this puzzler was in omni 1980s. big ups to my hs econ teacher mr geissler, who pointed out that
omni leaned socialist and in any case owned by bob guccione.
nevertheless, props to guccione, who used his kapital to buy art collections instead of a tacky grotto like hefner, consequentely making his
other mag, penthouse, look heads shoulders and *ss above playboy, lets see if you were paying attention in precalc:
a 1cm long inexhaustible worm
starts at t=1 sec at one end of a 1m (100cm) rubber band that is stretchable to infiniti like q45. every sec,
worm moves forward another cm, but before that, band stretches uniformly an additional meter.
when will worm reach the other end?
in 2006, math yr kids will learn - hs, undergrad, even m.s. level - is rendered essentially obsolete by symbolic software packages like mathematica.
why? because you're taught to follow recipes and games. take calculus. the way it's taught is the way it's been taught probably since leibniz,
as a game where you learn to play the
fundamental theorem against the chain rule, with a few trig identities sprinkled in. the question is moot:
mathematica can play games also, and output antiderivatives faster, cheaper than students from caltech to calcutta,
so why would you hire someone for that. it's like testing if you know states & capitals in the age of google. and meanwhile you dont
learn anything about integration itself. or prepare you for harder things, e.g. analysis is about manipulating infinite families
of infinite sets. unlike worm who only needs to cope with countable ones.
what do antiderivatives have to do with limit infimum limit supremum ... problem solving skills? yea most of the curriculum is
spent on that right? ... one last hint: ppl who feel
they're above simpleminded puzzles, grown ups whose jobs are about decision-making and statistical understanding, should be
aware that central limit in the form taught only applies to distributions with finite moments. there are systems with
divergent means, let alone variance. bottom line: the bell shaped curve aka gaussian aka normal is not the only stable distribution.
it's joined in that by fat tailed power laws, with their own central limit, better mirrors of "low probability",
events and risks.
yet exponentials underlie classical statistical analysis. ppl talking to me like they know things, 6-sigma schemes, dreams, fly by night like
reagonomics, if there's no variance there's no sigma you dumb birds.