How about math olympiads? They do reward you for solving complex problems and require to admit that your first conjectures were hopelessly wrong (unless, of course, you happened to get them right. Alas, this might come with practice faster than the habit of staring into the abyss)
I mean, it only gets to the stage staring into the abyss when you spend 1h+ on one hypothesis and get nothing and are getting desperate and are attached to your idea for proof of A but realize it’s probably \neg A. Mostly how it works is you collect observations then form hypotheses a test a few of those, and mostly you quickly realize what works and what doesn’t. And if I’m stuck and keep doing one thing it’s because I had tried many times to invent something better but I couldn’t. It’s a really, really difficult thing to pull yourself out of this “mode collapse” where you’re banging your head against the wall where there’s clearly a wall, but it’s a different skill from seeing the abyss because 1) it’s easy to notice your approach is lacking something but 2) “not making the mistake anymore” is not blocked by psychology but by g factor or something.
How about math olympiads? They do reward you for solving complex problems and require to admit that your first conjectures were hopelessly wrong (unless, of course, you happened to get them right. Alas, this might come with practice faster than the habit of staring into the abyss)
I mean, it only gets to the stage staring into the abyss when you spend 1h+ on one hypothesis and get nothing and are getting desperate and are attached to your idea for proof of A but realize it’s probably \neg A.
Mostly how it works is you collect observations then form hypotheses a test a few of those, and mostly you quickly realize what works and what doesn’t. And if I’m stuck and keep doing one thing it’s because I had tried many times to invent something better but I couldn’t. It’s a really, really difficult thing to pull yourself out of this “mode collapse” where you’re banging your head against the wall where there’s clearly a wall, but it’s a different skill from seeing the abyss because 1) it’s easy to notice your approach is lacking something but 2) “not making the mistake anymore” is not blocked by psychology but by g factor or something.