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We stick the garden hose in and turn it on full blast.
The water coming out of the hose is analogous to the continuous production of carbon-14 atoms in the upper atmosphere.
(The barrel is made deep enough so that we don't have to worry about water overflowing the rim.) Henry Morris argued that if we started filling up our empty barrel it would take 30,000 years to reach the equilibrium point.
Thus, he concluded, if our Earth were older than 30,000 years the incoming water should just equal the water leaking out.
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. Lingenfelter's paper was written in 1963, before the cycles of C-14 variation we described had been fully documented.
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. The point is that fluctuations in the rate of C-14 production mean that at times the production rate will exceed the decay rate, while at other times the decay rate will be the larger.
This argument was popularized by Henry Morris (1974, p.164), who used some calculations done in 1968 by Melvin Cook to get the 10,000-year figure. Whitelaw, using a greater ratio of carbon-14 production to decay, concluded that only 5000 years passed since carbon-14 started forming in the atmosphere!
The argument may be compared to filling a barrel which has numerous small holes in its sides.
Could it be that the whole scientific community has missed this point, or is it another case of creationist daydreaming?
It's a great argument except for one, little thing.
The water is coming out of the hose at a steady rate as our model assumed!
That is, the equilibrium point should have long since been reached given the present rate of carbon-14 production and the old age of the earth.
The next step in Henry Morris' argument was to show that the water level in our barrel analogy was not in equilibrium, that considerably more water was coming in than leaking out.