Expected value is a bit of a strange concept to apply to scientific research, as no-one really knows for certain what the full, long-term impact will be. The actual value of many scientific discoveries only becomes apparent years later on.

No one knows for certain, but... suppose you have two projects and can fund one of them.

Project A wants to investigate in as much depth as possible (given their budget) the effects of nail-biting on arthritis.

Project B wants to investigate in as much depth as possible (given their budget) the effects of learning a programming language on Alzheimer's disease.

I know which of these seems like a better choice for funding, even though I don't really know for certain what the long-term impact of either will be.

Which do you think is a better choice for funding, and why?

In support of project A: fibromyalgia, which has arthritic-type symptoms, is partly linked to anxiety, of which one of the common manifestation is nail-biting. Could evidence of nail-biting be a useful tool as part of differential diagnosis, or a predictor?

In support of project B: the idea of a 'cognitive reserve' in preventing the onset of Alzheimer's disease is fairly well established, even though it has no disease-modifying therapy once the symptoms of decline are already apparent. To what extent can learning a programming language aid that cognitive reserve?

I see your point though, but I'm not sure how well it applies to funding large-scale data collection work like the HGP. Or the LHC, to use an example in another field.

Couldn't we say that you have formed an estimate of both projects in your mind, and your estimate of the present value of all net benefits from project B is higher than your estimate of project A?

More or less. That sounds like it's giving me too much credit. I wouldn't say I have two estimates so much as one intuition - but that's what my intuition corresponds to, yes. If I made those estimates, I would expect to have a higher estimate for project B than project A.

(But I should note that I deliberately chose projects where it seemed obvious which one was better, so that I didn't need to do any calculations or even think very hard about which one to prefer. In reality, sometimes it's not obvious, and you should think hard and do calculations and it still might not be obvious, and the specific project being discussed is probably one of those cases.)

I don't think we can estimate the expected value exactly, but it nonetheless exists and our only option is to estimate it as accurately as possible (future value discounting the long term impacts of course). If the project doesn't have any practical use but opens up new avenues of research or just has value in any way then those benefits should count of course.

While I generally appreciate the way you think, the problem is likely that different people evaluate the expected value function of this project wildly differently - for perfectly legitimate reasons. The path to resolve this kind of conflict is not straightforward; barring some additional (and accepted) scientific insight, the matter is resolved politically.

That's the thing, though: There's no way to calculate the value of fundamental research. We have lots of examples of breakthrough fundamental research with world-altering consequences, and we have many more examples of projects that went more-or-less nowhere.

If we want the big advances, we have to push the boundaries of what's known, but it's unclear where, exactly, the big breaks will happen. But doing these kind of mega-projects is, I think, basically a good thing, as it gets us out of the day-to-day of publishing easy papers, and into attacking the 'big' problems in new ways.

I believe that Maxwell was occasionally asked what real-world improvements his work would make in peoples' lives.