One of the great lessons to take away from a differential equations class... in my more dour moments, I think it's the only lesson to take away for most student

One of the great lessons to take away from a differential equations class... in my more dour moments, I think it's the only lesson to take away for most students in the course... is how common it is for iterated systems (which is almost anything embedded in "time", which is to say, everything we deal with in the real world) to be very sensitive to the strength of the feedback loop. It is trivial to construct systems that slowly, but surely, go to zero if you start with 0.5000000000000, but slowly but surely go to infinity if you start with 0.5000000000001. Small differences can be a big deal. Also, it should be pointed out that our history is not full of industrial revolutions. There's the one that we're still living in, and arguably two or three that fizzled depending on exactly how you count and where you draw the line, and that's it. Industrial revolutions aren't easy in the real world!