Parable of the Hot Chocolate
There was a boy who wanted to find the perfect strategy for heating hot chocolate. His weapon of choice was the microwave, but he had to find how long to radiate it for.
He began microwaving his hot chocolate, first for 30 seconds, then for 15, and then for smaller and smaller increments as he approached the perfect temperature. Each time he would take it out, and give it a taste to check on his progress.
Finally he arrived at the perfect temperature. He knew didn’t want to have to repeat this process the next time, so he summed up the duration over which he had microwaved the hot chocolate, and arrived at 122 seconds. Excited to make use of his discovery, he began preparing another hot chocolate right away!
This time he put it in the microwave for 122 seconds all at once, and couldn’t wait for what he would find on the other side. As soon the ding sounded he pulled it out, smiled at his creation, took a large gulp… and promptly gave a yelp while spitting it out all over the floor and counter top! It was scaldingly hot! He was in disbelief!
The boy didn’t know what had gone wrong. He double and triple checked his math, and it all added up. 122 seconds should have resulted in the perfect hot chocolate temperature.
He then realized his fatal mistake: assuming that intermitantly microwaving the hot chocolate for a total time of 122 seconds would have the same effect as microwaving it for 122 seconds all at once. Of course the process of turning the microwave on and off several times during the process would have an effect on the final temperature. And it only then occured to him that he would have to recalibrate his measurement for different types of microwaves and power settings.
During all his future adventures, he would have this in mind. Never forget to account for control variables.