### Godin graphic understates nuclear safety compared to coal by 92%

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).

via Mike McCue via Andrew Sullivan via Seth Godin