Is It True That Humans Can’t Accurately Measure Areas?: Criticism and Misunderstandings About Bubble Charts (and Pie Charts)

Visualizations are often judged within the context of “good” vs. “bad”. There certainly are bad visualizations that fail to serve their purpose for specific objectives. However, the idea that there’s a single “good” visualization for any given purpose is simply not true.

Herein, I would like to talk about the criticisms and misunderstandings about bubble charts.

Bubble charts represent quantities with the size of circles.

Bubble charts are often presented as bad visualizations. A major reason is that ‘humans cannot accurately measure area.’ This issue is also cited as a reason why pie charts are considered poor visualizations.

I personally feel that it’s true, but why? What makes areas so special? What about volumes or logarithmic scales? Can you accept the explanation ‘This is the way humans are’ without any doubt?

Let’s speculate about it.

Example

The issue is discussed, for example, in “The Functional Art” (Chapter 2) by Alberto Cairo, published in 2012. Before I move on, I would like to note that this book is very well-written and I learned a lot from it.

Here is an example analogous to the one considered in the book.

This chart (which ignores units) aims to show changes in company sizes over time. The number label and the bubble size (area) both indicate the company size at the time.

If you look at the inner and outer bubble on the far left for instance, even if the size of a company is halved, representing this change through the size of a bubble might not visually appear to be half the size.

In “The Functional Art,” Cairo explains the reason for this difficulty in perception as follows:

“… the human brain is not good at calculating surface sizes. It is much better at comparing a single dimension such as length or height.”

I’m not convinced by this explanation. It simply states that it is the way humans are and lacks a scientific basis.

Because it’s non-linear

In my opinion (yes, this is still subjective), it’s more accurate to say that ‘humans struggle with measuring non-linear relationships’ or ‘People naturally tend to measure the diameters instead of areas when they look at a bubble chart.’

For example, for two bubbles with an area ratio of q, the following relationship holds:

A bubble that is twice as large in area (q=2) will have a radius (or diameter) that is √2 times larger (about 1.4 times).

If you look at the inner and outer bubbles at the center of the figure above, you’ll see that the ratio of their diameters is 2, even though the area of the outer bubble is 4 times larger than that of the inner bubble (q=4).

Therefore, if you think of the radius as “the size perception experienced by humans,” you’ll notice that changes become less pronounced. Even if you can understand the difference intellectually, it’s hard to make the visual correction.

Similarly, this explanation suggests that humans are not good at visually measuring the comparison of volumes (of spheres), the comparison of surface areas, or the comparison of logarithms, because they all have non-linear dependencies.

Misunderstanding leads to criticism of pie charts

It might seem that being “bad at reading areas” and being “bad at understanding non-linear dependencies” are the same thing.

However, if people take the lesson that “humans are bad at reading areas” too seriously, they end up with the criticism that ‘humans cannot accurately read areas, so pie charts (which quantify elements using areas) are not effective.’

But hold on.

Since all categories have the same radius, what’s actually being compared are the angles. Even when viewed in terms of area, the area ratio of two categories with a value ratio of q is indeed q because they have the same radius (it’s a linear dependence!).

Therefore, if you consider the difficulty in measuring non-linear dependencies, under this criterion, it cannot be said that pie charts are ineffective visualizations.

There are cases where pie charts are not suitable and there are various reasons (check out another post of mine if you are interested in), but the reason ‘humans cannot accurately measure area’ doesn’t make sense to me.

Why people use bubble charts?

Despite the issue with quantitative evaluation, bubble charts are often used in practice. It is often said that this is because humans prefer circles (another argument based on human nature…), but is that really the case?

I don’t have a clear, reasonable, or scientific answer to this, but I suppose it’s because patterns in data can be quickly perceived using bubble charts — a human nature argument again.

Although the quantitative evaluation can be inaccurate, you can probably distinguish between larger and smaller bubbles as well as you can in a bar chart.

Conclusion

I argued that it’s more accurate to say ‘humans struggle with understanding non-linear relationships’ or ‘people naturally tend to measure diameters instead of areas when looking at a bubble chart,’ rather than saying ‘humans cannot accurately measure area.’

You might argue that the book by Alberto Cairo also mentioned dimensionality, and thus, it already implies non-linearity. Yes, that might be true. The purpose of this post is not to criticize the author’s understanding or description, but to caution against inappropriate generalizations of issues in data visualization.

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