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 Krista Tippett, host
The science-religion “debate” is an abstraction, and a distraction. It isn’t true to the deep nature of science, or of religion, or to the history of interplay between them. These are convictions I’m left with after a cumulative conversation that began a decade ago. And after spending the spring traveling around the country talking about this in theaters packed with scientists and citizens, atheist to devout, I know that others share my sense that our sound-bite friendly, politically-fueled narrative of animosity has outlived its usefulness. There is a science-religion divide — these are two distinct and separate spheres of endeavor. But in the 21st century, we can’t help but hear echoes passing back and forth across that divide and changing the way we understand our humanity, our relationship to each other and the natural world, the contours of the cosmos.
It’s not just the passion and frequency with which mathematicians talk about beauty and physicists talk about mystery that intrigues me. It is also that every time the rest of us log on to our computers in the morning, or every time we eat a meal, we are steeped in the fruits of science. We may not be fluent in the language of science — mathematics — which Galileo called “the language in which the universe is written.” But in the most ordinary moments in our doctors’ offices, certainly in near-ordinary experiences like birth, illness, and death, we receive crash courses in science of many kinds. And we turn simultaneously, without time for debate, to inner territory of morality and meaning, which science has no language for addressing.
Einstein put it this way, helpfully: science is good at describing what is, but it does not describe what should be. That is one way to talk about the role that religious and spiritual practice, our sense of what is right and sacred, plays in human life. And for the record, I don’t believe that spiritual and moral life ceases in the absence of belief in God. Einstein didn’t believe in the personal God of traditional religion. But he did profess a “cosmic religious sense” driven by “inklings” and “wonderings” rather than answers and certainties. Its hallmarks were a reverence for beauty and a sense of wonder that, he acknowledged, he shared with lovers of art and religion.
And it’s worth remembering that, in Einstein’s day, zealous religion appeared less a threat to the future of humanity than science on the loose. He watched chemists and physicists become purveyors of weapons of unprecedented destructive power. He declared, chillingly, that science in his generation was like a razor blade in the hands of a three-year-old. Against this backdrop, he called his contemporary Gandhi — and other figures such as Jesus, Moses, St. Francis of Assisi, and Buddha — “spiritual geniuses.” Einstein soberly observed that these kinds of “geniuses in the art of living” are “more necessary to the sustenance of global human dignity, security and joy than the discovers of objective knowledge.”
It seems clearer and clearer to me that, in the 21st century, genius in the art of living must draw on the best insights of both science and religion, not as argued but as lived. Or, as the Anglican quantum physicist and theologian John Polkinghorne puts it, we come ever more vividly to see how science and religion are both necessary to interpret the “rich, varied and surprising way the world actually is.” I think that the surge of spiritual energy and curiosity of our time is precisely a response to the complexity we know by way of science and technology — not a flight from that, but a turn to sources of discernment to sort, prioritize, make sense.
I was especially intrigued by how the subject of climate change came up when I discussed Einstein’s God in a packed theater in Washington D.C. There the room included scientists from across government agencies — some of them personally religious, some of them not, but all open to engaging the moral aspects of human life that science touches but does not resolve. I heard from people who are working on frontiers of climate change research, including deliberation of how, in a worst-case scenario, we might intervene to change climate, change the weather. This is a cosmos-altering idea on the magnitude of those contemporaries of Einstein who split the atom. But they are deliberating now about the ethical ramifications of this burgeoning possibility, and they are aware of their need of all the resources humanity has to offer for thinking this through.
So what if, as a first step moving forward, we focused less on the competing answers of science and religion, and more on their kindred questions? The question of what it means to be human animates each of these vast fields of endeavor, though they approach and take it up in very different ways. If we just start seeing that, how much more cohesively might we be able to take in the best insights of science and religion, honoring more of the fullness of our humanity, living more gracefully and productively with all that we can know?
In the photo above, physicist Albert Einstein (left, standing behind girl) and theologian Paul Tillich (right, standing in front wearing glasses) at a conference in Davos, Switzerland on March 18, 1928. (Courtesy of Image Archive ETH-Bibliothek, Zurich)Comments
Shubha Bala, associate producer
For the past few interviews, we have been diligently tweeting away while Krista converses with our guests. We hope that this is a unique way for you to experience some of the highlights — and get the conversation started — before you experience the full edited (or unedited!) show.
