I remember from my classes in chemistry that boiling water has one temperature, and it depends on your elevation (and pressure, of course). So, when I cook, say, noodles, I keep a gentle rolling boil, because from what I understand, it is not necessary to put the burner on its highest setting. My girlfriend seems to think the opposite, and also tends to burn the bottom of the pot when cooking things like rice. Can someone please help me explain to her that it is not necessary to put the burner on high when cooking simple grains? Does a pot of noodles cook just as fast at a gentle boil as a raging boil (without risk of torching food)? Thanks,
Nathan

Once boiling you simply add enough energy to continue the bubbles.
Over heating wont make anything cook faster, but will heat up the metal pan and cause the solid contents to stick and burn.

If it's her pan let her burn it. If it's your pan tell her you don't want it burned. I doubt logic will apply to her behavior or habits.

This has nothing to do with science, but how YOU deal with your woman's flaws as you see them. She probably see's your logic as a flaw, and a control issue. Mine did. Wasn't worth fighting over because pans were cheap, and she was stubborn.

I think she needs to take a cooking class or two if she's always burning pans. I'm 53, and I didn't get married out of high school. I've been married for 24 years and still cook certain things..my wife isn't expected to cook everything all the time.

I believe I have actually burned a pan twice in all of that time.

Everyone should know how to cook at least a basic meal....and have it edible (male and female). Take out food is generally far less healthy and far more expensive.

Back to the science of the question. You are correct - sort of. Yes, a slowly boiling pot of water is just as hot as a raging boil, but... the hotest water (and the only water that is actually boiling) is at the bottom closest to the heat source. The rest of the water isn't at boiling temperatire, but is slightly cooler. One advantage of a fast boil is that heat is transferred through the entire mass of water at a faster rate, meaning that the temp of all the water in the pot has a more uniform distribution of temperature, and closer to boiling temp. This may make a difference when you dump in a relatively cool cup of rice or noodles into the hot water - naturally this cools the water off, so a pot that was at a hard boil should be able to heat back up boiling a bit faster and more uniformly than a pot that was at a slow boil. I can't tell you whether that makes a difference or not with respect to how fast the rice cooks, or how evenly, but it might.

PS - I've been married 35 years and long ago learned not to question my wife's cooking methods!