Class content I >Introduction to the class > Thinking about thinking and knowing > Knowing-how-we-know icons

Scientists use a wide variety of ways to represent information about physical systems – diagrams, numbers, graphs, equations, and specialized figures. Different ways of representing the same physical system often help us understand the nature of the system.    First, the use of multiple representations (visual and verbal, for example) may help us make better use of our working memory.

Second, different representations associate more naturally with different features of the data / situation we are trying to describe. As a result, the use of multiple representations can be effective in building links between different aspects of the situation.

The pictures below show three ways of representing the New York subway system.

• The subway entrances are there in the highly accurate satellite photo on the left, but it’s not useful.
• The central schematic map is to scale, and shows the train lines and stops magnified and everything else ignored. But the lines tangle together in the lower end of Manhattan and are hard to separate.
• The representation on the right stretches the city so that the lines are easier to identify but it does not correctly represent relative distances.

Each map shows a different aspect of the physical situation and each may be of most value depending on what the user needs. We'll use a bit of one of the NY subway maps to indicate when translating from one representation to another is going to be important to making sense of the physics.

Some of the representations we use in physics include

• words
• equations
• tables of numbers
• graphs
• specialized diagrams.

Translating how information is represented among these different modes will help you build a more complete "3D" sense of what is going on.

Joe Redish 7/5/11