After our interview with Mario Livio, we all sat down to discuss what constitutes a good tweet. So, this week, we ask you: seeing the entire tweeting transcript below, what tweets are helpful? Do links help? Is it too much to break information between tweets?
- For the next 90 minutes, we’ll be live-tweeting Krista’s ISDN interview with Mario Livio, a Romanian astrophysicist who grew up in Israel.
- Mario Livio’s latest book is “Is God a Mathematician?”
- Livio asks if mathematics discovered or is it an invention of the human mind. Picks up from Krista’s interview with two Vatican astronomers.
- "Mathematics turns out to be too powerful in describing all these things." -Mario Livio
- Mario Livio: Newton takes observations that aren’t so accurate, + his mathematical equations are more accurate than the observations!
- Livio: the theory of knots are very important application for string theory even though it was initially thought to have no application.
- Livio: The conclusion I reached about math being discovered or invented is that the question is being posed wrong. It’s a mixture.
- Ex. of mixture: imaginary numbers like square root of -1. We invent the concept and then we discover the relationships among these concepts.
- Ancient Greeks invented concept of prime numbers. And then the discoveries were forced upon us.
- Livio: Roger Penrose, mathematical physicist: three worlds and three mysteries - physical world, consciousness, mathematical forms.
- Penrose’s 3 mysteries: 1) out of the physical word, consciousness 2) consciousness gives access to math forms 3) math explains phys. world
- Livio: Chomsky will tell you that there is more universality to languages than we think.
- Livio “The Microsoft Effect”: once a particular OS starts to dominate, all have to adapt it. Mathematical notation is a little bit of that.
- Mario Livio: “Our perception system is universal. This had to help in inventing natural numbers like 1,2,3,4,5…”
- "Like beauty in the arts, it is somewhat more vaguely defined [in mathematics] …but perhaps it is a little bit more defined." -Mario Livio
- We try to formulate a few laws of physics + try to explain all phenomena. We do the same thing in mathematics - like in symmetry. -M. Livio
- "I have heard very few people think that Einstein’s general theory of relativity is not beautiful." -Mario Livio, astrophysicist
- Mario Livio: You could argue that the principal behind Einstein’s general relativity is simpler than Newton’s gravity.
- M. Livio: Symmetry is a quantity that does not change. Mathematicians came up with a system to describe ALL these symmetries. Group Theory.
- Funny moment where Krista starts to ask Livio about his love of art and Mario Livio responds, “You seem to be well prepared.”
- Mario Livio, in response to Krista’s question: “I don’t have a good explanation for my passion for art.”
- Livio: “…it would be false to say that science + art have influenced each other. Or that science + religion have influenced each other.”M. Livio: “A person who feels a need for God does not want a God that created the universe and then left the universe to its own devices.”
- M. Livio, picking up on that last point: “Science has nothing to say about this. … People try to force the connection.”
- M.Livio-ppl who try to say Genesis is completely accurate scientifically does science & religion a disservice
- M.Livio-Is God a Mathematician? “I mean God as an Einsteinian God-synonym to the working of the cosmos.”
- M.Livio-Physics has changed over time but “Mathematics has evolved, but the math the ancient greeks did is still true today.” Eternal truth?
- M.Livio-As physics became more predictive, people went away from religion to talk about nature - talked about precise sciences
- M.Livio-cont. a development of 20th century-with quantum physics, things are no longer deterministic, can only calculate probabilities
- M.Livio-“Biology today is..at the state physics was…..-many of the major breakthroughs are yet to be made”
- Krista tells a funny story of Goedel, accompanied by Einstein, applying for US citizenship - http://www.ias.edu/people/godel/institute
- M. Livio - About math and life… well “in science, unless you have a well defined problem it is virtually impossible to try to answer it”
- Livio-“Things like life these are inherently complex situations where..often I don’t..know what question to pose, let alone find the answer”
- Livio-April 24 is Hubble 20 year anniversary. He talks about the importance of Hubble images - http://hubblesite.org/gallery/album/
- Krista and M. Livio recall SOF interview about human & mathematical limits with Janna Levin - http://bit.ly/axpPBy
- M.Livio-pushing boundaries-we used to think the earth was the center of a universe, and now “200 galaxies like ours just in the observable”
- M.Livio - but each discovery we make, we find out there’s something “even more mysterious”
- M.Livio-In all this, our physical selves seem more&more minuscule, but our minds making the discoveries are more&more important & central
- Thank you Mario Livio! For more information on him and his book : http://www.mariolivio.com/