The exponential age is happening but we’re picturing it wrong

That famous exponential line chart fails three key tests

When we enter a new technological era there’s often a scrap over terminology. Are we living in the digital age or the knowledge economy or the age of agile? Or, the latest frontrunner, the exponential age?

I like the idea of the exponential age because of the way it captures the explosive character of our times. I also really enjoyed Azeem Azhar’s book, Exponential, which makes a similar argument to my book, End State, particularly when it comes to showing how the state is falling behind an exponential economy.

But if there’s one thing I don’t love about the whole exponential debate it’s that famous line chart.

It’s quickly become the main image we use to represent the exponential age but the more I see it the more I think a) it’s not very useful, b) this is a problem, and c) there’s a better image available.

So in this post I want to share three reasons why I think we can improve on the line chart, and I’ll also touch briefly on why I think this matters.

Planting a tree

So what’s wrong with the exponential line chart and what could we use instead? I think the best way to answer this is probably to propose an alternative and explain why I prefer it. And the image I want to propose as a representation of the exponential age is a tree. Something a bit like this.

There are three reasons I think a tree is better than a line as a way of visualising the exponential age.[1] They amount to three criteria by which we can judge the usefulness of a visual representation: salience, form, and function.

First, does the image capture the most salient aspects of the thing it’s trying to represent?

To be fair, I think the line chart does an OK job on this front in that it obviously captures the sense of exponential acceleration. But I think the tree does better because it also visualises one of the other salient aspects of the exponential age in a way the line fails to do, namely complexity.

For me the critical thing about the exponential age isn’t just the accelerating quantitative change we see all around us — the way technology is getting faster, smaller, or cheaper. It’s also the way technology, and the possibilities unleashed by technology, are getting more complicated, so that the number of possibilities/combinations is itself exploding.

The thing that’s so game-changing about technology today, as Azhar shows so well in his book, isn’t just that computers are getting faster or that solar panels are getting cheaper or that chips are getting smaller. It’s that all these things are happening at the same time. And, because digital is a kind of universal language that can translate across previously separate domains, these innovations can then combine together in an explosion of fresh possibilities.

Yet when you look at the line chart, if anything you see the opposite of complexity. In fact, when it’s used as a general representation of the exponential age, the line chart sits in a long tradition in economics, running from Ricardo to Rawls, in which we visualise the world as if there is only one thing or commodity in it, or at most two. i.e. we assume homogeneity or near-homogeneity so that the world is simple enough for our models.

One of the most important aspects of the exponential age, as reflected in the rise of complexity theory in economics, is that this approach no longer cuts it. An assumption of homogeneity misses the heterogeneity that is a decisive aspect of today’s world. So it’s quite problematic if we visualise our new technological age in a way that lulls us into a sense of simplicity or homogeneity.

Second, I think it’s useful to ask of any visual representation: is the form of the image structurally appropriate to the thing it wants to represent?

I like the tree because its formal structure, which is a fractal, is the same as the formal structure of technological change.

We could spend all day on this point but let’s just say it’s not a coincidence that fractals appear whenever you read about economic history since the Industrial Revolution.

Whether it’s David Landes on the ignition of industrial capitalism or W. Brian Arthur on the nature of technology, the process of growth and innovation in a technology-based economy has recursive qualities. In Landes’s words, “change begets change” or, in Arthur’s words, “technology builds itself out of itself.” The whole thing feeds on loops.

This might sound like a purely aesthetic point. Sure, it’s quite pleasing if our main image of the exponential age has the same form as technological change, but does it really matter? I think it does, because when a visual representation of a thing shares the formal structure of the thing, this gives the image explanatory power.

You can see what I mean by this if you look at the tree and ask: why are we seeing exponential growth? A big part of the answer is there in the image itself. Every time a branch divides, it creates new branches that can then themselves divide, just as each new technology or innovation also creates fresh possibilities and fresh potential combinations to create yet more technologies and innovations. Try asking the same ‘why’ question of the line and it will just look back at you blankly.

