Journey to the 1Oth Dimension!

To reiterate: I’m not making this up. I am only attempting to report to you, dear reader, what I have heard smart people say, and what I have read in scientific papers and heard at conferences, and to report it in a way that you and I might be able to get our heads around it all. My attempts will necessarily be futile and inaccurate, because I write in English.


When scientists talk about extra dimensions, they actively avoid the use of English, tied as it is to our everyday experience of space and time and reality. English is by its very nature misleading, imprecise. So they use the language of math, whose concepts and terms are easily generalized into any number of dimensions or spaces or inconceivable, unphysical situations.


Consider how mathematicians think about the difference between a circle and a sphere. To a mathematician, a sphere and a circle are essentially the same thing, a collection of all the points that lie equidistant from a single point. (Think about this for a moment: If you took a piece of paper, then marked a point on the piece of paper with a dot, then marked all those places on the paper that are exactly, say, 1 inch away from the dot, you’d have a circle. Same thing with a sphere, but you’d have to mark all the points in three dimensions.) Mathematicians call circles 1-spheres, as creating them requires only a one-dimensional line, properly curved. Mathematicians call actual spheres 2-spheres, as creating them requires a two-dimensional surface. To mathematicians, the distinction between a 1-sphere and a 2-sphere is insignificant. They prefer to study n-spheres, spheres that can have any number of dimensions you like. No matter that we cannot imagine what even a 3-sphere would look like, sitting as it would in four-dimensional space. No matter that we cannot describe its appearance in English, or Japanese or Latin. Mathematics describes it with precision, and mathematics is the only language that counts.


I learned this when I took a graduate-level mathematics course from Brian Greene, the Columbia University physicist who has done a very nice job popularizing string theory, the theory that requires our universe to be made of 10 dimensions. (Actually, recent developments in string theory suggest
that there may be yet another dimension, for a total of 11, and that this new extra dimension is invisible because it is “curled up” into an infinite number of tiny loops. But to avoid further brain pain, let’s stick with 10.) At the time I took the class, I was working toward a master’s degree in the philosophical foundations of physics. This course was by far the most difficult one I have ever taken. After Week 3, I understood very little of what was going on. Yet the dimension stuff, that was Week 2, I think. Anyway, the course was this year-long journey through the world of differential geometry, which, as far as I could tell, should have been named abstract geometry, concerned as it was with the properties of surfaces and spaces of things in n dimensions. (Remember, n here can be any whole number you wish—2, 5 or 12,497.) The culmination of this course, which paused only once for a quiet moment of repose somewhere around Week 8 when Professor Greene revealed to us that we had just derived the fundamental equation of general relativity (who knew?!), was an introduction to the basics of string theory.


Now, recently I’ve been busy with the day-to-day of magazine work. My string theory, if I could ever claim to have had any string theory, is a bit rusty. But when I dipped back in, I was lucky to find a Virgil to guide me through the various levels of theoretical-physics hell, someone informative and protective who understands both my fascination and my confusion with the whole enterprise. His name is Subdoh Patil (call him Sub), and he’s a graduate student studying string theory at Brown University. He invited me to what I understand to be the eighth circle of hell, full of the astrologers and the diviners, otherwise known as the Second Northeast String Cosmology Workshop. Here, in a lecture room at Columbia University, wise men spoke of the ways that string theory and cosmology—the study of the universe—may intersect. While I learned much from Sub’s break-time translations of what was going on, I was heartened to find that he himself occasionally
didn’t get it. The field is too broad, too rich for any one person to grasp it all.


And why wouldn’t it be? The reason we were at a workshop on string cosmology was that string theory carries with it great hope for both particle physics—the study of the very small—and cosmology. Both fields are beset with problems, “problems” here meaning deep chasms of ignorance in our understanding of the physical world. Both fields have been
challenged by recent discoveries we don’t understand. And both fields hope that string theory—which explicitly requires the existence of 10 dimensions for the math to work—will provide a way out of this mess.