Thinking with boxes

Well, we did meet in the Coffee Box. But beyond that, there was a history of exploring reasoning with boxes.

What not to do

Since pretty much any three-term multiplicative relationship can be construed as a box, and there are plenty of them (F = m × a, P = F × A, x = v × t, and so on), this could get exhausting.

So, three constraints to give a direction.

What we are trying-out boxes on

Right Lines: Conservation laws
Conservation laws are a special way of thinking about the may-be's. Of the six conservation laws in physics, we chose to explore mass and energy separately (thinking of current pre-19 practice in schools) and momentum because it is a vector. Angular momentum did not make the cut because it is not widely exploited, and we did not thinking reasoning with boxes had much to say for the conservation of charge, lepton number or baryon number. So, here follows an exploration of reasoning with boxes about:

We're after exploring boxes as tools for thinking with

The boxes contribute to the quantity to be compared across may-be's, allowing insight into the way that the value of the quantities can be altered. But comparing the boxes directly across may-be's is not, in our experience, as a result of considering a number of examples, fruitful.