Wow, that's awesome to hear! One of my fears is having to keep blogging continuously, but luckily math is pretty evergreen, so my intermittent writing schedule doesn't punish me too much.
Hi, I hope you take my comment well. This need to avoid some theoretical logical contradiction far down the road is similar to explaining the perils of split infinitives before teaching a child to say "I want food."
99.9% of calculus students are there to expand their mind. They will never design a quantum mechanical reactor and think "Wow, I'm getting all these weird results, my calculus education must have held me back."
It's generally preferable to give students a first order approximation at first, the successively refine with additional terms down the road. The fact that most calculus students will have no idea I'm referring to a Taylor series explanatory strategy highlights the problems with an overly rigorous introduction. Math at this high level should primarily expand your thinking, and secondarily your storehouse of previously proven rigorous statements.
Thanks for the link! I remember reading that study somewhere. A salient part of the article:
"This is what economists call "the commuting paradox." Most people travel long distances with the idea that they'll accept the burden for something better, be it a house, salary, or school. They presume the trade-off is worth the agony. But studies show that commuters are on average much less satisfied with their lives than noncommuters. A commuter who travels one hour, one way, would have to make 40% more than his current salary to be as fully satisfied with his life as a noncommuter, say economists Bruno S. Frey and Alois Stutzer of the University of Zurich's Institute for Empirical Research in Economics. People usually overestimate the value of the things they'll obtain by commuting -- more money, more material goods, more prestige -- and underestimate the benefit of what they are losing: social connections, hobbies, and health. "Commuting is a stress that doesn't pay off," says Stutzer."
I don't think reading studies is the only way either, but I don't think most of us have questioned what makes us happy outside of soceity's default settings (money/fame/toys/vacations).
People make all sorts of tradeoffs which are non-optimal:
* Extra commute to a better job with $XX,XXX more for +1 hour/day of travel (less time for good food with family/friends)
* Move away from good family/friends to pursue better job
* Pursue career X because it's more lucrative than career Y (even though Y is more enjoyable)
There are lots of biases like this, under the assumption the change will increase our net happiness.
I agree -- it's easy to forget the tradeoffs technology & specialization gives us. The fact that we spent years learning to read, write, do math, etc. means that most of us don't know much about farming and wilderness survival compared to our ancestors. They'd probably be shocked at our lack of knowledge in these "basic life skills".