Entry tags:
Mathematical Density
Imagine a cauliflower that's started to go bad. It's got a few brown spots, but it's still mostly white. Unfortunately the brown spots are *all over* the cauliflower. You start cutting out the spots with your chopping knife, and quickly realize that you're taking so much good cauliflower with the bad that soon you'll have nothing to eat.
You switch to a paring knife. The brown spots are inside the cauliflower too. In order to be sure you've gotten all the bad spots, you have to cut off a little of the good cauliflower around each bad spot. There's still more good cauliflower than bad, but it's vanishing quickly as you cut out the bad spots.
You could switch to a scalpel, or do laser surgery. If the bad spots are distributed densely in the cauliflower, it doesn't matter how precise you are. Any tool you use will remove a bit of healthy cauliflower of radius epsilon about the bad cauliflower, and the bad spots are close enough together that that means it'll be all gone once you've finished clearing them out.
That's what mathematicians mean when they say "the rationals are dense in the reals".
Jerry Folland's Alu Gobi
Heat 3T olive oil to medium high.
Add: 1/4 t fennyreek seeds, 1 t fennel seeds, 1 t cumin seeds, 1-2 dried chili peppers.
Stir once, add 1 head chopped cauliflower and 1 lb chopped boiling potatoes.
Stir again, lower to medium heat.
Add 1 t coriander, 3/4 t turmeric, salt & pepper to taste.
Saute (until outsides are crusty?)
Add 1/2 c. water, cover.
Cook slowly until tender (15-20 min.)
Sprinkle with 1 t garam masala.
Stir, serve.
You switch to a paring knife. The brown spots are inside the cauliflower too. In order to be sure you've gotten all the bad spots, you have to cut off a little of the good cauliflower around each bad spot. There's still more good cauliflower than bad, but it's vanishing quickly as you cut out the bad spots.
You could switch to a scalpel, or do laser surgery. If the bad spots are distributed densely in the cauliflower, it doesn't matter how precise you are. Any tool you use will remove a bit of healthy cauliflower of radius epsilon about the bad cauliflower, and the bad spots are close enough together that that means it'll be all gone once you've finished clearing them out.
That's what mathematicians mean when they say "the rationals are dense in the reals".
Jerry Folland's Alu Gobi
Heat 3T olive oil to medium high.
Add: 1/4 t fennyreek seeds, 1 t fennel seeds, 1 t cumin seeds, 1-2 dried chili peppers.
Stir once, add 1 head chopped cauliflower and 1 lb chopped boiling potatoes.
Stir again, lower to medium heat.
Add 1 t coriander, 3/4 t turmeric, salt & pepper to taste.
Saute (until outsides are crusty?)
Add 1/2 c. water, cover.
Cook slowly until tender (15-20 min.)
Sprinkle with 1 t garam masala.
Stir, serve.