Powers of Ten and the Power of Wonder in Data Visualisation
By: Cass Barton
Tags: Scale, Illustration, How To, Art, Data Visualization

It isn’t easy to understand just how big some of the really big numbers are. But there are works of data art and data visualisation that try to put big numbers into perspective — and when they’re successful, they can inspire a sense of wonder about the universe. That’s worth doing on its own, but a sense of wonder can also serve as a stepping stone to other emotions, both pleasant and harsh.

The effect of adding another zero

Powers of Ten is probably the shortest film to ever blow my mind. Made in 1977 by designers Charles and Ray Eames, it is in its own words “a film dealing with the relative size of things in the universe, and the effect of adding another zero.”

It starts with a bird’s-eye view of a couple lying on a picnic blanket, a space of one square metre. Every ten seconds, the camera pans out to cover a space that’s ten times bigger. First ten square metres, then a hundred, then a thousand.

You can see where this is going. The picnic blanket soon disappears from view, as does the city it’s in, as does North America. The Earth becomes a circle, then a dot, then nothing. The film keeps going, out past our solar system, until within minutes, even our galaxy is put into its own tiny context. And just when you’ve started to process that, the view starts to zoom in again — we’re rapidly at the picnic blanket and then zooming in further, to the level of cells and then atoms and then quarks.

The film accomplishes all of this in a little under nine minutes. Watching it for the first time at school, I felt my teenage mind expanding in a way that only a teenage mind can when it learns new truths about the universe. At the time, I thought I was having a deep epiphany about the nature of reality, one that perhaps only a select few had had before me. In reality, my thoughts could pretty much be summarised as: Wow. Space is Really Big.

The problem with millions and billions

Humans aren’t very good at understanding big numbers. We do fine when we’re thinking about small amounts: few of us have trouble telling the difference between two and three potatoes, for example. But the bigger the quantities we’re thinking about, the less the differences between them seem to matter. 102 potatoes and 103 potatoes feel like they’re basically the same amount. By the time we get up to the millions and billions — the powers-of-ten numbers — our brains really fail to grasp how much bigger one is than the other.

This cognitive limitation isn’t an evolutionary flaw, necessarily. The really big numbers are obscure to us, but that doesn’t often get in the way of everyday life. We don’t often find we really need to be able to imagine a number with lots of zeros at the end in order to survive, so why would we have evolved to be able to?

We can sort of imagine those numbers, though. Modern science wouldn’t have gotten very far if we couldn’t. And what’s more, we have the capacity to be deeply awed when the big-ness of a number is explained to us in a way that we understand, however briefly.

Charles and Ray Eames clearly knew this. Powers of Ten is brilliant at showing, rather than telling, the size of the universe. It begins grounded in something that we understand — two people having a picnic — and then builds on that at just the right speed for us to keep up. Before we know it, we’re taking in the grandeur of deep space. And what’s more, we’re probably having feelings about it.

This sense of wonder isn’t so useful in the traditional, evolutionary sense. But it’s a gift to people who make art that’s driven by data. If we can crack a way to get people to really see a big number, then we’ve got a way to access all kinds of emotions: from delight and wonder to fear and anger.

xkcd and existential dread

One piece that has taken me straight from wonder to fear is an xkcd webcomic. Earth Temperature Timeline is well-regarded in the data visualisation community, and it works like this:

The comic is a chart and it’s really, really tall — you have to scroll a lot to read it. A time axis runs along the left-hand side, spanning 22,000 of the years that humans have existed on Earth. A line plots the global average temperature across those 22,000 years.

Through a series of annotations and illustrations, all in classic xkcd style, we learn how the world has changed. The Earth warms slightly and ice-age glaciers withdraw. Humans spread across the globe. The temperature stabilises a bit. Humanity starts to move from hunter-gatherer societies towards our current way of life. Like all the best xkcd comics, it shares some knowledge about science and history in a way that makes you feel excited to live in the world — with a few jokes thrown in.

But at the very end, the chart lurches wildly to the right. The line has stopped plotting a best estimate of the average temperature so far, and instead shows a projection of what’s expected to happen next. Even the most optimistic scenario for the next hundred years takes us well out of the narrow range that gave us writing, modern religions and the English channel.

When I reached that part on my first reading, that sense of wonder I built up reading about the first 22,000 years immediately curdled into existential dread. It’s not that I didn’t know about climate change before, but I didn’t feel the sense of potential loss in the same way. The comic opened a path for me to have deeper feelings about our future by making me amazed at how old humanity is and how far we’ve come.

The great and mysterious universe

The Powers of Ten film isn’t an original concept, by the way. The Eamses based it on a 1957 book by Kees Boeke, a radical educator. In the introduction to the book, Boeke writes:

“We tend to forget how vast are the ranges of existing reality which our eyes cannot directly see, and our attitudes may become narrow and provincial. We need to develop a wider outlook, to see ourselves in our relative position in the great and mysterious universe in which we have been born and live.”

Boeke isn’t talking about widening people’s eyes for the sake of it. He uses the word “need”, after all. Keeping our minds on the everyday, one-potato-two-potato world eventually becomes a threat if we fail to care about the bigger picture. So maybe I was wrong earlier: maybe it is a flaw that we don’t have an instinct for big numbers, and maybe our ability to be dazzled by them anyway is not just useful, but essential.

We’ve never had more tools at our disposal to help people understand the scale of things. So why not try to blow a few minds and see what happens?

Cassie Barton works in data analysis and communication, and writes about the art that people make with data. Find her on Twitter @cassier_barton.