I often wonder how people get so wrapped up in something that clearly doesn't work. Is it the chance of getting rich? Not all of these investors are stupid, I wouldn't think. Some times people become so deluded with money that they start believing their own lies.
Reflect on what it means to be an investor.
You supply money to a myriad of possible markets. It is physically impossible for you to understand all of them in depth (or you're the one single person in the world who is totally amazing, but there aren't very many of those). If you're wise, you'll at least do some superficial research on where a given market is going. But many probably don't have the time for that, or they simply don't bother. (90-10 rule: most of them will have more dollars than sense.) Or if you don't have the time to research it yourself, you can hire a consultant or analyst to give you an opinion.
But opinions are just that. The 90-10 rule applies to analysts as well. Unless you're going to get a statistically significant review from many analysts (in the process, wasting all the potential profit you had hoped to get from the proposal in the first place), it's up to you to make the decision.
It's all just opinion, and speculation, and gambling. It's the refined businessman's casino. Even better than a casino: you don't know the odds, and the house doesn't always win.
It looks very bizarre to a person of science. Remember, it's the CEO's duty to give direction: if we can solve
just this one thing, we can hit it big.
It is not the CEO's business to have complete understanding of the many fields he oversees: from marketing to research. That would be highly impractical.
No, it doesn't matter if that
thing happens to violate thermodynamics (those water-from-air crowdfunding campaigns), or is unprovable, unsolvable or impractical (say, NP-complete problems, breaking hard crypto, proving the Riemann Hypothesis...), or just happens to be some average every-day engineering problem that needs a little more research behind it (a bigger team, smarter eggheads, better direction, whatever).
To the CEO, to the investor, to the businessman, it's just another problem that needs to be solved, directly or indirectly.
It looks very bizarre to a person of science. There are exactly this many types of problems: those that are proven true, those that are proven false, those that
can be proven true or false, and those which
cannot be proven true or false.
But the CEO can't possibly take the time to understand why some particular problem might be provably unprovable. It's just someone's opinion whether it is or not. And what if that opinion is mistaken?
It's all just opinion.
This is the main reason why businesses and investors frequently entertain proposals, that -- to those with in-depth knowledge of the subject, looks ludicrous -- and, indeed, why they necessarily
must entertain such things, because it's all just different opinions.
Now, if I haven't bored you enough, your homework assignment is this: read about what a "legal opinion" is, and what "evidence" and "testimony" are. Reflect on these subjects, and write a short (500 word) essay about them.

Tim