EDITOR Hugh Dubberly hugh@dubberly.com

guide

Our models guide our actions.

attention) and yet we have an accident or make a mistake, the cause may be some defect in our models. That is, our models suggested one outcome, but we have found another. The difference between expectation and outcome creates an opportunity for learning.

Learning involves forming models and reforming them based on feedback. We observe some behavior in our environment; it suggests models, which we use to predict future behavior and guide our actions. Additional observations provide feedback, which helps us revise and refine our models. We learn.

When outcomes do not match our predictions, we have two choices: 1. Reject the data

• Were measurements inaccurate?

• Was the test procedure flawed?

• Was the reporter biased?

2. Accept the data

• Is it relevant to our model?

• Is it a special case? Meaning our model is less useful at the extremes or our model needs refinement or extension.

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models
actions

• Was previous data inaccurate or insufficient? Meaning we need to revise our model.

Under this frame, we modify our models based on the results of our predictions—we subject them to feedback. Learning is inextricably linked with models and involves:

• Creating new models.

• Revising existing models.

– Extending a model so that it corresponds to

more observations (broadening).

For example, Ptolemy introduced cycles within cycles to account for the retrograde motion of Mars.

– Refining a model so that it more closely cor-

responds to observation (deepening).

For example, Kepler found that Brahe’s observations showed that the planets follow an elliptical (not circular) path around the sun.

• Generalizing models—reframing a model of a specific event as a model of a more general set of phenomena.

For example, the shift from the Ptolemaic to Copernican model is an example of a general case that recurs throughout the history of science as one important model gives way to another. Kuhn named this a “paradigm shift.”

• Identifying model primitives—finding patterns that recur across many models, often based on fundamental rules of geometry or topology.

For example, the earth orbiting the sun is a special case of a more general model of satellites orbiting primary bodies, which describes other cases such as the moon orbiting the earth or

predict

future events

suggest

guide

affect

compared

yes

reinforce

no

observations new models

actions

what happens

existing models

May + June 2009

may suggest

frame + filter