All metaphors are wrong – some are useful

I’m hanging out at the Systems Thinking in Action conference, which has been terrific so far.

The use of metaphors came up today. A good metaphor can be a powerful tool in group decision making. It can wrap a story about structure and behavior into a little icon that’s easy to share and relate to other concepts.

But with that power comes a bit of danger, because, like models, metaphors have limits, and those limits aren’t always explicit or shared. Even the humble bathtub can be misleading. We often use bathtubs as analogies for first-order exponential decay processes, but real bathtubs have a nonlinear outflow, so they actually decay linearly. (Update: that is, the water level as a function of time falls linearly, assuming the tub has straight sides, because the rate of outflow varies with the square root of the level.)

Apart from simple caution, I think the best solution to this problem when stakes are high is to formalize and simulate systems, because that process forces you to expose and challenge many assumptions that otherwise remain hidden.

2 thoughts on “All metaphors are wrong – some are useful”

1. Richard Turnock says:

“We often use bathtubs as analogies for first-order exponential decay processes, but real bathtubs have a nonlinear outflow, so they actually decay linearly.”

I read your original post and this one, and would like to suggest that your use of nonlinear and linear seem to be inconsistent and confusing to this reader. I have experience with modeling and engineering. The relationships between volume, water column height and outflow rate that you talk about are incomplete without the equations to show the relationship of the outflow rate to volume and height.

You talk about water volume and outflow rate. I would write about the height and outflow rate.

2. Normally I’d reserve linear/nonlinear to refer to system structure, per engineering convention. That is, a linear system implies that all the rates are linear functions of the states. The behavior over time would not normally be linear in time, unless it happens to be in equilibrium (rates = 0) or open loop (states are integrating constant rates).

The bathtub is a bit of an odd case in that the structure is nonlinear (i.e. outflow rate is a nonlinear function of the state) in such a way that the behavior is a linear function of time. I guess you could call it a ramp, though I usually think of that as a test input, not an output.

I guess I also implicitly assumed that the profile of the bathtub is uniform, so that volume is a constant multiple of depth (height), making those effectively interchangeable state variables.

This make sense?

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