Four Values Can Still Be Worth A Chart

A while ago, Kaiser Fung criticized a chart for its uselessness because it only showed four numbers. The chart appeared on the smart web comic Abstruse Goose (which, as of this writing, is down for a site reorganization).

First, I think Mr. Fung was trolled by his reader, and fell for it hook, line, and sinker. The point of this chart is not to communicate a lot of data or to inform, but merely to entertain and perhaps to make people pause and think for a moment.

But the chart is actually kind of interesting because of some clever choices. The two axes are logarithmic, and they are both cropped. That is understandable, given the large differences in the frequencies involved in sight and hearing.

However, the axes are scaled the same: one order of magnitude takes up the same amount of space on each of them. That provides an interesting comparison, that I don’t think a lot of people have seen before. Sound frequencies cover three orders of magnitude (if we go with the usual 20Hz to 20,000Hz range), while light covers less than one (roughly 400THz to 800THz). Those frequencies are vastly different of course, and the difference in light frequencies contains the sound frequencies many billions of times.

But our perception largely works in a logarithmic way, so this kind of comparison is still interesting (as a data point, our perception of brightness covers about six orders of magnitude). It’s not useful, and rather arbitrary, but it does illustrate a little fact that I had never thought about (similar to the things you see on xkcd).

Then there’s the amount of additional data. Fung criticizes the chart for not including at least some context:

What’s missing is a histogram of the stimuli. I’d guess that the distribution is uneven, and there is a concentration inside the humanly perceptible zone.

But that misses the point. Of course there are many signals around us that we don’t perceive, the overwhelming majority of which have zero relevance for us. That is even true for the near-visible light spectrum (ultraviolet and infrared) that various animals see and put to great use, and it continues from there into the more esoteric (x-rays, gamma radiation, etc.).

The point, though, is to demonstrate how little of the world we see, whether there is something to be seen there or not. Without lots of machinery, we would not know. And because this is such a, well, blind spot, that we need to be reminded of it. That’s what this chart does. It makes us stop for a moment and consider. In that sense, it works like artistic visualization.

It’s a clever little image, and quite effective. Despite its simplicity, some good thinking went into its design. And even though its message can be summed up in a sentence or two, as Kaiser Fung points out, I think the image still makes for a much more impressive expression of that information than a few words would do.