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| A point to ponder |
HomepageIan Gallon
Some forty years ago I became aware of a curious theorem in Applied Mathematics called ‘The Schrauder Fixed Point Theorem’. Stripped of all the esoteric technical jargon, the theorem says that when you stir a cup of coffee, at least one point of the surface does not move! So what? As a scientist I could see the importance for mathematics, but I did not foresee the practical consequences!
Of course there is nothing special about a cup of coffee! It applies to any body of liquid, such as the oceans of the world. If there is one fixed point, the water close to this point will be moving very slowly, the speed of flow increasing slowly with distance. Any flotsam that moves into this area becomes trapped, and it further slows the movement of the water around it. The consequence is that the area of trapped flotsam grows. An area of floating plastic some three hundred miles in diameter has been discovered in the middle of the Pacific Ocean! This disc blocks the Sun's rays killing the plankton and depriving fish of food.
One Californian company has started ‘mining’ this virtually limitless supply. This has no immediate impact on the world at large as it is not crossed by a shipping lane and is not a fishing ground. However, the phrase ‘at least one’ means that there can be more than one! Satellites have located around 130 such ‘fixed points’ in the oceans. One of these is in the Caribbean, where the accumulation of flotsam and pollutants has destroyed the local fishing industry!
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