Machines are increasingly replacing humans across many walks of life. Huge numbers of jobs are being made obsolete. Historically this trend has been a positive force in terms of living standards. Additionally, as old jobs have been replaced, humans have found new work to do.
The claim that machines will eventually replace humans is often dismissed as being a "Luddite Fallacy". Many people who disagree with this claim appeal to history, pointing out that each time machines have replaced humans for some task, humans have found other work to do. This is correct. Nevertheless, I believe this reasoning is flawed. My thoughts are illustrated in the following graph:
Note that the point where machines replaced horses has already occurred. As a result of the automobile revolution, the "wage" for pulling a cart dropped far below the level of horse subsistence. As a result, the number of living horses dropped dramatically. (Hat tip: Robin Hanson, who I believe was the first to make this argument.)
But clearly, it hasn't happened to humans, so it can't ever happen, right?