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The Idea of Holonomy

  • 08 Oct 2015

President of the American Math Society to speak at UCC

Throughout the year of Bicentennial celebrations in honour of George Boole, scholars have gathered at University College Cork to reflect upon the Boolean Legacy. This coming Monday will see Professor Robert Bryant, President of the American Mathematical Society, give a public lecture at UCC on his specialty Holonomy and of course, George Boole. We’re delighted to bring you an interview with Robert Bryant, edited by Nicola  Stathers.

George Boole 200: What is Holonomy? Is Holonomy something that a general audience could readily understand?

Robert Bryant: Anyone who has ever parallel-parked a car or wheeled a loaded handcart about has experienced holonomy directly.  Holonomy is a feature of many mechanical systems in which constraints on motion do not prevent one being able to maneuver from one position into another.  For example, a car (normally) cannot get into a parking place on the street merely by sliding sideways into the spot, and, yet, an experienced driver can create sideways motion by combining going backwards and forwards with turning the wheels.  A robot hand can correctly reorient a convex object by carefully rolling it (without slipping or twisting) into both the right place and right orientation simultaneously.  What is not obvious, is that this general concept appears in many other physical features in the world, from navigation on the surface of the earth via inertial guidance systems to the curvature of space-time in general relativity to the geometry of string theory in theoretical high-energy physics.  My talk is intended to try to help people without any special training at least see the beginnings of this road and hear a little about the exciting places these ideas are taking us.

George Boole 200: As a mathematician yourself, when do you first recall learning about George Boole?

Robert Bryant: I believe I first heard about George Boole, when I was in the seventh grade (about age 13).  I was just beginning to learn about binary arithmetic and logic circuits, so, of course, Boole’s ideas were fundamental to that.

GeorgeBoole: Explain Boolean Logic in 1 sentence

Robert Bryant: Boolean logic is an ingenious way of expressing enormously complex chains of reasoning as a combination of very many simple steps, for which the outcome of each tiny step is either ‘true’ or ‘false; without it, modern computers would be impossible.

George Boole 200: What’s your favourite math joke?

Robert Bryant: Two men are in a hot-air balloon.  Soon, they find themselves lost in a canyon somewhere.  One of the men says, "I've got an idea.  We can call for help in this canyon and the echo will carry our voices to the end of the canyon.  Someone's bound to hear us by then!"

        So he leans over the basket and screams out, "Helllloooooo! Whereare we?"  (They hear the echo several times).

        Fifteen minutes later, they hear this echoing voice:"Helllloooooo! You're lost!"

        The shouter comments, "That must have been a mathematician."

        Puzzled, his friend asks, "Why do you say that?"

        "For three reasons.  First, he took a long time to answer, second, he was absolutely correct, and, third, his answer was absolutely useless.” 

George Boole 200: How would you describe the boundary between computer science and theoretical mathematics?

Robert Bryant: It’s hard to say because it’s ill-defined.  Many beautiful things in mathematics have found their most felicitous home in computer science, and many seemingly mundane problems in computer science have led to deep theoretical developments in mathematics.  The idea that there is some fundamental difference between being able to compute and being able to understand is itself a very suspect notion.  Speaking as one who holds a joint appointment in mathematics and computer science in my university and whose work has relied heavily on computation, I’m inclined to say that it’s more a matter of social connections than it is a matter of fundamental differences.

George Boole 200: How do you view the role of commemorations like ours, the George Boole  Bicentennial, which examine the history of math and science for a public audience?

Robert Bryant: I think it is very important to understand the birth and growth of ideas.  It stimulates an appreciation for how our concepts change over time and for how interrelated so many things are, even when they don’t appear to be at first glance.  Many lay people think that scientists and mathematicians live mentally in a very abstract world and feel that they are forever cut off from appreciating, experiencing, or contributing to it, but a celebration of how fundamental ideas take root and how imagination can take simple ideas and develop them into techniques that reshape our world is both inspiring and welcoming (not to mention humbling to those of us who are in danger of being more impressed by our knowledge than by the fruits of imagination).

George Boole 200: How can technical literacy become more widespread?

Robert Bryant: This is a very difficult problem, but there are many people attempting to address it.  I think that the main thing is to make available to everyone experiences with fundamental technical and scientific ideas that are both fun and intriguing, so that all of us can experience the pleasure that comes with understanding.  I believe that people who are convinced that there is something interesting about a phenomenon will put in enormous time and energy to understand it, and that kind of dedication has to come from within, sparked by a desire to know.


Robert Leamon Bryant (born August 30, 1953) is Phillip Griffiths Professor of Mathematics at Duke University and formerly Professor at UC Berkeley and Rice University. He specializes in using geometric ideas to study differential equations. He was chairman of the Mathematical Sciences Research Institute at Berkeley, 2007 to 2013. Although a pure mathematician, his research has been influential in string theory and in the theory of control of electrical and mechanical systems. In 2007 he became a member of the National Academy of Sciences and in 2013 he became a fellow of the American Mathematical Society. In 2015, he began his two-year term as president of the American Mathematical Society. He has mentored 19 Ph.D. students.

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