A singular impact?

Abstract

While I worked at Teeside Polytechnic I had some difficulty in arriving in the morning by 9.00. Not being an early bird my desire was to pull into the carpark at 8.58, but this I did not seem able to achieve. If I left home at 8.15 the journey was smooth and trouble-free, and I was at my parking place by 8.50. Whereas if I left a moment later there were a couple more cars at the estate exit, each succeeding roundabout and set of traffic lights was busier, and eventually I drove into the car-park at 9.05—not only five minutes late, but also quite likely finding the spaces all full and having to resort to street parking. It seemed that no matter how I varied my start time the arrival interval of 8.50 to 9.05 was somehow inaccessible to me. Of course some people did arrive in this interval—if I did the sensible thing and left early I enviously watched them arrive at the time I would have wished. But they did not start from where I started. So I was drawn to the belief that the relationship between start and arrival time was a genuine discontinuous function, and not simply a continuous function with a rather steep critical section. Maybe the catastrophe theorists could analyse this further (but to call my misfortune a catastrophe would be a bit strong).