Nothing is "Obvious"
There is a lot behind this statement, both historical and deep, including:
- When I hear a child keep asking "Why? But why? But why? ..." I realize that is not infrequently my
string of questions too. More broadly, I find if I think about most anything sufficiently
deeply, I realize there is so much I don't know. (It turns out that is the perspective of many prominent scientists and eastern mystics as well.)
- I find nothing easy. This is in part because anything I see, I connect to 1000 other
threads and — on a good day — realize could be otherwise.
(Indeed, if you look at the
history of mathematics generally, you will find the entire human species, across multiple
cultures, considered something to be obvious and self-evident and the only way it could be ...
until someone wondered if it could be otherwise and in consequence developed a whole new
field of mathematics. An example of this is the "discovery" of non-Euclidean Geometry, where
from 4th century BC when Euclid lived until the 19th century — over 2000 years — people
thought Euclidean geometry was all there was, and could not be otherwise. See Non-Euclidean
- Following a conversation with a longtime friend and colleague of mine, with whom I
frequently engage in explorations of how people think, we realized that, in our minds,
faster than we can process and typically without conscious awareness: He chooses to go down
all the branches that he understands, while I choose to go down all the branches that I
don't. This tends to improve his effectiveness as a business person and engineer (and boost his
confidence generally), while it tends to improve my empathy as a teacher (and increases my concern at all that I don't know).
- When I was an early teenager, my father — an MIT Research Scientist — decided I was
behind where I should be in mathematics, and took it upon himself to tutor me. The process
was quite stressful, with my father repeatedly saying things that I did not
immediately understand were "obvious". I learned a lot of math in a short amount of time, but the experience left scars.
(My father was overall a very loving person, and supportive of me through his life in more
ways than I can count.
I mention this far-from-optimal interaction simply to let you know that "I have been
there...", and deeply understand the importance of emotional tone within student-teacher interactions.)