Coloring The Plane

Dr. Doug Riley, a professor at Birmingham Southern College, kicked off math week at Altamont.  His topic: the Hadwiger-Nelson Problem, which, according to Dr. Josh Barnard, “…is an open problem in graph theory about coloring the plane.” 

I know metaphors.  I know literary and cultural criticism.  I know some linguistics.  I know some history and enough philosophy to start a conversation in a humanities party of pretentious, detached academics or adjuncts posing as such. 

I also know what an open problem is.  I understand that it’s possible to theorize about the nature of graphs.  “Coloring the plane” sounds like the combinatorics equivalent of color-by-numbers.  But considered together, the statement vanquishes my cognitive abilities.  I fall into the fetal position . 

I love the idea of math, of this elegant discipline—a fluid language—that can explain physical and theoretical phenomena. I had to remind myself that I loved the subject as I labored through this fine lecture, whose contents streamed by, just eluding my grasp.  To be sure, I felt fortunate to hear it; Dr. Riley normally presents a modified version of it to his seniors.  So while I labored, adrift in the doldrums, to find terra firma, I was at least flattered!

Towards the end of the lecture, Dr. Riley discussed the history and evolution of the problem.  Open problems in mathematics are widely known among students of the discipline.  I love that I can google the expression and find a clearinghouse of what’s current.  If on a free evening I have some time… 

And then the bit that resonated.  Professor Riley explained that, over the years, mathematicians have used several approaches to solving this nearly 70 year old problem.  They've tried geometric, algebraic, and calculus-based approaches, and, while they've gotten close, none have unequivocally solved the problem.  But that's ok.  The collaboration, based on diverse approaches, is a beautiful thing.

Imagine entering a big intellectual, often theoretical, playground.  What problem do you want to tackle today? What adventure of the mind—at the moment happily impractical—entices you?  Remarkably, one might make her name in a field by noting patterns in problems, or suggesting emendations to the rules.  It’s given that solutions may be elusive for some time.  And that’s ok, too.  What matters is the attempt, the recognition of one’s predecessors, the trends, and the failures. 

This theoretical playground is our world, the games are global conflicts, and the stakes are very palpable.  Consider the problems that afflict us: resource management; hunger, gender equality, education, climate change, the U.S. and Russia butting heads over Syria, etc.  Now, consider how we approach them.  In university labs and the offices of think-tanks, in middle school classrooms and community centers, these problems are parsed, negotiated, and debated.  We Skype with people across the globe to hear their tactics, and we try them at home.  Google reveals staggeringly successful strategies from the far corners of the globe that were previously unavailable in a pre-networked world.  We read a profound white paper and change our approach completely.  We open up to what has been done and what is being done.  We assimilate that knowledge with our own.

The analogy resonates.  Just as the Hadwiger-Nelson Problem has been approached by different mathematical perspectives, vast and unresolved global problems must be approached with the same diversity.  Science reminds us that we are interconnected.  We exist as crucial cogs in titanic systems.  Each perspective may be completely unique from the next, but each is essential, nonetheless.  We have a mutual incentive to find solutions, to be part of solutions.  And, often we need a diversity of approaches, or some sum of several to find resolutions.   

Humanity is messy, fraught with ego and fickleness and ignorance.  In echo chambers, we make righteous, monochromatic proclamations.  But the echo chamber is an illusion, and our divisions our own handiwork.  They can be unmade.  Games are usually won by the team that displays rigor and creativity.  In a polychromatic world, we must relentlessly pursue every hue.  Who knows which plant in the wilderness will yield a cure?

It stands to reason that we could spin the globe, stop on any point, and proclaim: "We’re all meeting here, on Tuesday.  Leave your baggage at the door.  Bring only your ideas. We're going to get some things done." 

If we would just check our egos at the door.  And embrace some color.


Niko Tsivourakis
Director of Altamont's Global Initiative