Visualizing Exponentials

We Live in Exponential Times, but We Humans are Naturally Lame at Understanding Exponentiality

Abstract:
– Analysis of the visual representations of exponentials.
– Proposals to solve current visualization issues.
– Call to discussion to come up with a better visual representation convention.

“The greatest shortcoming of the human race is our inability to understand the exponential function.” 

Albert Allen Bartlett, Physics professor

Our big brains brought us the capability to predict the future, and it worked great when our environment was moving on a (rather slow) linear progression, when our ‘food’ moved around the fields from A to B at a constant pace. But many critical aspects of XXI century life move at an exponential rate: human population, computer power, online virality, virus virality, etc.; and we are not trained to predict exponential futures.

Graphs and data visualization have been helping understand complex numerical information for centuries with one of the most powerful human tool, an image.

Scientific Visual Representations

Science has two ways to visually represent exponentials: linear & logarithmic.


Both are accurate, valid and perfectly understandable by people with a scientific background, but it shows some issues when it comes to the mainstream intuition interpretation.

All the Same, All The way

Any section of a linear exponential representation will give you the same trajectory because we tend to escalate the Y axis. The spread of a virus will look similar in a graph of the first 10 days and the first 100 days.

Tendency to Infinite

An exponential curve seems to tend to infinite, but infinite is a rare thing in the real world; actually, most exponential growth or decays are interrupted by some event. It is the lack of a limit reference that makes it feel an endless progression.

Lack of details

A linear graph will only show more details on the high part of the chart.

A logarithmic graph will only show details on the low part of the chart.


Exponentials for the People

Human culture is poor in exponential references. The most relevant ones being:

Legend of Paal Payasam

The Indian Legend of Paal Payasam, in which a reward consisting on doubling the grains of wheat on the squares of a chessboard ends up with an overwhelming amount that surpasses all the amount of wheat grain in the world.

Powers of Ten

The film Powers of Ten by Charles and Ray Eames, which zooms out from our ‘human scale’ exponentially to the scale of the entire universe and then zooms in to the scale of an atom.


A Better Visual Approach

To help the lack of natural human skills to understand exponentials it seems relevant to find new ways to visually represent them in a humanly intuitive way.

Nowadays, Infographists develop amazingly creative ways to make abstract data understandable to everyone, but they are mostly individual solutions per each case.

It seems necessary to find a visual system relevant for exponentials, accurate and simple enough to be easily implemented and understood.

As a Graphic Designer myself, I approached this issue and come up with some early concepts that can help better understand exponentials.

While there are out there some examples of exponential visualizations showing its progress as an animation or video –the same way Powers of Ten does or like this example of computing exponential growth– I consider that motion generates more complexity in terms of creation and readability, and we miss the simplicity of a single visual impact. So, while I don’t discard a dynamic solution, I prioritize a static image system.

Layered Landscape

Logarithmic graphs visually remind me of a landscape perspective, where closer objects look bigger and further objects look smaller.

But in logarithmic graphs there’s a disruptively wrong element that kills the perspective, the line. Imagine the line as a path. If we scale the thickness of the line proportionally to the change of scale it matches our ‘perspective language’ and it makes it more comprehensive.

Different visual codes would even make it more equal in terms of data details inside the same chart; for example using escalated circles.

Finite Reference

As mentioned before, despite the impression of a curve to the infinite, exponentials have limits and representing this reality (as far as possible) would help understand where is this curve going.

While a context reference is sometimes used in a graph explanation or in the graph itself, the suggestion is to close down the graph itself where the trajectory seems to continue to infinite.

Work in Progress

Those are very simple approximations to solve the issues above mentioned, not except of issues themselves. I’m personally invested in the topic and will try to learn more about it and find better solutions.


A Call to Discussion

I write this article from a designer perspective and with no scientific background, my purpose is to open a debate for science and design to reach a convention that feels natural for everyone to understand. My approaches are just a kick-start and I’d like to hear the thoughts of other creative brains –either scientific or designer.

I encourage others to explore the topic and I propose the hashtag #VisualizingExponentials (any platform) to follow up on other comments and approaches. I’ll look at putting together a compilation in short time. I’m thrilled to see where this can go.


Related Links

Visual explanation of exponentials: https://setosa.io/ev/exponentiation/ by Victor Powell

An approach to exponential bias applied to SARS-CoV-2 spread case https://towardsdatascience.com/dealing-with-our-systematic-misjudgment-of-covid-19-exponential-growth-3d367c9546d9 by Yannis Kopsinis