system
Given the following post, respond as if you're commenting on Reddit:
human
When I cook food in the oven, what does hotter temperatures versus a longer cooking time do to the physical structure of my food?

This is something I wonder about whenever I fire up my toaster oven. How does turning the heat up versus leaving it in for longer affect my food? 

Do they have discrete properties that affect the food? Or is it just a mathematical function? heat x time = heat energy radiated into my food. Could I halve the cooking temperature and double the cook time and have the same result? 

I see how some kinds of food like meat or fish would only cook at a certain temperature, so some recipes would necessitate a certain cook temp. 

What combination results in the most even cook? As in, the inside of the food heats up at the same speed as the outside. 

Why are almost all recipes either 350F, 375F, or 400F? Why is nothing at 200F or 800F?
gpt
Although you can sometimes tweak the temperature and time ratios in a recipe to get the same result, cooking is a *chemical* process -- this means that there are some specific, critical temperatures above/below which certain processes will/won't happen. 

For example, meat/fish items usually have to be cooked in such a way that the entire object reaches some minimum temperature (160F, or so) in order to ensure that dangerous bacteria and the like have been destroyed. 

Heat flow equations tell us that if we want the core of an object to reach a certain temperature, there are two extreme ways we can do this. If we want to do it quickly, we just have to make the outside really hot (the rate of heating will increase with the magnitude of the temperature gradient), but this might end up burning and/or drying out the food. The other extreme is to make the oven temperature equal to what we want the inside of the food to be, and wait for the temperature throughout the entire object to reach equilibrium (which will probably take a really long time). Balancing these two extremes tends to mean heating things in the temperature ranges you mentioned; 200F would take way too long, and 800F would probably end up burning the food before the inside got hot enough to be "done".