While you're right that current institutions, inertia, and laws prevent shorter workweeks, that is an argument for removing these barriers, not an argument for trying to game the GDP numbers in the (false) hope that this will somehow translate into sustainable employment because of the historical correlation.

Oh, definitely.

Okay, but that still looks like a case of lost purposes and fake utlity functions. If you're spending money to redistribute, then spend the money to redistribute! Don't spend it on a project that hogs up real resources just to get a small side-effect of transferring money to people you want to help. ("What's your real objection" and all.) If it's important that they feel they earn the paycheck, then require that they take job training.

I basically agree with this; if you want to redistribute, then certainly it's better to just redistribute than to "employ" people to do completely useless things. (For example, extending unemployment benefits is a form of redistribution.)

And the reason I call the projects worthless is this (and it doesn't require an ideological commitment to being against government projects): people couldn't justify asking the government to provide these things before the recession. But if the recession is a contraction of productive capacity, then the projects we commit to should also contract -- it should look like an even worse deal.

Well, what matters is the opportunity cost. A project that wasn't worth doing before can become worth doing if the better alternatives aren't there anymore; a contraction of productive capacity doesn't have to affect all sectors of the economy equally. For example, people in a country experiencing an oil shortage may find that investing in more expensive, non-oil energy sources has become worthwhile; it's worse than what used to be possible, but it's the best remaining alternative. Given that people are willing to lend to the federal government more cheaply now than before the recession, the new equilibrium might end up involving more "investment in government", not because government has become more productive, but because the alternative investments have gotten worse.

And I'm not necessarily sure that absolute productive capacity went down all that much in the current recession. During the Great Depression, the factories were still there, there were people willing and able to operate the factories, and there people who wanted the goods the factories could produce, yet the factories were idle, the would-be factory workers were unemployed, and the would-be consumers didn't have the goods they wanted. (The Keynesian position is that there was a collapse in aggregate demand, leading to a general glut, followed by a reduced output level.)