No-one is disputing that mathematics can be useful. The question is, if we had slightly more advanced number theory slightly earlier in time, would that have been particularly useful? Answer - no.

Answer: Yes. Even today, number theory research highly relevant to efficient crypto is ongoing. A few years of difference in when that shows up would have large economic consequences. For example, as we speak, research in ongoing into practical fully homomorphic encryption which if it is implemented will allow cloud computing and deep processing of sensitive information, as well as secure storage and retrieval of sensitive information (such as medical records) from clouds. This is but one example.

But no-one complains about the worse stuff, only the book burning. Which makes me disbelieve that people care about the taboo for that reason.

Well, there is always the danger of lost-purpose. But it may help to keep in mind that the book-burnings and genocides in question both occurred a long-time ago. It is easier for something to be at the forefront of one's mind when one can see more directly how it would have impacted one personally.

Or, we could just allow a market for organ donations. Boom, done. Where's my Nobel?

So, I'm generally inclined to allow for organ donation markets (although there are I think legitimate concerns about them). But since that's not going to happen any time soon, I fail to see its relevance. A lot of problems in the world need to be solved given the political constraints that exist. Roth's solution works in that context. The fact that a politically untenable better solution exists doesn't make his work less beneficial.

But I am definitely questioning the value of this enterprise, compared to bringing cheap food, clothes, etc, to hundreds of millions of people like Sam Walton did.

So, Derstopa already gave some reasons to doubt this. But it is also worth noting that Walton died in 1992, before much of Walmart's expansion. Also, there's a decent argument that Walmart's success was due not to superior organization but rather a large first-mover advantage (one of the classic ways markets can fail): Walmart takes advantage of its size in ways that small competitors cannot do. This means that smaller chains cannot grow to compete with Walmart in any fashion, so even if a smaller competitor is running something more efficiently, it won't matter much. (Please take care to note that this is not at all the mom-and-pop-store argument which I suspect you and I would both find extremely unconvincing.)

I don't see why "saves lives" is the metric

Ok. Do you prefer Quality-adjusted life years ? Bill is doing pretty well by that metric.

but I bet that Microsoft products have been involved in saving far more lives

"Involved with" is an extremely weak standard. The thing is that even if Microsoft had never existed, similar products (such as software or hardware from IBM, Apple, Linux, Tandy) would have been in those positions.

Moreover, people are willing to pay for Microsoft products, despite your baseless claims of their inferiority.

Let's examine why people are willing to do so. It isn't efficiency. For example, by standard benchmarks, Microsoft browsers have been some of the least efficient (although more recent versions of IE have performed very well by some metrics such as memory use ). Microsoft has had a massive marketing campaign to make people aware of their brand (classically marketing in a low information market is a recipe for market failure). And Microsoft has engaged in bundling of essentially unrelated products. Microsoft has also lobbied governments for contracts to the point where many government bids are phrased in ways that make non-Microsoft options essentially impossible. Most importantly: Microsoft gains a network effect: This occurs when the more common a product is, the more valuable it is compared to other similar products. In this context, once a single OS and set of associated products is common, people don't want other other products since they will run into both learning-curve with the "new" product and compatibility issues when trying to get the new product to work with the old.

Gates's charities specifically go around doing things that people say they want but don't bother to do with their own money.

That some people make noise about wanting to help charity but don't doesn't make the people who actually do it as contributing less utility. Or is there some other point here I'm missing?

I don't know much about the malaria program, but I do know the educational stuff has mostly been disastrous, and whole planks have been abandoned.

Yes, there's no question that the education work by the Gates foundation has been profoundly unsuccessful. But the general consensus concerning malaria is that they've done a lot of good work. This may be something you may want to look into.

No-one is disputing that mathematics can be useful. The question is, if we had slightly more advanced number theory slightly earlier in time, would that have been particularly useful? Answer - no.

My answer is "probably yes". Mathematics directly enables entire areas of science and engineering. Cathedrals and bridges are much easier to build if you know trigonometry. Electricity is a lot easier to harness if you know trigonometry and calculus, and easier still if you are aware of complex numbers. Optics -- and therefore cameras and telescopes, among many other things -- is a lot easier with linear algebra, and so are many other engineering applications. And, of course, modern electronics are practically impossible without some pretty advanced math and science, which in turn requires all these other things.

If we assume that technology is generally beneficial, then it's best to develop the disciplines which enable it -- i.e., science and mathematics -- as early as possible.

Why focus on the negative externalities rather than the positive?

Because corporations make a deliberate effort to privatize gains while socializing expenses.

GDP is a pretty worthless indicator of wealth production, let alone utility production; the economists who developed the measure in the first place protested that it should by no means be taken as a measure of wealth production. There are other measures of economic growth which paint a less optimistic picture of the last few decades in industrialized nations, although they have problems of their own with making value judgments about what to measure against industrial activity, but the idea that every economic transaction must represent an increase in well-being is trivially false both in principle and practice.

The point is that some academics are useful and some are not; there is no market process that forces them to be so.

???

Academics need funding. The ability to get funding is well correlated with usefulness in most fields (to be fair, other things are in play, like institutional inertia, fashion, etc. etc.) Useful research also results in spin off companies, and fame. There are all sorts of incentives to be useful in academia.

There is also the issue of hedging, and diversification of intellectual effort -- you want people doing long term payoff and long shot research as well. Modern business culture is generally much worse at this than academic culture is at being useful. Google, a company started by two ex graduate students, is one of the few notable exceptions.

Can you briefly taboo 'useful' for me? What do you mean by that?

I see. And does the fact that much academic research produces positive externalities/public goods, which thus aren't easily funded by private employers says what in this context?

In absence of substantial evidence either way, my prior probability assignment that none of the knowledge stored a major library is useful is very small.

Are there any technologies that go missing after the destruction of the library (similar to the loss of Greek fire that happened 600 years later)?

Well, it is hard to say, since direct technologies leave as more of an archaeological record as say math texts which are essentially technologies. But one can't help but notice that the Antikythera mechanism predated the library, and we didn't have anything like it again until the 1400s. However, this is imperfect in that it looks like a lot of wars and problems occurred between the height of the Greeks and the burning of Alexandria so pinning this sort of thing on it is tough.

Ok. The comment wasn't directed at you. It's just another of the many problems of trying to evaluate eveything by monetary worth.