Thursday, July 15, 2004

there were a few good hours early this morning. i made progress in "modeling random systems." an exponential random variable models wait times. it slopes down towards zero as time approaches infinity; as long as there is some probablity of rain, there is no chance that a drought can last. i thought about the cassini orbiter. there must be some probability of a space rock ripping through the hull, but it survives because the tail of the exponential collision variable remains vast, even as years go by. stephen jay gould, after being diagnosed with cancer, examined the mortality statistics and realized that it was the dimensions of the probability tail that mattered, not the frightening average. he lived for 20 years after being told he only had a few years to live. probability and statistics can suck when you think in terms of "how" before "why." people have a fundamental need to describe things that don't occur in plain sight. instead of leaving for an appointment at an exact time, we recognize a range of time as "the leaving time." this time begins quietly and then crescendoes into a "now or never" moment, and then trails off into an "oh shit we're not going to make it" moment. we usually give the mean when we tell somebody when we're leaving. we already know the bell curve. however, when you crack a textbook there is this disorienting overload of information. the author doesn't think the way you do. as the day goes on, from a peak in the early morning, the ability to concentrate trails off.