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How Scientists Know An Idea Is a Good One
Physicist Chris Lee explains one of the toughest judgment calls scientists have to make: figuring out if their crazy ideas are worth pursuing. He says:
"Research takes resources. I don't mean money—all right, I do mean money—but it also requires time and people and lab space and support. There is a human and physical infrastructure that I have to make use of. I may be part of a research organization, but I have no automatic right of access to any of this infrastructure. ... This also has implications for scale. A PhD student has the right to expect a project that generates a decent body of work within those four years. A project that is going to take eight years of construction work before it produces any scientific results cannot and should not be built by a PhD student. On the other hand, a project that dries up in two years is equally bad. ... the core idea also needs to be structured so, should certain experiments not work, they still build something that can lead to experiments which do work. Or, if the cool new instrument we want to build can't measure exactly what I intended, there are other things it can measure. One of those other things must be fairly certain of success. To put it bluntly: all paths must lead to results of some form."
That's not a description of a good idea. That's a description of an idea that fits into an arbitrary 4-year timescale that fits with a PhD program's average length.
Just because you're paranoid doesn't mean there isn't an invisible demon about to eat your face
Ancient Persians would debate ideas twice - once sober and once drunk. It had to sound feasible in both states to be a good idea.
Four years? Ha! That's a good one!
The easiest way to enforce that is for the awarding institution to say that if it isn't done in 4 years, it will be taken as a complete failure.
No, that rule would result in a lot of thesis committees approving completely crap theses. Believe it or not, thesis committee members are human and have a lot of difficulty telling kids that their last four (or five, or eight) years of work are worth no recognition and please leave. Thesis advisors become emotionally attached to their students and want to see the succeed/graduate, even if those students are incompetent. Sometimes you can compensate for the incompetence with time. Only rarely will a thesis committee 'over-rule' the advisor, with their input generally taking the form of 'this would become acceptable if the student adds [foo] over the next year or so.' Mandated time to completion is a recipe for diminishing the quality of theses and migrating a PhD from someone prepared for reasonably independent work to a glorified MS. Probably already moving in that direction, as many 'PhD's aren't really ready to work independently until they've finished two or more post-doctoral internships.
It is obvious that you're a mathematician. Your equation is dimensionally wrong.
No, it's correct. Let's do the analysis: $= (time + obtanium) / desire * beer
time is in seconds
obtanium is in seconds (how long to obtain it)
desire is in seconds/liter (the longer you wait, the more you want)
beer is in dollars/liter
so we have (seconds + seconds)/(seconds/liter) * (dollars/liter) = dollars
Q.E.D.
I feel sorry for people that don't drink, because when they get up in the morning, that's as good as they're gonna feel
The only way to know if an idea was good, is after you've already done it. Future prediction is always a crapshoot. People who claim to be good at it were typically just lucky, and are deluding themselves into thinking it was all skill.
While you are theoretically correct, you are real-world dead-in-the-water. A big problem with getting science funding these days is what I'll call the Golden Fleece Award Effect (for Sen. William Proxmire's Golden Fleece Award - wikipdeida it). While funding organizations are well aware that a solid negative result in a difficult research area is just as pertinent and useful as a positive one, Congress (the source of all funding) doesn't understand it and doesn't like it. Money out needs to be balanced by succes in. I know many researchers who do 90% of the research needed for a given NSF (or NASA) proposal before they propose it so they can (a) show it will indeed result in success, and (b) it will succeed so they can get more NSF funding. Nothing breeds lack of funding like failure. This is a dumb-ass way to do science, but since all funding comes from the Kingdom of the Dumbasses you get what you'd expect.