Several readers have written to criticize my examples as being too far removed from the real world. They find that the assumptions that have to be made to pose simple probability or decision theory problems make the results unrealistic. In response, I will start to feature a series of examples with more relevance to the real world. These will cover many different aspects of measurement and decisions. Given that change in direction, I will start off with a relatively simple physical problem with no complex decision aspects at all. Today’s feature event is taken from the real world of academia and backed with precise measurements. We will consider the implications of the world-famous UCSD watermelon drop.
The legend is that almost forty years ago, Prof. Swanson, who was then a young physics professor at the new campus of the University of California, San Diego, gave his beginning physics class what started as a harmless problem in simple dynamics on its final test. The tallest building on the new campus was then seven stories tall. He asked his class if a watermelon were dropped from the top floor, how far could a piece of the smashed watermelon fly? That is, how far from the point of impact would one find pieces of the poor melon?
The school year was almost over, and as summer break approached, students, as they will, got a bit frisky. These students decided they were more experimentalists than theoreticians. So they selected a watermelon queen who picked a watermelon and climbed the outside stairs to the top of the building with hoots and encouragement along the way. Upon reaching the top, to the cheers of many, she tossed the melon over the side, and appointed officials dutifully hunted and found the furthest piece and measured the distance it had flown.
That became a yearly custom that has been re-enacted every year since amid much pomp and circumstance. The 39th drop occurred in June 2004 with Prof. Swanson officiating. As part of the ritual, the maximum distance each year is recorded. The record to date was set in 1974 at 167 feet, 4 inches (UCSD has not gone metric yet – at least not when it comes to watermelons).
So the puzzle for today is to ask if this record is consistent with the simple physics solution that would be expected of freshman students. That is, derive an expression for the distance and compare it to the reality. Does it agree? If not, then why not? What assumptions did you have to make to derive a distance? Qualitatively, how would your result change if you relaxed those assumptions? Would the derived distance move in the direction of the experimental result?
For those who wish to delve further into decision theory without wading through a lot of equations, I have posted a tutorial on elementary decision theory. It shows examples of faulty physicians’ diagnoses (important for those considering surgery) and how to evaluate anti-terrorist activities (important for everyone). That tutorial can be found here.