Thursday, March 05, 2009

in which math is not unlike apple pie.

another week, no theorems proven.

american economy or not,
maybe i'll need that second postdoc after all.

this past week i read and thought about a topic that most people in my field know of and some who use the structure regularly: differentiabi1ity of real-va1ued 1ipschitz functions on certain metri¢ (me@sure) spaces, as discussed in the work of j. ¢heeger in his 1999 9af@ paper.

so i did learn a few things, despite my lack of productivity. one proof makes more sense: where the differentiabi1ity comes from. before, that has always been a mystery to me.

now, it's confusing but not mysterious.
to explain, there is a difference:

your grandmother's apple pie would be mysterious if there was a wonderful flavor unlike any other pie, and you couldn't figure out why. on the other hand, by acquiring a complete list of ingredients for the pie recipe, the mystery disappears. it turned out that the spices which escaped you were garam masala and cloves, and it is now possible to bake that pie.

however, you're still uncertain about how exactly to make the crust, whether one boils the apples first before baking the pie, and as a result, will your version of grandma's pie be just as tasty .. or even edible?

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