Somehow when physicists model stuff in space they keep coming back to one sweet shape: the donut.  Okay, a torus if we're being exact, but a donut is more fun.  They've predicted the possibility of donut shaped planets and universes and even said our universe could be a donut.  While these models are still hypothetical there are also real donut shaped tools that have helped humans navigate space.  But why the donut, of all the possible shapes?  Here's Reid to tell us how they've reached the donut conclusion.

It's kind of weird thinking about the universe having a shape; it's the universe, right?  It's universe shaped.  But it does have one.  We just aren't sure what that shape is.  And some cosmologists have proposed that of all things it might be shaped kind of like a donut.  When we're talking about the shape of the universe we're really talking about it's topology.  The topology of an object has nothing to do with how many sides it has, or where parts of it are relative to one another.  It only depends on the number of holes.  A sphere has none, a donut has one, and so on.  A sphere and a donut are both round, but they have different topologies because there's no way to take a sphere and stretch it or smash it to make it look like a donut without, shall we say, tearing it a new one.  On the other hand a lot of objects we think of as clearly being different shapes have exactly the same topology.  A coffee mug has one hole in the handle so ,topologically speaking, there's no difference between a mug and a donut.

There are a lot of proposed topologies that the universe could possibly have.  From plain shapes with no holes, to some that are much more complex.  But one of the most common ideas is what's called a 3-torus.  It's impossible for our puny human minds to visualize what that looks like from the outside because you'd need a fourth spacial dimension.  A line is one dimensional, a flat plane: two, and with the third dimension, you get depth.  Usually when we talk about the fourth dimension we mean time, but in this case it's a fourth spacial dimension.  The next level up from 3D.

And as beings who've lived our whole lives in 3D space, we can't really imagine what 4D would look like.  That doesn't mean you can't model a 3 torus, though.  You just have to step everything down a dimension.

You can take our universe with it's three spacial dimensions and model it as a two dimensional flat plane.  Think of it like a piece of paper, except pretend it stretches to infinity along both axes.  If you take that piece of paper and wrap it into a cylinder it stays infinite in one direction, but becomes finite in the other, because eventually you loop around the cylindar.  If you then wrap both ends of the cylinder together making it connect along both axes you have yourself a three dimensional version of a 3-torus.  There you go: donut universe.

Topology is different from geometry.  It doesn't care if or how space is curved, or about the distance or angles between different objects.  Geometry does.  It knows the difference between our mug and donut and we're actually pretty sure we know what the geometry of the universe is.  Measurements have shown it's almost definitely flat as opposed to positively or negatively curved.  Which, again, gets a little brain-breaky because flat is not normally an adjective we use to describe things in 3D.  

But cosmologists talk about 3D space as being flat or curved because it's the best analogy we have for what we're trying to describe which basically boils down to this.  If you shine two laser beams in parallel do they stay parallel, or do they eventually cross or diverge?  When we say the universe is flat, we mean that the beams stay parallel.  Space isn't warped in a way that would curve them toward or awy from each other.  The donut universe is actually a topology with a flat geometry.  Which our simplified 3D model can't, well, model.  But the idea is that instead of a simple plane that stretches to infinity in three dimensions, It connects at multiple points.  In other words, it's finite.

But it mimics an infinite universe because light wraps all the way around the shape, so you get the effect of standing in one of those infinity light boxes.  The 2D version of this is a classic video game.  Where if you move to one side of the screen, you pop out on the opposite side with the same speed and trajectory.  In 3D space, if the universe were incredibly small, and you look directly up, you see the bottom of your own feet.  Or if you look over your  own shoulder, you see yourself repeated in an infinitely long line.  But our universe isn't that small.  So how could we possibly tell if we're living in a 3-Torus?  

Basically, astronomers hunt for recurring patterns in astronomical images.  The same cosmological structures showing up in multiple parts of the sky.  That would mean light is wrapping around the universe and we could run models on those patterns to determine its topology.  Or at least we could, if the true size of the universe is smaller than the distance it takes  the light of everything to reach us.  Because, remember, light takes time to get to us.  there could be things out there so far away, that even though the light coming from them has been traveling almost since the beginning of time, it still hasn't reached us yet.  If there is stuff beyond where the earliest light we can see originated, the light wouldn't have the opportunity to wrap around and create any repeat images.  The universe could be a donut, and we'd never know. 

That said, results as recent as 2015, courtesy of the European Space Agency's now defunct Plank satellite, have failed  to find any evidence of a 3-Torus topology or any topology.  So as far as we can tell, the universe is not a donut.  But, what if it were?

