What is the Shape of the Universe?

The other night while waiting to visit Slumberland, I lay in my bed thinking about Einstein. Long ago before people knew the Earth was round, people imagined our world to be a vast plane. Some people imagined the plane to be infinite in all directions and others speculated finding the edge and falling off. Then along came some smart Greek dudes, no, not Geeks, but Greeks, but maybe Geek Greeks, who suggested that maybe Earth was round. If this was true they theorized one test of their theory’s validity would be to start walking in one direction and eventually you’ll end up back where you started. Imagine how mind-blowing that bizarre concept was to fathom back then. We know it’s true, but then we know the ending of the story.

Now I’m reading Einstein and I’m trying to imagine the shape of the universe. Like our ancestors who felt that Earth was one vast plane, we feel the universe is one infinite three-dimensional space and Einstein, like the smart Greeks of long ago, is suggesting something different. And guess what, the same test would apply. You head out in one direction and eventually you’ll get back to where you started. Boy is that hard to imagine.

I’ve always loved astronomy and all my life astronomers have talked about how big or how old the universe is and they argue whether it’s 12 billion light years or 14 billion light years. And it’s never 7 billion in that direction, and 14 billion in that direction and 2 billion in that direction. No, they always talk about the size of the universe as if we’re smack in the middle of it. My mental picture of the universe is a giant cube of black Lucite embedded with grains of galaxies that occasionally make swirls of clusters. But that begs to ask what’s outside of the universe.

According to Einstein and others there is nothing outside of the universe. No space-time, no empty space, not even non-existence – the only thing that exists is our universe. How can that be? It hurts to think of such a universe. To grasp that we have to ask: what is the shape of the universe? This has gotten me to read The Poincare Conjecture by Donal O’Shea which is the history of developing a geometry that answers that question. I’m slowly working my way through the book and O’Shea is carefully building the background that I hope will give me a slight cognitive glimpse. It is beyond any fantasy I might have to think I’ll actually understand it.

While thinking and reading about all of this I got the idea if the universe is finite in one direction, what about the other direction, the world of small. This reminded me of that classic film The Powers of Ten and wondered how many magnitudes of distance up is compared to down. It turns out its roughly 10²⁶ expanding out and 10^-18 shrinking down until we reach the current barrier of perception. So in this case we’re not in the middle of things unless we haven’t gone all the way down as small as possible. Wouldn’t it be weird if we were always in the middle of everything? If on the cosmological scale the universe can’t be infinite, then it would also seem on the microscopic scale we’d reach a finite end to the world of tiny.

This doesn’t make mental sense does it? It’s like the Greek who argued that the universe was infinite because no matter where the edge was if he stood there and stuck his arm out wouldn’t there be more of something? Or if we found the smallest particle our minds just beg to break it in two. It’s like the old story of kids asking about what made God, and then asking who made whatever made God. It’s damn strange, but we just can’t comprehend a finite world.

Doesn’t the universe feel smaller already when you think its size is just twenty-five magnitudes greater than our own little space in the world? There have been a number of people who have made Powers of Ten films, books and websites. There’s an excellent IMAX film you can rent from Netflix called Cosmic Voyage that gives a fancier version of Powers of Ten with a lot of fantastic computer animation. The link takes you to a web version, but it’s worthwhile to get the DVD – it’s quite beautiful.

Also visit Quarks to Quasars for another conceptual approach to this subject and be sure and look at the index page, which is a quick one page summation. This Powers of Ten has a great little ruler menu. Click on 10⁸ and 10^-8 shows the Earth from space and DNA. I wonder if that means we’re the size of DNA if seen from a high orbit.

The fun thing about playing with the powers of ten is to try and conceptualize our place in the universe. Essentially these films, web sites and books try to create a very simplified map of reality. It’s wonderful to meditate on each power of the scale. A big chunk of the scale from 10^-12 to 10¹² is from the realm of the atom to the Sun, both objects we have intimate relationships with, so we should try to comprehend them. While we send rockets up to explore the higher positive powers ten we work with nanotechnology to capitalize on the negative powers of ten.

