Monthly Archives: November 2008

Why cartography is such a good communication tool

Maps are a brilliant way of communicating information.

For me, maps work on two levels. The first is that they provide a visual representation of a landmass — or figurative landmass, like the organisation of a companythe brain, or the Dewey Decimal System — some structure with which we are largely unfamiliar and need to be better acquainted. The world gets smaller when you can map it and contain it within a single image: by delineating the boundaries, you are effectively constraining what lies in the Here Be Dragons quadrant of known unknowns. Having a map of the terrain is useful for developing confidence: just as you wouldn’t tackle a mountain without having checked out the map first, students find it reassuring when they know what you are going to cover in a lecture, even if they don’t yet have a handle on the details.

The second reason maps are useful is to provide a familiar structure for new information. The most obvious recent example of this is Mark Newman’s fantastic 2008 electoral maps of the US, in which this



US electoral map.jpg

becomes this


US electoral map_distorted.jpg


becomes this


US electoral map_really-distorted.jpg


though by that point it almost starts looking like something out of Babylon 5.

Because — it is assumed — we are sufficiently familiar with the underlying structure, we are free to explore the new data: how did a given state, county or timezone vote? What could potentially be a really complex information set if just dumped on us wholesale (for example, in the form of statistics) now becomes easily graspable, because it’s framed by a known structure.

We could do this more in teaching: provide an early, basic road-map to students about the borders of the area under discussion, and progressively revisit and colour in the missing pieces. This is not always how we do things: a popular pedagogic M.O.  seems to be to introduce Topic A and then fill in all the details before moving on to Topic B, etc. — but what we could do is show a map of Topics A through H first, and then revisit each topic once students have understood where the edges of the map are.

Good teaching practice means being more explicit about maps.

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Ignore visual metaphor at your peril

I went to a research talk recently. It was a brilliant example of how to talk lucidly about science despite having poor graphical representations of the data.

The the speaker was youngish, eloquent, and unashamed of it (more people should really use the word perforce). He even referred explicitly to the narrative: “The story I am going to tell you today …” So he had me on-side from the start, because I am a sucker for narrative, and the storytelling aspect of scientific communication.

Unfortunately, his graphs and tables and figures were pretty bad. Most of the time it was all I could do to figure out what the data actually were actually saying. About halfway through his presentation, I more or less stopped looking at the slides because I couldn’t understand them, and trying to figure them out was making me miss what he was saying.

So here’s an example of how not to illustrate the relationship between two variables, A and B, under conditions 1, 2, 3 and 4:

mean-difference_bad.jpg

Straight away, we are having to work harder than we should, because the scale is inverted, and doesn’t follow the conventional metaphor of “up is more, down is less”.  (Yes, I understand that negative scales should go downward, but when you are emphasising increases in the difference between two variables, it’s just clumsy presentation.)

What he could have done instead was this, in which up and down retain their metaphorical values of ‘more’ and ‘less’, respectively:

mean-difference_better.jpg

Here, the x-axis crosses the y-axis at zero, and that the magnitude of the difference between A and B is the same, but that I’ve ditched the negative scale. Why? Because it’s just more intuitive to think in terms of positive values: we do this every day when we handle pieces of fruit, or money.

Also, I just don’t find ‘mean difference’ graphs all that intuitive. Why show people the results of a subtraction when they can work it out by eyeballing the difference between variables, like this?

mean-difference_good.jpg

(This last figure is also more information-rich, since it retains the absolute values of A and B.)

I didn’t have enough ego to approach this guy and say “listen, this stuff is great, but your diagrams kinda suck.” Maybe I should have — sure, I’d have been more diplomatic than that — but I didn’t feel like I had the moral authority. Plus, he was a very good speaker, and it would’ve been rude.

Einstein allegedly wrote that “The supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” Maybe we shouldn’t be in such a hurry to surrender those experiential data.

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