In almost every class I teach, I give the same paper assignment: Write a grant proposal. If it's an undergraduate class, then it's the NSF GRFP. If it's a graduate class, then it's the NRSA. But I love the NSF assignment. Write a three-year proposed line of studies, with methods and motivation and hypotheses and broader impacts. And do it in two pages (with references). Holy @#$#, that's hard. It's one of the reasons why I love giving that assignment.
But here's the other one. If students go on in academia, they will need to learn how to write a grant. Only way to learn is to do it. And if students don't go on in academia, there's lots of other skills that come from grant writing. Valuable skills.
(Just the other day, I was at a board meeting for my temple -our treasurer was struggling to apply for a federal grant that gives money to houses of worship for security. I volunteered to help out. Grant writing is a transferable skill).
That's the real reason I give this assignment, instead of a random 10 page paper - students are never going to look at a paper they wrote in college.. But they will remember grant writing, and if they ever need to do it, the skills transfer.
But writing a grant means that you have to have an idea for a grant. And that's the hard part. Generating ideas is fundamental for doing research, proposing a thesis, or just doing science.
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There are two kinds of ideas for experiments. Incremental ideas start with something established, and tweak it in some way. Vary one thing at a time, and you can have an entire career based on incremental ideas. It's good, safe science, and funding agencies love incrementation. And this is the best place to start. Read other peoples work and build variations. That's about 90% of science.
But everything thinks the glory is in innovation - thinking up something completely new. And it's what students think they have to do. They don't. It can be fun, and some people are naturals at it. But it's not necessary. Let's face it, innovation is even a cooler word than increment. But it's not necessary. There are lot of hall of fame scientists who only ever did incremental work.
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But, that's not going to stop you from asking the next question: How do you innovate? Beats me. But here's a question for you that might help. Read it. Give yourself 30 seconds to try to solve it before reading further.
Imagine that there are 10 stacks of 10 bricks each (so 100 bricks total). In 9 of the 10 stacks, the bricks weigh 10lbs. In 1 of the stacks the bricks weigh 11lbs. You don't know which stack has the 11lb bricks. You have an accurate bathroom scale (you put things on it, it tells you the weight). You can use it exactly once. How do you find out which stack of bricks is the one with 11lbs bricks in it?
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OK. 30s later. Good.
There are people who will try to outthink the question (like, can't I feel all the bricks, and won't I just be able to know which ones are 11lbs instead of 10lbs by feel?). This is loopholing. It has some advantages as an approach to problem solving, but not here.
There are people who just figure out the answer quickly. This question, by the way, was posed to me by my college roommate. It was given to him when he interviewed at JP Morgan for a job as a stock analyst when we were seniors in college. And they timed him. He got it in 16s. He timed me when he gave me the problem. I got it in 29. He still teases me about it.
Then there are people who figure it out, but much later (if you don't get the answer after 3 days, feel free to email me, and I'll give you a hint).
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The brick problem is a type of problem called an "insight" problem. They differ from "algorithmic" problems, which are problems that have step-by-step solutions. If you know the algorithm, you'll solve any algorithmic problem if you have enough time. Solving insight problems used to be thought of a way of measuring creativity. And there was a movement in business and finance that the better you were at these types of problems, the better you would be in industry. I'm not sure this is actually true, but I'm not sure it's false either. But it did matter for the JP Morgan interview - my roommate mentioned that only the people who got this question in under 30s were asked back for a second interview.
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I doubt whether solving the brick problem quickly (or even at all) is related to innovation. But ideas are like that. They are slippery. Often, having one means getting a small kernel of something, and then working it out. It's the working it out part that takes time and effort. The hope is that they have "truthiness" (that's a Colbert word), which ultimately can be proven or disproven empirically.
The other thing that I think is important in trying to think about ideas is talking with people. In the US (and in WEIRD - Western, Educated, Industrial, Rich, and Democratic) countries, there's a concept of "scientists" as a lone genius. Most fields, however, are not like that - they are much more collaborative. In psychology, many empirical papers are written by multiple authors. More is usually better, because ideas are more diverse and there are more diverse voices contributing to their construction. Everything I wrote above about the brick problem and insight problem solving being related to creativity or innovation fosters a myth that we are all just generating ideas alone. To quote Newton, "If I have seen further, it is because I am standing on the shoulders of giants." He credits his ideas to the fact that he had the ideas of others. We all do incremental work, and we all innovate.
There's probably one more thing. Fear. Sharing ideas is scary. People might not like you, or might think the ideas are bad. Or that you are bad (if so, then maybe think about who those people are). I get it. Sharing ideas is hard if you have never done it. So, if you are afraid of sharing your ideas, remember the following. The success rate for federal grants (i.e., professional scientists putting their ideas down on paper and asking for money to work on them) is about 20%. A really good academic has a success rate of getting grants at around 30% (basically, no different from a really good baseball player). We fail 70% of the time - because someone else (or a few elses) think our ideas are bad (or just not good enough). And that's a lot. Some people take their balls and go home. Others don't and share again. And again and again, until they get better, which is the only way they do. Sharing again - communicating your ideas with others - is probably much more important for generating ideas than whether you solve the brick problem.