Complexity

As a physicist I try to simplify everything. Now that I am working on Math Education, whatever that means, I am trying to simplify everything. I need a more nuanced approach. This is an effort to state a more useful methodology.

I hear my colleagues belaboring what for me seem like simple situations. What is the Social Representation (SR) of grammar school mathematics? Hour after hour I hear the many, many nuances, this question has. My colleagues even debate whether a conjunction for or on should be used in a paragraph. Grammar is not my forte; they were really arguing not about a conjunction, but about a coordinating conjunction. I am in trouble.

Are SRs that important? Yes. Do I know one when I see one? No.

Is it really true that the Theory of Quantum Cosmolgy is simpler? Maybe not, and that is why theoretical physicsts are stuck. I do want to contribute to Quantum Cosmolgy as I do to Math Education, but in any case I have to confront the intrinsic complexity of our lives.

I assume that the place to start is the Principle of Computational Equivalence (PCE), discovered by Stephen Wolfram.

Once one reaches a threshold of complexity, all complex systems are equivalent. The good news is that the threshold is low, a Cellular Automata is enough, the bad news is that it is complicated once the automata is run long enough.

I had the same feeling, I guess most people do, when I run my first "simple" iterated equation:

x_n+1 = λ x_n(1 - x_n)

Now I have to search for an equivalent guide in Math Education, whatever that means.