Can you believe in something you cannot see?

Why would the Darby’s have given up when they were so close? The surface level answer is because they could not find the vein of gold. But the real answer lies beneath the surface. They gave up because they had stopped believing. Moreover, their beliefs were based on sound logic. The evidence seemed to support their beliefs. After searching, and searching, and searching, they could not find the vein of gold anywhere. They were tired, and running low on cash. But if they had truly believed there was a mountain of gold within their reach, they could have found a way to hire an engineer just like the junk man did, right? Surely they had enough cash to dig three more feet, right? If the Darbys had kept believing, it would have prompted their brain to come up with the creative solutions they needed to achieve their wildest dreams.