Morris concluded that the barrel was still in the process of being filled up and that, given the present rate of water coming in and leaking out, the filling process began only 10,000 years ago.
It's a great argument except for one, little thing. The water is not coming out of the hose at a steady rate as our model assumed! Sometimes it slows down to a trickle so that much more water is leaking out the barrel than is coming in; sometimes it goes full blast so that a lot more water is coming into the barrel than is leaking out. Thus, the mere fact that the present rate of water coming in exceeds that of the water leaking out cannot be extrapolated back to a starting time. And, that destroys the entire argument!