Seth Godin posted a striking graphic on Tuesday (“The triumph of coal marketing“) showing how coal energy generation kills about 4,000 times as many people per watt hour as nuclear energy generation. Incredibly, I think his representation of the data actually understated that figure.
Godin shouldn’t be representing one-dimensional information with two-dimensional areas; if I understand Stevens’ power law correctly, human perception of the graphic will understate the difference between coal and nuclear by about 91.7%.
Now, human perception is very tricky, and I’m not at all sure I do understand Stevens’ power law correctly (check my math below). So here’s the same data represented as a simple one-dimensional bar chart.
As promised, the (less concise than necessary) math:
Note that the theoretical perceived ratio will depend pretty sensitively on the assumed value of Stevens’ exponent a. Just so I can throw another trivial graph in here, let’s watch the theoretical perceived ratio (purplish) hit the true ratio (blue) as the exponent hits 1:
Stevens’ power law has also been roundly criticized, but I think (a) we’ve had fun here today and (b) the point that people misjudge areas stands.
If you’re interested in this sort of thing, I recommend Edward Tufte’s The Visual Display of Quantitative Information (as well as his other books).
And, in defense of critics of nuclear power: coal kills relatively predictably, whereas nuclear power may be more likely to unleash truly catastrophic consequences. If you’re interested in that sort of thing—the impact of the highly improbable—I recommend Nassim Nicholas Taleb’s The Black Swan (as well as his other books).