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In mathematics an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of expansion and contraction. Unfortunately, school districts have all the symptoms of an Anosov map - it is far more difficult to expand (and increase quality) than it is to contract. Worse, all evidence suggests that when one contracts a district actual quality measured across individual students declines. Worst of all, the decline is not linear. Another warning sign from the Fibonacci series is that it matters a great deal what values one starts the series with. Whenever initial conditions powerfully influence convergence and other properties one enters the murky domains of chaos theory. While fascinating, this is usually not desirable for education which is aiming to produce a uniform product: literate citizens. What we get back when we simulate the educational and economic impact of closing schools is a Fibonacci series that involves fractals. We'll be publishing the graphics from our NILGAI application shortly - they are very compute-intensive even on an Intel quad core. If we were students, teachers, parents or leaders in Butte County, we'd want to take a long look at increasing school revenues with solar power. One might want to invoke the spirit of Colonel Joshua Chamberlain at Little Round Top during the Battle Of Gettysburg. He's taken terrible casualties, his lines are broken and bent, his men are almost out of ammunition, everyone's exhausted from having to march the day before and then fighting, often hand to hand, against enemies superior in quality and quantity. There are no reserves. The regiment may not survive a retreat - the Union position certainly will not. So the order goes down the line: "Fix bayonets. Follow me." We doubt it is important who leads the modern day equivalent of the 20th Maine. It is only important that the lines hold now. After all, one can always fire teachers and close schools. As for Kansas City Missouri, our models suggest closing 28 schools lacks elegance. The famed brachistochrone or curve of fastest descent, is the curve between two points that is covered in the least time by a body that starts at the first point with zero speed and is constrained to move along the curve to the second point, under the action of constant gravity and assuming no friction. The same curve, a cycloid, also shows the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point. So, if the citizens of the state for whom a steam frigate, a Civil War ship that fought on both sides, and battleships BB-11 and BB-63 were named would rather not enlist in the Legions of Light, and fix their photonic bayonets our advice to Kansas City Missouri is go for the fastest descent: close all 61 of the schools in June. |