The Box and The Leaf

Our world is increasingly complex- it morphs and rearranges itself faster than we can manage it through rigorous analysis. In situations that change faster than we can possibly understand them, analysis generally just makes things worse. In these situations the tools of problem solving make a fundamental shift to be unorthodox, intuitive and incredibly effective.

Ever notice how little nature cares for Euclidian geometry? Right angles are rare, an honest to goodness square is much harder to come by, and cubes are unheard of outside of crystals. Contrast this with our utter obsession with cubes across the industrialized world. We wake up in cubes to drive in cubes to larger cubes where we get in a cube that moves up a tube to our personal cube so we can type on little cubes about moving cardboard cubes around the planet. Cubes are fantastic to arrange things with: built from 6 flat panels, stackable and soothingly uniform. But nothing smarter than salt has ever arranged itself into a cube.

Boxes are abysmal for the same reason that they are so convenient: they form very simple relationships with the outside world. They can sit next to things, on top of them or in larger boxes, but that’s about it. They can be easily pushed around, but they’re not particularly well suited to engage with anything that’s not another box unless they’re containing it.

Nature prefers a different sort of geometry: that of the fractal. Only recently unveiled by mathematics (Mandelbrot is still alive and teaching math at Yale), fractals are geometric arrangements of infinite complexity that resemble themselves across scale. Think of the way that a trail of raindrops resembles a stream which resembles a river, or the way that a tree resembles a branch which resembles the lines of a leaf. All of that complexity makes fractals messy to organize but fantastic to organize yourself into. They’re fantastic for connecting with things that are different than you are and always changing- like sunlight or the complex system of nutrients and moisture in the soil.

The box and the leaf are icons for two fundamentally different types of systems: those arranged by us, and those which arrange themselves. They are also two fundamentally different lenses for looking at the world. We can see the world as made up of boxes: distinct units which neatly stack together to form a larger whole.  We can also see it as made up of leaves: dynamic, self-organizing fractals which constantly morph in response to changes in their environment.

Since the enlightenment, our intellectual heritage has skewed heavily towards the former. From physics to biology to economics, the general idea is to break a problem down into parts, put the parts into appropriate intellectual boxes, and then work on understanding the boxes. Once all the boxes have been solved some numbskull engineer (or worse yet MBA) will be able to easily stack them back in place.

This theory works remarkably well when the boxes behave like boxes: that is when the relationships between them are simple. A Fedex plane which ships boxes around the world has thousands of highly analyzed, precisely engineered parts that all have very simple relationships with one another. Contrast the plane with a system that has far fewer parts: a 15 student classroom studying plant biology. The classroom not only has more complicated parts, those parts have far more complicated relationships with one another. As students and the teacher connect over time they perform better while the airplane only degrades. While the plane is uncertain in ways easily tamed by a bell curve, the classroom is genuinely unpredictable. It can yield not only learning but new discoveries, punk bands, romantic relationships and scientific careers.

We can try to design classrooms the way that we design airplanes, but we might as well try assembling a leaf. Studies can been done on the muscle tension caused by different ways of holding a pencil and on the precise impacts of diverse test-taking measures, but it’s just as important to understand the way that these components relate to one another and to the environment around them. Cut off a leaf to put it in a box and it will quickly die. It’s not just that the whole is more than the sum of its parts. Without the whole, the parts quickly become meaningless.

How intellectually daunting is that? We need to understand EVERYTHING in order to understand anything? Any scientist would throw their hands up in frustration at such a prospect, which may be a sign that science, with its historic focus on reduction and analysis, is not the most appropriate tool here. When it comes to emergent complex systems, the kinds with leaves in them, parts don’t matter. Relationships do.

Relationships are the dynamic, immeasurable, lines which connect one thing to another, and they are key to exploring systems with leaves in them. Try to understand the leaf as a unit and you’ll be lost- it’s infinitely complex, it dies off the branch and every other leaf out there is unique. Instead try to understand what the leaf is FOR. The leaf has a story, one that’s about connecting water and nutrients in the soil with energy from the sun. Get that story and you’ve not only developed a basic understanding for how the leaf grows, designs itself and dies, you’ve got a basic plotline for the tree, the ecosystem it lives in and all life on earth. Not bad for a little shift in perspective.

If the key to understanding boxes is reducing them to their component parts, the key to understanding leaves is using narratives to explore their defining relationships. Narrative is something of a dirty word in disciplines which seek authority through statistics and hard experimentation, but there’s no denying its power. Stories communicate complexity and meaning like nothing else, especially about the way that complex relationships interact. In complex environments like classrooms, emerging sectors of the economy and social movements stories are often more useful, more inspirational and more descriptive than studies.

Unfortunately stories are messy. We have good scientific systems to decide when one structural analysis is better than another, but no objective standards for good narratives. What would they look like? In a world where a billion stories can describe any one event, how do we decide which story to pay attention to?



Filed under Uncategorized

3 responses to “The Box and The Leaf

  1. Excellent post. I love the way you used the box and leaf analogy to emphasize the importance of narratives in our studies as well as life. Our individual paradigms make it near impossible to come to any objective analysis of relationships, but isn’t that falling back to the box analogy again? Do we really need to stuff everything into a neat little box? Or can’t we just enjoy the journey- learn and grow as we go?

  2. Pingback: De-Nerding the Integration Emergence, Fractals, and Uncertainty « Schooled Green

  3. Jay Ogilvy


    Great post! Clear, evocative, and beautifully expressed! I will borrow with attribution (not steal) the iconic images of the box and the tree.

    I recall sharing a podium with Mandelbrot way back in 1982. We had both been asked to speak at the Aspen design conference whose theme that year was, “The ultimate design challenge: The Future.” He had developed his ideas, and had a bunch of beautiful slides, on fractals; but he had not yet published his work. I very distinctly recall how we were all so amazed by what he showed us. We knew it was really important stuff. But at the time, 1982, before anything on complexity or emergence had yet come out of the Santa Fe Institute or anywhere else, we really had no idea of just how his ideas might apply or prove important.

    I also like what you say about narrative. Check out the following book that I just finished a few weeks ago: Brian Boyd, The Origins of Story. Big book. Important message. Boyd is the author of an amazing two volume work on the life and work of Vladimir Nabokov. Anyone who can master and shed light on the amazingly erudite Nabokov deserves our great respect.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s