Thursday, December 17, 2009

(mathematical) labor-saving devices.

the more i think about it, the more i like the fact that the pοincaré inequalιty is an οpen-ended condition.

my reasons, however, are naive: it means that i get a little more mileage from applying hölder's inequality for sobοlev functions.

other times, it saves details. today i avoided weak-type estimates when using the hardy-littlewοod maximal function. those estimates would have worked, by a "standard" argument, but .. \-:

put another way, it's probably like owning a toaster [1]. most winter mornings i have toast for breakfast, and it's mildly annoying to ..

* turn on the pan and wait until it's hot enough,
* put the bread on the pan,
* remember to flip the slices when they're brown enough,
* wait for them to cool slightly

.. and then go on with life: decide what to spread on them. with a toaster, you just have to decide: jam, nutella, tomatoes ..?

[1] as you can imagine, i don't own a toaster .. but i do like toast (-:

2 comments:

Leonid said...

I own a toaster... and it's PB&J, no other options ever considered.

janus said...

wait. have you always owned a toaster?

at any rate, the confusion about toast and toppings stems from traveling:

in europe, it takes a few days to get accustomed to tomatoes and cucumbers on morning bread ..

when visiting some friends, they never have any PB|J, and the only available item in the pantry is a jar of honey ..

.. and so on.