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Even the brightest brain will have been stuck on something which, after the penny has dropped, will seem trivial. I agree with the author that there is a dange
by yomly 10y ago
Even the brightest brain will have been stuck on something which, after the penny has dropped, will seem trivial.
I agree with the author that there is a danger of "dumbing down" concepts which risks casting a lower ceiling on our capacity for lofty thoughts. There is another risk, though, that as someone becomes overfamiliar with a subject, they lose the ability to empathise with people who cannot immediately grasp the same concept. See [0] for a mathematician's reflections on revisiting his own DPhil thesis five years on.
I would counter that making abstract concepts accessible, broadens the reach of concepts which allows for the greater potential of new concepts being synthesised. Put in another way, the more people that have some grasp of an idea, the more humanity will progress.
Using Group Theory (strictly Point Groups) as an example, there are plenty of Chemists out there who are doing great work building catalytic organometallic compounds who use Group Theory. I'm sure plenty of them wouldn't be able to tell you what a Group was nor even express what the general basis of a Group are.
So yes, while there is a need to push ourselves our capacity to think increasingly abstract, we should also not be afraid to ruthlessly simplify as the world is big enough that individuals will derive benefit from diluted concepts for generations to come. What's more is that as concepts get simplified, the next generation can short-circuit their learning to achieve greater understanding at an earlier stage in their lives.
As I've always thought: if every human is born roughly equal, thank god we haven't had to "re-derive" making fire every generation otherwise how would we ever have time in our lifespans to learn about quantum mechanics and more.
[0]https://medium.com/@fjmubeen/ai-no-longer-understand-my-phd-dissertation-and-what-this-means-for-mathematics-education-1d40708f61c#.v3nwdc7uc https://medium.com/@fjmubeen/ai-no-longer-understand-my-phd-...
- hderms 10y agoIndeed. I think the point about allowing people to understand the subject at various stages in their lives very apt. We apply pedagogical simplification to almost everything we teach children anyways, but it's quite possible that we could be much more far reaching in our attempts. It would be interesting to see a world where children are taught basic abstractions of group theory. Mathematics is one of those fields where it is difficult to simplify. Period. But in addition, the practitioners often actively resist this simplification. Mathematics is firmly rooted in proof, but not all mathematics education needs to be firmly rooted in proofs, and for that matter, not all mathematics education must be rooted in mechanistic repetition of solution techniques. There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving.
- catnaroek 10y ago> not all mathematics education must be rooted in mechanistic repetition of solution techniques. Actually, coming up with proofs often requires creativity. If anything, the emphasis on memorizing formulas and solution procedures comes from an aversion to teaching proofs.
- tmptmp 10y ago>> There is perhaps a way to endow people with these concepts when they couldn't otherwise arrive at them through rigorous proving. Indeed it would be great if there is such a way. But sadly, without proofs, these concepts are half baked and are thus harmful as they give a false sense of understanding and thence the more harmful overconfidence. I remember the great thought that applies to entire math education (and also to education in general) - "There is no royal road to geometry." [1] [1] https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2.80.9CRoyal_Road.E2.80.9D_in_famous_quotations https://en.wikipedia.org/wiki/Royal_Road#A_metaphorical_.E2....