture of Andrew "blowing" a balloon from the outside, and can be generalized smoothly to the filling of a balloon with anything, as demonstrated by Andrew blowing ballons with his crazy ideas.
More trivial uses of the balloons-as-containers paradigm include storage of useful items, like whiteout, money, water, ice tea cans, mobile phones, pens, and so on -- we let the reader guess in which balloon is which item.
More serious applications shall be explored. For example a balloon can be used as a security device allowing one to know that nobody has used his mouse -- however, some details need to be worked out as limited interactions with the mouse are still possible.
Another interesting application is the levitation of balloons. By embedding an magnetic device instead of the usual Helium in a balloon, we've been able to have it fly. Two efficient techniques to initiate the process have been developped. This involves a new theory of which the basic principles and properties are sketched below.