which part of the mushroom gathers nutrients from the soil or dead material that the mushroom is decomposing?

The Mycelium is usually hidden in the soil, in wood, or another food source. A Mycelium may fill a single ant or cover many acres. 

the old alchemists made significant contributions to science even though there starting premises were off a bit. their conclusions after failure would steer them into better directions for investigation. science is no more than close observation and the initial mistakes result in rethinking and retrying experiments.

dynamic equilibrium is the answer.