On Friday 05 August 2011 11:43:04 BGB wrote: > On 8/4/2011 6:19 PM, Alan Kay wrote: > > Here's the link to the paper > > > > http://www.vpri.org/pdf/rn2005001_learning.pdf > > inference: > it is not that basic math and physics are fundamentally so difficult to > understand... > but that many classes portray them as such a confusing and incoherent > mess of notation and gobbledygook that no one can really make sense of > it...
It's often been said that to explain a concept simply, one has to understand it intimately. My favourite example of this, also from Physics, is the various ways that elastic bands can be described: * Approaching an elastic band from a Newtonian point of view, you will find that the force you apply when stretching it, integrated over the length you stretch it over, gives the elastic potential energy of the band. When it's released, the derivative of this energy over the length the band contracts makes the band accelerate. * Approaching an elastic band from a Thermodynamics point of view, you will find that the "work" you're putting into the band when you stretch it is decreasing its entropy, and thus increasing its heat (but increasing your own entropy). When it is released, this heat drains into the band's pool of entropy. * Approaching an elastic band from a Statistical Mechanics point of view, you will find that the multiplicity (and therefore probability) of a stretched band is far lower than a relaxed one, and thus to stretch it you will need to modify the system's contraints such that the stretched probability dominates. Likewise, to contract it, such contraints must be removed. There are even more ways of describing an elastic band, all of which are valid. However, if you want to 'get' how an elastic band works, in an uncomplicated way, just ask Feynman ;) http://www.youtube.com/watch?v=XRxAn2DRzgI Only when one truly understands something, are they confident enough to throw away enough of the pompous and historical cruft to make it simple. Those who don't truly understand something end up thinking that the cruft is part of what's important. The problem is, there are nowhere near enough Feynmans in the world compared to the number of teachers and educators we need :( Thanks, Chris _______________________________________________ fonc mailing list [email protected] http://vpri.org/mailman/listinfo/fonc
