Or: Luddites still wrongheaded.
Toy economy microcosm: iPods and mining, nothing else.
Let's say an iPod costs $1000 to make, $500 for labour, the rest for ore from the mine. Let's say we mechanize so cleverly the iPod no longer takes any human labour at all.
Normally, the lowered input costs will make iPods cost much less, indeed around half as much. This will cause more iPods to sell, requiring more ore. Demand curves being what they are, they won't sell twice as much, but four or five or ten times as much. (Ctrl-f "Holiday.")
For every $500 of ore Apple was buying, they're now buying $2100 of ore. If the mining company spends more than $160 of labour to mine that $500 of ore, the economy will now be spending more overall on labour than it did before the jobs were 'lost.' (Real companies would kill to have such low labour costs.)
The cotton gin added net jobs, because like every other mechanization so far, it did not eliminate labour entirely, and the higher demand for the remaining labour more than compensated for the 'lost' jobs.
Certainly there's some short-term pain, which I think should be treated compassionately. The iPod workers will be out of a job while the economy adjusts, and I for one don't want to rip them away from their roots, their friends and family and geographical familiarity, so they can go work at a mine halfway across the country.
However, the idea that mechanization costs jobs is still wrong.
The government costs jobs.