Solving Problems with Diagrams

When physicists are presented with a problem, they reach for a pen and scrap of paper. Sometimes we go straight to equations, but more often, we draw a diagram.  This is part of the culture and discipline of physics (see Forbes here).

We do it because it reduces the load on our working memories. An interesting physics problem can’t be solved in your head. We use a powerful computational tool – a sketch.

But not just any sketch. There are rules.

  • We simplify. Only put down relevant information – we don’t care how you attached the pulley to the ceiling, just that it is attached.
  • We prefer 2D (we’ll go 3D magnetic fields, but we don’t like it).
  • Our sketch-diagrams are typically line-drawings in one colour for speed.
  • They are ephemeral – they usually get thrown in the bin as soon as we’re done.

A rationalisation of how these characteristics help us solve problems more efficiently can be found in Larkin and Simon’s 1987 paper: Why a Diagram is (Sometimes) Worth Ten Thousand Words. They identify three features of computationally efficient diagrams -diagrams which help solve problems:

  1. Is the diagram easy to search?
  2. Does the diagram reduce the amount of inference the solver needs to do (e.g. the solver needs to ‘infer’ from a text the arrangement of items or the physics rules to apply.
  3. If the diagram is provided, is it recognisable? Is the solver familiar with this diagram and how it works?

Below is a poster summarising Larking and Simon’s paper and illustrating it with my own example:

Computational Efficiency Poster (pulley) v2 (2)
A summary and application of Larkin and Simon’s 1987 paper: Why a Diagram is (Sometimes) Worth Ten Thousand Words

I think there are two main implications for the classroom:

  1. Physics diagrams need to be explicitly taught. Solvers need to recognise the diagram and know how it is used, otherwise they will not refer to it.
  2. Learners need to be taught how to sketch computationally efficient diagrams so that they can use them in their own problem solving. Their diagrams need to be:
    • simple to search
    • be standardised (e.g. always draw a block on a slope the same way) and
    • they need to reduce inference. They should show the layout and important details clearly.

This all takes practice.

In this post, I haven’t described the flip side of sketching diagrams: communication between physicists. Two physicists talking together will often reach for pen and paper for the same reasons described above. Forgetting to teach diagrams in your physics teaching is the same as forgetting to teach literacy.

With thanks to @olicav for sending me to Larkin and Simon.

Ben

@benrogersedu

 

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