At 10⁰ we’re at the one meter vantage. That’s roughly the world of personal contact with other people. I like to think the starting point is the point of consciousness that reside behind my eyes. Within that one meter world is the distance to my monitor. People and pets we love the most are the beings we let into this range of magnitude.

At 10¹ we’ve expanded our world out to ten meters, or roughly the size of a large room. This takes our conscious minds into the sphere of homes and offices and cars interiors. This is the magnitude of our social world. At 10² or 100 meters we reach the limits of very large social events like football stadiums, shopping malls, downtown areas, and where we lose our ability to distinguish other individuals.

It’s hard for our minds to grasp the area of 10³, or 1000 meters, which is 5/8^th of a mile. This is a whole neighborhood, a large farm, an area of woods, even a small town. It’s difficult to know all the people in an area this size but most people can maintain a fairly intimate social relation within this magnitude. It’s like living in a small town. For people who can’t comprehend maps or geography this is probably the limit of their conscious world.

Expanding out to 10⁴ brings us 10,000 meters or six miles, about the size of a large downtown city. There have been whole populations that never ventured out of a world this size. I’d guess in some populated cities they could squeeze in a million people at this scale. And the next jump to 10⁵ brings us to 100,000 meters or about sixty miles. This is a large city and its surrounding towns, but it isn’t so big that many people can’t commute to work such distances. At 10⁶ or a million meters we’re getting into the size of states and small countries.

The next two jumps 10⁷ and 10⁸ take us to 10 million and 100 million meters and we’re seeing a large segment of the Earth like an astronaut to zooming out to see the Earth as a marble in the sky as if seen by travelers heading to the moon. At 10⁹ we could see the orbit of the moon because we’re looking across 1 million kilometers of space. We’ve now reach the limits of manned exploration and we’re into the magnitudes of space age awareness.

All of world politics happen on the scale between 7 and 8 magnitudes and few people try to keep up with events at that level. Most people’s conscious world of events remains below magnitude 5. It is between magnitude 7 and 8 that we see that our world is a sphere and the end of human territory. Few people in the course of a day think about things outside of magnitude 7.

People at the Jet Propulsion Laboratory (JPL) think and work in magnitudes 10¹⁰ through 10¹³, which take us out to the edge of the solar system. Anyone willing to study astronomy can grasp a basic idea of this territory. It’s the territory of popular science, and even though objects within this scope are immense, like the Sun or Jupiter, they are within our ability to imagine.

At step 10¹⁶ we reach one light year and expanding out to 10¹⁷ we pass by our nearest neighbor star before we hit the 10 light year sphere. Astronomers and science fiction writers explore this territory often, but most of humanity never thinks this big. We have to expand out four magnitudes to 10²¹ to see our home galaxy. Very few science fiction stories have ever been written about traveling beyond our galaxy. We can still imagine that space is a huge three dimension void speckled with a bit of matter.

Few people can make mental maps of expanding out further than our galaxy. Imagine the three dimensional positions of galaxy clusters at 10²⁵ or a billion light years of volume is mind numbing even to think about. Making that last jump or two in magnitudes to see the whole universe as it really is, is a feat of imagination beyond all but a few humans. The idea that someone can imagine it, even mathematically, is beyond my abilities. How many magnitudes of mental power must Einstein have needed over us normal people to see what he saw?

It’s out in this territory where we’ll find the shape of the universe, where it continues to expand. It’s so hard not to think of the universe as an explosion of matter shooting out in all directions in infinite empty space. If I knew what I know now as a little kid starting school I sure would have studied harder, especially math.

Maybe they should start kids out by teaching them all the far out puzzling facts about the universe and then tell them if they want to understand the answers they better study math. They never really gave me an incentive to study math – hell I didn’t buy into that whole grade thing back then. What motivation is having the letter A marked in a box over the value of having the letter C? Damnation, why didn’t they warn me that one day I’d want to read The Poincare Conjecture and understanding mathematics was the key.

Jim