by S. James Gates
Physicists have long sought to describe the universe in terms of equations. Now, James Gates explains how research on a class of geometric symbols known as adinkras could lead to fresh insights into the theory of supersymmetry — and perhaps even the very nature of reality.
Complex ideas, complex shapes Adinkras — geometric objects that encode mathematical relationships between supersymmetric particles — are named after symbols that represent wise sayings in West African culture. This adinkra is called “nea onnim no sua a, ohu,” which translates as “he who does not know can become knowledgeable through learning.”
In the land of theoretical physics, equations have always been king. Indeed, it would probably be fair to caricature theoretical physicists as members of a company called “Equations-R-Us”, since we tend to view new equations as markers of progress.
The modern era of equation prediction began with Maxwell in 1861, continued through the development of Einstein’s equations of general relativity in 1916, and reached its first peak in the 1920s with the Schrödinger and Dirac equations. Then a second, postwar surge saw the development of equations describing the strong force and the electroweak force, culminating in the creation of the Standard Model of particle physics in about 1973. The equations trend continues today, with the ongoing struggle to create comprehensive equations to describe superstring theory. This effort — which aims to incorporate the force of gravity into physical models in a way that the Standard Model does not — marks the extant boundary of a long tradition.
Yet equations are not the only story. To an extent, geometrical representations of physical theories have also been useful when correctly applied. The most famous incorrect geometrical representation in physics is probably Johannes Kepler’s model of planetary orbits; initially, Kepler believed the orbits could be described by five regular polygons successively embedded within each other, but he abandoned this proposition when more accurate data became available.
A less well known but much more successful example of geometry applied to physics is Murray Gell-Mann’s “eightfold way”, which is a means of organizing subatomic particles. This organization has an underlying explanation using triangles with quarks located at the vertices.
For the past five years, I and a group of my colleagues (including Charles Doran, Michael Faux, Tristan Hubsch, Kevin Iga, Greg Landweber and others) have been following the geometric-physics path pioneered by Kepler and Gell-Mann. The geometric objects that interest us are not triangles or octagons, but more complicated figures known as “adinkras”, a name Faux suggested.
The word “adinkra” is of West African etymology, and it originally referred to visual symbols created by the Akan people of Ghana and the Gyamen of Côte d’Ivoire to represent concepts or aphorisms. However, the mathematical adinkras we study are really only linked to those African symbols by name. Even so, it must be acknowledged that, like their forebears, mathematical adinkras also represent concepts that are difficult to express in words. Most intriguingly, they may even contain hints of something more profound — including the idea that our universe could be a computer simulation, as in the Matrix films.
by Shubha Bala, associate producer
My favorite dog-earred, page-stained book growing up was The Phantom Tollbooth. I must have read over 40 times about Milo’s quest through the Kingdom of Wisdom to reconcile the rulers of Dictionopolis, the lover of words, and Digitopolis, the lover of numbers. The conclusion of this book, and of John Allen Paulos’ recent post in The New York Times, is that both language and math should reign equally.
Paulos, a mathematician and professor, argues that while narratives and statistics play important roles, people approach them both with different mindsets:
"Despite the naturalness of these notions, however, there is a tension between stories and statistics, and one under-appreciated contrast between them is simply the mindset with which we approach them. In listening to stories we tend to suspend disbelief in order to be entertained, whereas in evaluating statistics we generally have an opposite inclination to suspend belief in order not to be beguiled."
He goes on to demonstrate this tension by citing examples of statistical errors that are completely natural in storytelling, like the conjunction fallacy.
Journalism, to me, seems to be the attempt to reconcile that tension by finding common space between the data and the narratives. Do you think there is an inherent difference in how we mentally approach statistics and stories? Or is it a tension which can be bridged?
Image above: The dodecahedron, from the children’s book “The Phantom Tollbooth,” has 12 faces each showing a different emotion. (illustration by Jules Feiffer)Comments