We can also go further than this, since when you look at the tree you even get a sense that there’s a frontier of change at which the most energetic combinations are happening. We see this more clearly if we imagine laying the tree on its side, and if we picture the tips of the branches as the frontier of technological change. We can then go further and imagine the tree being animated, and the image becomes even more powerful. We see an ever-quickening and intricate frenzy of branches at the frontier of change, which just feels so right — and certainly more right than the image of a line just shooting upwards. The whole thing comes to life.

So, the tree is more formally appropriate and, as a result, it has more explanatory power.[2]

Third, I think it’s healthy to ask if a visual representation gives us something to work with. And, again, I think the tree outperforms the line on this front.

We might say that the tree is generative, in that it generates fresh insights into the exponential age. Alternatively, we might say that the tree is functional, in the sense that we can work with it in the way a potter works with clay.

To give an example of what I mean by this, here’s a link to an earlier post in which I took the metaphor of the tree and extended it to explore the role of technological path dependency and even the role of power, bias, and economic incentives. What I proposed was a modified version of the tree: I suggested that maybe the exponential age isn’t just a tree, maybe it’s a skewed tree that is growing towards an off-centre light.

The idea was that the light represents the role of bias and economic incentives in encouraging the tree of technology to grow in a particular direction. When we visualise the body of technology in this way, we see that it grows not straight up toward human progress in an uncomplicated or inevitable fashion, but that it grows in a skewed shape that is determined by the incentives and power relations that happen to stem from our institutional settlement at the time. This insight then points us to fresh avenues of enquiry with respect to policy and institutions.

I’m not saying I’m necessarily right to extend the tree metaphor in this way. I’m just saying that the tree gave me something to work with — a tool with which to explore life and politics in an exponential age.

Why it matters

So those are the three reasons I prefer a tree to a line. The tree captures one of the exponential age’s most salient qualities: complexity. It has the right form — a fractal — which means it helps us see not just what is happening, but why. And it gives us something to work with, so we can build fresh understanding.

As I’ve worked through these reasons, I hope it’s also become clear why I think this matters. The basic reason is that pictures can shape our thinking in ways that are helpful or unhelpful, and this has real world implications.

One of the best sustained versions of this argument is made by Kate Raworth in her book Doughnut Economics. Raworth shows how a simple visual representation like a chart can have a profound impact on the way we see the world, and therefore on the world itself. A diagram can turn a complicated and non-intuitive theory into a way of seeing and interpreting reality. And the way we see the world then goes on to shape the choices we make as societies.

In Doughnut Economics, Raworth focuses on the foundational charts of classical economics which came to prominence in the mid-to-late 20th century. She shows how these images, from the intersecting lines of supply and demand to the idea that the economy can be represented as a closed system of flows, omit or downplay certain critical ideas like climate constraints or behavioural biases. Rawson then traces the influence of these pictures, showing that it’s not a coincidence that our societies went on to formulate policies that also underplayed these important ideas.

So the way we visualise the exponential age will shape how we understand it, which will shape our response, which in turn will shape how the exponential age plays out. And while I’m not sure if the exponential line chart is quite as problematic as those foundational charts of orthodox economics, it does fail some important tests. And so, whether we prefer the tree or not, it’s at least worth having a look for something better.

If you’re interested in how we govern the exponential age, you can buy my book End State (or Azeem Azhar’s book Exponential.) To read along with this blog, you can follow me on Medium here or support the project for £3 a month (and get a free book) on Substack here.

This is the eighth post in a year-long series exploring how we govern the future. Here’s my last substantive post, on political optimism.

Footnotes

1. Of course the tree represents the same information as the line, it just visualises it differently; in a sense, the exponential line is just a count of the points at the end of the tree’s branches. So the debate isn’t about whether the line is ‘untrue’ or ‘inaccurate’, the debate is over things like salience and explanatory power.
2. The other thing I like about the tree is that it visually represents the idea of dependencies. If a particular technology dies or is made redundant by a new discovery, it’s as if a branch of the tree has died, and its dependent technologies — the little sub branches — die too. This is another aspect of the formal appropriateness of the tree and another way in which it trumps the line. For more on this whole way of thinking about technology, read my post here or buy W. Brian Arthur’s book, The Nature of Technology.