4 ms·
John von Neumann once told a confused young scientist, "Young man, in mathematics you don't understand things. You just get used to them." I don't think that's
by pash 15y ago
John von Neumann once told a confused young scientist, "Young man, in mathematics you don't understand things. You just get used to them."
I don't think that's quite true, but developing familiarity with a difficult concept is tantamount to coming to understand it, in my experience.
For me, the process seems to go like this:
1) assemble the disparate pieces of a concept, and try to wrap my head around the novel ones;
2) work out how Piece A relates to B, and B to C, and ... ;
3) forget what the hell Piece X is;
4) repeat steps 1–4 several times;
5) convince myself that all the pieces work together as they should.
And only later, after I've worked with this collection of pieces several times, do I stop seeing the pieces and start seeing something new, the emergent phenomenon of the new concept. And it's not until I've forgotten the details of how Piece X fits into Piece Y, and maybe why we need Piece Z in the first place, that I feel like I really grok this new concept.
- mechnik 15y agoI recall a section in Halliday and Resnick freshman Physics text where the authors advise to 'do exercises until you convince yourself that the solution method is correct'.
- Lost_BiomedE 15y agoI think this way as well. I was told that I am a slow processor of information, by a credible source. Also, that I would have a harder time learning on the fly but would have a deeper understanding due to making more cognitive links to each idea, and this would allow for tackling harder problems and long projects. It has turned out to be spot on, and if I would have to guess, I would say about a quarter of engineers that I know seem to think this way. In the general population it seems much lower.