 When I was about six years old, my father rocked my world by drawing a series of concentric circles in the sand. And at their center, he placed the sun. This picture of our solar system fascinated me because it had never occurred to me that the Earth is not the center of everything, and therefore neither am I. Back then, we didn't know of a single planet outside of our solar system. But in the last few years, we have discovered so many that we now estimate that there are probably billions, perhaps hundreds of billions of planets in our galaxy alone. Our Milky Way may be teeming with life. The idea that we are not special is known today as the Copernican principle. And it's the basis of modern science. It's the basis of the scientific method and things like evolution. So we may not be special in our galaxy, but you might ask, what are we special on a larger scale, on the scale of the universe? Well, what you're looking at here is the largest computer simulation of a universe ever done. It's just been finished by the day's collaboration. What you see is roughly 200 billion galaxies. It may look like a carpet. It's actually what we think the universe looks like. And the key point about this, if you stare at it, is that there is no center. That is what the Copernican principle typically means in cosmology. And we can zoom in on two small regions and ask, how are they different? Well, what you can see when you zoom in is this beautiful intricate filamentary structure of gas, millions of galaxies, and dark matter. But they're essentially identical. And that's the essence of the Copernican principle. But 14 years ago, things got interesting. Two teams of astronomers were studying supernovae. These are exploding stars. And they made an astounding discovery, namely that the stars that had exploded when the universe was younger were further away than we expected. Now, they interpreted this as meaning that not only is the universe expanding, as we've known for 80 years, but that the expansion is speeding up with time, as if someone is stepping on a cosmic accelerator pedal. Why this is hard to understand can be easily summarized in this graffiti. Gravity sucks. Gravity tries to pull things together, whether it's a Newton and an apple, planets, galaxies, or the whole universe. We expect the gravity to be slowing the expansion of the universe, not pushing it apart. Instead, what the teams had found was effectively an anti-gravity, which we now call dark energy. And if this picture is correct, only about 4% of the universe is made up of material that we can see, of energy that we can see. Everything that we know and love probably only forms 4% of the universe. The rest, like this keyboard, is dark and mysterious. We have no idea really what's going on. It's not surprising that this discovery was awarded the Nobel Prize in physics in 2011. But the story gets stranger still, because if dark energy is the explanation of the supernova data, then what is happening? The universe has been accelerating, but it's only been doing so for about 5 billion years, which is roughly the age of our Earth, a rather astounding coincidence, and one that is a profound problem. And the key point about it is that it suggests that we live at a very special time in the history of the universe. But that violates the Copernican principle that we are not special. So it didn't take long for cosmologists to realize that they could explain this a different way without dark energy and without living in a special time. By exploiting what Einstein gave us in his theory of relativity, we have the ability to warp space and stretch space. And so we could push the supernova further away but at a big cost. And that cost is that we would have to live in a universe with a center and we would have to live close to that center. Either way, if we live at a special time or a special place, the Copernican principle appears to be violated. Now, there may be some clever way to reconcile the observations, the supernova data, with the Copernican principle. And personally, I don't think we do live at this end of the universe. But frankly, it doesn't matter what I think. What matters is what the data says. The observations say, that is the scientific method. That is the key to science. And you and I are living at a special time because unlike Einstein or Copernicus, we live at a time whereby within 10 or 20 years, wonderful new telescopes like the square kilometer array will answer the question of whether we live at a special time or special place. And I think that will be one of the great advances of the 21st century because it will profoundly affect how we view ourselves and our place in the cosmos. And I think that would have made Copernicus rather happy if a little jealous. Thank you very much.