shape of inner space

Professor Shing-Tung Yau gave a lecture last night at the Smithsonian (Carmichael Auditorium of Museum of American History), based on his book, The Shape Of Inner Space. He basically described the trajectory of his career over the past 40 years or so, along the way describing “Calabi-Yau” space and how it relates to String theory and maybe even the real world.

The basic tenet of String Theory is that all particles, at their most basic level, are made of vibrating bits of tiny strings. Yes, strings. The way they vibrate basically dictates which particles they manifest as. I won’t even pretend to know the math involved. One non-intuitive (to me as a non-mathematician, anyway) upshot of the string theory math is that it requires (reveals?) a total of 10 dimensions – 6 more than the 4 with which we are most familiar (3 dimensions of space plus time). Turns out according to theory that the extra 6 dimensions are hidden away in Calabi-Yau Space. This invisible space exists at every point in “real” space.

At this point, Prof. Yau asked, “Who cares?”. Well, it turns out the exact shape/geometry of this “Calabi-Yau Space” dictates the properties of our universe and the kind of physics we see.

The lecture was sold out…

Keep reading to see how Yau’s discussion of Mirror Symmetry (spaces) can be related to eating at a British-themed pub…

After the lecture I managed to take some pictures of Washington, D.C. in the evening light. I had a half-mile hike back to the Metro anyway, as I used the Archives stop on the Green line. This involved no train changes, and the weather was just perfect for a walk downtown. It’s actually very relaxed in the evening, as most people have gone home for the day. The downside is that it can be a bit hard to find someplace to eat around the Smithsonian in the late evening. I asked a security guard who happened to be taking a break, and he pointed me to the Elephant and Castle Pub on Pennsylvania Ave. Ok, his exact words were more like, “not much open right now except super-fancy places- just that sports bar over there…”. That was not really what I was looking for, but I was going that way anyway and I had missed dinner, so I stopped in. Glad I did! Got a nice table outside (did I mention perfect weather) and had some Fish and Chips and a London Porter. Yum! Not too pricey, and the fish was delicious – just lightly breaded/ fried crispy and golden. The porter was delicious too- chocolately and coffee undertones.

Mirror Universe? I was quite intrigued by something the waitress said when she brought me my fish and chips (she was a different person than the waiter who took my order): “Hey, that’s funny, I thought I must be seeing things – there’s a guy inside who is also having a Porter, fish and chips, and using an iPad”. Neat!

I wonder if he is in a Mirror Geometry (Mirror Symmetry)? Turns out you can have two Calabi-Yau spaces with different topologies (shapes) but the same resulting set of physical properties (simplistic: i.e. same universe). I wonder what shape the other guy was? :)

Mirror-symmetry is powerful: if you have a hard time solving a problem (typically in string-theory) with one of the spaces, just use its mirror space! This has been successful in many cases, sometimes allowing problems to be solved that have eluded mathematicians for over a century…

From the lecture description at Smithsonian Resident Associates page:

Do we live in a 10-dimensional universe? String theorists believe we do, even though we can sense only four dimensions.

Geometer Shing-Tung Yau has mathematically proven the existence of the elaborate, twisted six-dimensional shapes at the center of string theory. If that theory is correct, these “Calabi-Yau manifolds” (pictured here) may dictate the forces and particles of nature.

Yau tells the story of how physics met geometry and the new picture of the universe that has emerged as a result. He concludes by describing the ongoing exploration of Calabi-Yau spaces and the quest to uncover the shape of this small, hidden domain that may govern almost everything in our universe.