Dan picks up a \(15-\mathrm{m}\)-long pole and begins running very fast, holding the pole horizontally and pointing in the direction he's running. He heads toward a barn that is \(12 \mathrm{~m}\) long and has open doors at each end. Dan runs so fast that, to Farmer Brown standing by his barn, the ladder is only \(5 \mathrm{~m}\) long. As soon as the pole is completely inside the barn, Farmer Brown closes both doors so that Dan and the pole are inside with both doors shut. Then, just before Dan reaches the far door, Farmer Brown opens both doors and Dan emerges, still moving at high speed. According to Dan, however, the barn is contracted to only \(4 \mathrm{~m}\) and the pole has its full \(15 \mathrm{~m}\) length. Farmer Brown sees the pole completely inside the barn with both doors closed. What does Dan see happening?