When the recipe writer wants me to pop the dish into the oven, he/she writes, "Oven at 350 degrees". But earlier, when the dish is in the skillet, the direction is, "Over medium-high heat...." Are there objective, verifiable standards for the five-or-so burner heat levels? My intention is to apply the Standard, locate that spot on the burner control on the (electric, dammit) range, and thereafter be more precise with my heat levels. If, for illustration, you prescribed, "At medium heat, a tsp of water spilled into the skillet will sizzle for five to ten seconds before evaporation, while at High, the water will evaporate instantly upon contact" that would tell me what I (think) I need to know. And too, you'all may have a much smarter solution to my problem. Thanks for any help you can provide.
How high is High?
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I understand your desire to systematize the somewhat subjective terms that non-scientists use to describe rather meticulous methods. Unfortunately, the best means to understanding these terms are to experience them yourself. There are so many other factors that can lead to systematic error that, whether our "highs" are the same temperature doesn't make too much of a difference. If it says medium, use 1/2 available power. If it calls for high, use it all. Odds are, they're the wrong temperature either way. Just let your intuition guide you and you'll start to hear and see when the temperature is right.
On a stove top, the important factor is speed of even heat transfer, not so much a specific temp.
An example. America's Test Kitchen, they were talking stir fry. With a US home-style stove on High, the carbon steel wok get's hot quickly, but when you add food, the temp drops quite low and stays low. The US burner can't put enough heat into the wok quickly enough for the amount of food ATK added to the wok. This is why US stir-fry recipes cook in batches so often. For ATK's purposes, they prefer a 12" non-stick skillet. It doesn't get quite as hot initially, but doesn't drop to as low a temp and holds a higher temp during cooking of the same amount of food. They had a spiffy graph and everything. For how they want to stir fry easily, a non-stick skillet on high worked better. There are flavor trade-offs they neglected to discuss, but I think it shows the issue.
If you ever cook on induction, you'll see the difference in speed of heat transfer compared to gas cooktops as well.