I just started the Kingkiller Chronicle, and I have gotten to the general explanation of how Sympathy works. I'm wondering if there's an explanation for what happens to the extra energy when you sympathetically bind dissimilar objects and energy "leaks".
Specifically, the concern I noticed is this:
Energy is supposed to be conserved. In a theoretical perfect sympathetic binding, lifting one object requires as much force as lifting both objects, but usually the binding "leaks", and lifting one object requires more energy than lifting both, and this leakage becomes even worse with dissimilar objects. Kvothe gives an example: he attempted to bind a piece of chalk with a bottle of water. The bottle only weighed about two pounds, but lifting it sypmathetically through the chalk was like lifting 60 pounds.
So now some math:
(at 9.81 m/s^2 of gravitational acceleration):
- A piece of chalk weighs about 0.02N
- A 2lb bottle of water weights about 9N
- 60lbs is about 250N
- Lifting the chalk and water bottle 1m would require 9.02J of energy
- Lifting 60lbs 1m would require 250J of energy.
So if you lift the the two objects using sympathy, you expend 250J, but if you break the sympathetic link while the objects are elevated, the two resulting objects have only a combined 9.02J of gravitational potential energy. What happens to the other 240.98J of energy you expended to get them there?
This also applies in reverse, if you lift the objects normally, then sympathetically link them, and drop one. If dropping one object while they are sympathetically linked exerts significantly more force on the other object, then creating the sympathetic link creates 240.98 extra joules of energy instead of removing it. You could theoretically build a a perpetual motion machine this way.