The Dwarf miner knows where his pickaxe is at all times. He knows this because he knows where it isn't, by subtracting where it is, from where it isn't, or where it isn't, from where it is, whichever is greater, he obtains a difference, or deviation. The guidance system of his beard uses deviations to generate corrective commands to drive the pickaxe from a position where it is, to a position where it isn't, and arriving at a position where it wasn't, it now is. Consequently, the position where the pickaxe is, is now the position that it wasn't, and it follows that the position where it was, is now the position that it isn't. In the event of the position that the pickaxe is in is not the position that it wasn't, the beard has required a variation. The variation being the difference between where the pickaxe is, and where it wasn't.