If we make contact with extraterrestrials, what could we possibly trade with them?
Wolfram's puzzlement rests on the fact that any aliens we contact would almost certainly be unimaginably richer and technically superior to us. They would be better than us at everything. But of course, this doesn't preclude trade. What matters is comparative advantage*. We could sell aliens the goods and services which we are relatively less inefficient than them at supplying.
What would this stuff be? It certainly wouldn't be anything that makes intensive use of the physical sciences. By very virtue of contacting us, aliens would have a vast superiority over us in these. And they are highly likely to have mechanized away any need for hard labour. So they'd have little demand for either our physical sciences or our unskilled labour. And the likely enormous difference in our physiologies rules out any demand for our biological sciences or pharmaceuticals.
Could it be that aliens would just want us for our cuteness, in the way Doctor Who seems to regard humans? Not likely. Although an attraction to Martha Jones is probably shared by all intelligent life-forms, she is not, alas, remotely representative of humankind.
It's possible that aliens might want some minerals. But this is dull.
So, here's my theory. Mankind's comparative advantage lies not in our science or our labour-power but in our arts - and in particular, music, as this is less rooted in human language and specific emotions than other arts.
This isn't mere idle sci-fi. Our comparative advantage influences our self-image. Traditionally, mankind's self-image has been that we are an intelligent species. This has always been a delusion; if we're so smart, how come we go out to work all hours whilst cats lounge around the house? So shouldn't we replace it with a less stupid image - that humans are (though not uniquely so) a music-making species?
* I'm assuming a civilization that has overcome scarcity would still apply this principle, perhaps in the same way we make children work for their pocket-money - to teach them good habits. I'm also assuming aliens don't believe they would lose out from trading with backward planets - though who knows, maybe this is why they haven't made contact.