One of the constant threads of my work from the start has been the curious gaps between the world our minds present to us as a whole, and the one nature builds for us to *work* as a whole (using a considerably more complete deck of cards, you might say)… Here’s a good note to a mathematician and physicist, John Baez on his Azimuth website, prompted by the interest he expressed in studying the math of real world problems in his comments regarding mathematical economics.
John, in your first comment at the top I noticed your intent to go back to teaching math differently next time, as you said:
“but now I’m more keen on real-world examples that illustrate the big problems facing our civilization..”
What could be challenging and intriguing is to try to model the elemental problem of “complex systems with thinking parts”, or “learning systems”.
The problem is how a network of independently “observing, interpreting & responding” agents would interact. They are not follow rules, exactly, but following discoveries instead.
Learning systems share their own original learning and responses and developed a combined viewpoint of their dynamically changing environment. Economic markets do that for example. Continue reading The limits of learning machines… (drawing a blank!)