|
|
|
|
|
by candu
3073 days ago
|
|
There are most certainly human inventions / discoveries that are, in some sense, "hard" (either to discover in the first place, or to explain / grasp). We have a biased view here: we can look back at, e.g., Einstein's general relativity and summarize its development as "well, he just thought to explore the logical implications of having a constant speed of light!" We have that luxury of hindsight (and several decades of steadily improving explanations of the original insight). Then you go and start reading Actual Science: Minkowski spaces? Tensors? Paradoxes about long objects and barns? Gravitational lensing? Figuring out where to go with that initial idea is decidedly non-trivial. In the extreme, there are papers at the bleeding edge of mathematics that can only be meaningfully reviewed by half a dozen people worldwide. Understanding these papers (or anything at the limits of species-wide knowledge) is a far cry from grasping algebra / calculus: eventually you hit a point of diminishing returns, where further advances in your understanding of the problem require months or even years of dedicated study... ...and yet (assuming we refrain from destroying ourselves) these same problems may eventually find their way into high school textbooks, where they will be succinctly (and approximately / incompletely) summarized so as to make them look easy and incremental. That's great! It means we've permanently moved the pedagogical starting point forward for future generations, so that they can go and struggle with truly hard problems that we don't even know to ask. My point: yes, some things are hard, even if most are not. I'd say that the trick to advancing humanity lies less in convincing students that everything is easy given enough time / patience / curiosity, and more in getting them to stick with hard problems: to normalize failure, as it were. That said, I do agree that we should avoid presenting things that aren't truly hard as though they are :) |
|