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xkcd #3187: High Altitude Cooking Instructions
(imgs.xkcd.com)
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If you're cooking something at altitude you shouldn't lower the heat - you still need to cook it properly.
Boiling water is a fixed temperature at a given air pressure. Turning up the heat doesn't make the water hotter. You just lose it faster. If you need higher temperatures and are cooking in boiling water, then you have to use a pressure cooker.
Who said anything about turning the heat UP?