Tuesday 13 July 2010

Treasure Hunts, Bus Queues and Cancer

The authors of this paper HERE explain that there is a growing problem in cancer research, which they call a paradigm instability, which can be modelled as two analogous but slightly more everyday problems - treasure hunting and waiting for the bus.

Their description of the treasure hunting one is in full below

"For one hypothetical example of paradigm instability, imagine you and four other treasure hunters disembark on a deserted island. You have two treasure maps, each of which marks a different location of the buried treasure on the island. The vast majority of experts believe Map A is correct, but a few experts offer cogent reasons to support the veracity of Map B. You have 5 days to dig for treasure before the boat returns to pick you up and you run out of food and water. Let us say the common wisdom is that there is a 95% chance Map A is correct and a 5% chance Map B is correct. Also, because the exact location of the treasure is imprecise, you will probably need to combine efforts to unearth the treasure. Your best initial strategy is for all ﬁve of you to start digging in the location designated by Map A. The more you dig at the location speciﬁed by Map A, the closer you believe you are to the buried treasure. You ﬁnd a piece of wood that you interpret as part of the treasure chest that had broken off, but it could also be a random piece of wood. Random pieces of wood are, after all, more common than treasure chests. After 4 days of digging, you have not found the treasure; nonetheless, you think you are very close to ﬁnding the treasure and that the next shovel of dirt will unearth it. To give up when you may be so close may be foolish. However, the fact that you have not yet found the buried treasure despite your extensive efforts makes you entertain the thought that you are digging in the wrong place. At this point, you think the chances of ﬁnding treasure at the location speciﬁed by Maps A and B are approximately equal. You have reached a point of paradigm instability. Therefore, you agree that two of the treasure hunters should dig at the location speciﬁed by Map B."