> blindly hammering away on the wrong problem is a failure mode for many intelligent people. The key is not just sticking to things, but also having enough taste to know when to drop a problem.
Agreed. In my original comment, I was trying to imply that those exceptional people did (ad you say) have enough "taste" to know when to stop, but I don't think I made that aspect clear.
The crystallographer I was talking about definitely failed more often than not, but I was always struck by his ability to keep floating reasonable ideas after the rest of us had reached what we thought was an intellectual cul-de-sac.
If you have ever read the transcript of Richard Feynman's speech "There's plenty of room at the bottom" [1] you get the same feeling--here's an incredibly bright person who can't seem to stop when he's told that "x is impossible."
I love this part of Feynman's speech: "The reason the electron microscope is so poor is that the f- value of the lenses is only 1 part to 1,000; you don't have a big enough numerical aperture. And I know that there are theorems which prove that it is impossible, with axially symmetrical stationary field lenses, to produce an f-value any bigger than so and so; and therefore the resolving power at the present time is at its theoretical maximum. But in every theorem there are assumptions. Why must the field be axially symmetrical? Why must the field be stationary? Can't we have pulsed electron beams in fields moving up along with the electrons? Must the field be symmetrical? I put this out as a challenge: Is there no way to make the electron microscope more powerful?"
I think the deeper explanation here is that unusually clever people know how to locate the unquestioned assumptions and have no problem throwing them out. Or put another way, they ask questions of the form, "I know this sounds dumb at first, but hear me out. Why don't we..."
Most problems come with a slew of constraints we take for granted, and then a set of constraints we consciously impose on the solution because we think it helps. Most reasonably bright people try lifting those conscious constraints, but rarely touch the less apparent ones.
I think that more neatly explains what you both are going for with "gives up too soon" (not identifying all constraints), "hammering away" (also investigating non-obvious constraints), yet "have enough taste to stop" (there are no more constraints to lift).
I've been encountering this effect in rapid succession in the last couple of years as a new parent.
First few weeks: Everything is new and you have no firm assumptions other than what you've observed from the outside of other families, so you try to build a new model on how your child behaves, how you should react and the routines needed to function as a family.
A month in and every other month going forward for the next year: Everything you think you know about your child has changed, and all (most) assumptions about what works when comforting, putting to sleep, and feeding goes out the window and you start over building a new model.
Of course everything doesn't change, but this scenario of developmental changes has really ingrained the idea in me how easy it is to make assumptions (deliberately and not) that you assume are static truths. It has made me go back and reexamine everything from old wives tales I learned through osmosis as a child through my politics through technical decisions in my work.
Whether you consider Jobs, Musk, Wozniak, Brin, Page, etc creators/innovators or something, I think a lot if not most successful ventures has come from reevaluating assumed truths, ranging from the market, state of technology, or paradigms. I'm not saying you should throw out everything old, but merely that learning from history should be a scheduled process, not a one-off.
Sorry for the unwarranted rant, but your comment just resonated with my own experiences.
Musk, in particular, appears to me to be refreshingly naive when confronted with a problem. His suggestions sometimes sound like something a kid would say, and that's not a bad thing.
I wonder if there is a way to train yourself to have the intuition for quickly lifting those less apparent mental constraints in all situation.
Anyone have any thoughts on achieving this or resources. I recall some dual n back game posted from a website called gwern that supposedly helps speed up your recall time or how many items you can recall.
Sometimes. Forward motion is always important. In incident command scenarios, I’ve seen situations where people will sit around and wait... you need to move forward at all times or you get used to nothing happening.
I somewhat disagree with this idea -- it's important to drop unrewarding lines of enquiry, but more because you've reached the point where it becomes clear the answer would be boring than because it won't pay the bills. I mean, you have to get with the program sometimes and drop an interesting problem because you can't afford to continue working on it, but at that point it's not really dropped. It's just become an itch you can't scratch. If the problem is interesting enough, the pursuit is its own reward.
The key is not just sticking to things, but also having enough taste to know when to drop a problem.