It's been a long time since I've added a complex skill and become sufficiently advanced to experience the jump in level. Reading this made me remember how exhilarating that can be.Sometimes, in your mathematics career, you find that your slow progress, and careful accumulation of tools and ideas, has suddenly allowed you to do a bunch of new things that you couldn’t possibly do before. Even though you were learning things that were useless by themselves, when they’ve all become second nature, a whole new world of possibility appears. You have “leveled up”, if you will. Something clicks, but now there are new challenges, and now, things you were barely able to think about before suddenly become critically important.
It’s usually obvious when you’re talking to somebody a level above you, because they see lots of things instantly when those things take considerable work for you to figure out. These are good people to learn from, because they remember what it’s like to struggle in the place where you’re struggling, but the things they do still make sense from your perspective (you just couldn’t do them yourself).
Talking to somebody two or levels above you is a different story. They’re barely speaking the same language, and it’s almost impossible to imagine that you could ever know what they know. You can still learn from them, if you don’t get discouraged, but the things they want to teach you seem really philosophical, and you don’t think they’ll help you—but for some reason, they do.
This also reminded me of the Wheaton Eco Scale that Jacob has referred to a bunch of times in the past. (Edit: http://www.permies.com/t/3069/toxin-ect ... -Eco-Scale) You can learn from people that are a 'level' removed from you, but are mentally separated from people that are two or three levels away. From the article, this apparently applies to your cognitive skill / level of education also.
I can think of some personal examples of this:
1. Language acquisition - Once you have sufficient vocabulary to understand written news stories, it's easy to pick up new vocabulary based on context and exposure, so you jump a level. The same happens after you have enough listening comprehension.
2. Jazz soloing - requires many skills that are not correlated, but when they all reach a certain point, suddenly you are very good. You have to be able to operate your instrument, memorize scales, understand harmonic theories, internalize stylistic inflections, etc. You don't gain a level until all dimensions improve
So anyway, I think the concepts in the article are really interesting. What other ERE implications are in there?