Well, in day to day life, even in certain fields of astronomy, it wouldn't matter very much.  Just like there's a lot of physics we can still do with  old-school Newtonian equations, changing how we think about the universe's topology wouldn't require rewriting the rules of stellar life cycles or planetary formation.  But there is one bit of cosmology a donut universe definitely threatens: Inflation.

Cosmologists think the universe suddenly expanded in size when it was super duper young.  When we look at the light left over from the Big Bang, what's known as the cosmic microwave background, or CMB, we can see evidence of that inflation.  But there's nothing in the theory that would case inflation to produce a universe big enough to house all the galaxies, yet small enough to see itself repeated within the observable horizon.  So, knowing the universe was a donut would force astronomers to find a new explanation for why the CMB looks the way it does.  But one of the cooler consequences of a donut universe: somewhere out there, some of the oodles of galaxies would actually be the Milky Way itself, but we wouldn't be able to tell just by looking at them because they'd appear billions of years younger.  So, you could actually wave to yourself.  But you'd be very dead before you receive the message.  But hey, it's the thought that counts.

Reid mentioned that a coffee mug could be considered a donut.  And if you'd like to bring home the exact mug he used in that visual comparison, you can do that at dftba.com.  But if you'd rather keep your theoretical donuts in space, then just keep watching, because Caitlin is about to tell us why donut planets might exist.

Have you ever looked at a globe and thought, "What if it had a hole in the  middle?"  Me neither!  But some researchers have because it turns out that planets don't have to be shaped like spheres, or what the really are, which is more like stretched out spheres.  Under the right conditions, a planet could end up shaped like a donut.  Or what an astrophysicist might call a Toroid.  It's unlikely, but physics tell us that is possible.  And if such a world did form, life on a donut planet would definitely be weird.  And not just because you'd be walking around craving donuts all the time.  

Planets generally form from spinning discs of gas and dust that get clumped together by gravity.  And normally that clump just gets bigger and bigger until it becomes mostly spherical.  But based on computer simulations that physicists have put together, we know that if one of these clumps is spinning fast enough it can form a ring instead.  Now this ring wouldn't be very stable; if it got hit by an asteroid, for example, it would break up into a bunch of particles which would eventually reform into something more stable, and less delicious, like a globe.

And planets tend to stick around for a while, like, billions of years, so odds are that a toroidal planet, if it did exist, would get hit by at least an asteroid or two.  But it's a big universe out there!  Out of all the planets in the whole universe it's possible that some of them are shaped liked donuts.  Life on a toroidal planet would be different from what we're used to.  The most obvious differences would have to do with the sky. 

For one thing, if this planet had any moons, they might be orbiting in some pretty awesome ways because gravity from a donut shape would be a lot more complicated than froma  round little blob like Earth.  The poliverse(?~8:35) gravity is practically the same in every direction so our moon can orbit in a relatively simple, well balanced elipse.  A ring shaped planet might have a moon like that too, with a circular elliptical orbit around the outside of the ring, but gravity from the donut would also be trying to pull the moon through the hole which means there are plenty of other options.  One possibility is that its moons could have a figure 8 shaped orbit where the moon would loop around one side of the toroid, through the hole in the middle, around the other side, and back through again.  But it could also just move up and down exactly in the middle of the hole in the ring like some kind of perfectly balanced ping pong ball, which would be pretty cool to see. 

Depending on where you were on the planet's surface, though, the sky might feature more than just the sun, moon, and stars.  If you were on the inside of your donut world, you'd also see the planet itself; the part of the ring opposite you.  So if you wanted to watch a soccer game on the other side of the world there's no need for TV or the internet.  Just sit back with some beer and a telescope. 

The life on a donut planet wouldn't be all gorgeous skylines and free sports.  The ring would also affect things as fundamental as your exposure to daylight, and your weather.  Though exactly how it would change those things would depend on the planet's size, shape, and tilt.  For example, the ring would block sunlight, so any time you were in the shadow of the other half of the planet, it would be dark.  Which means that if the planet weren't tilted at all, then the inside half of the ring would just be all dark, freezing winter, all the time.  the seasons could get slightly more earth-like if the ring was tilted, though, in certain seasons there would be places that experienced what we call midnight sun and polar night here on Earth.  But of course, we still don't know if donut planets actually exist, and even if they do, odds are we won't be able to spot one anytime soon.  But assuming you find a spot with decent weather, and a view of the other side of the ring, a donut planet seems like it would be a pretty nice place to retire.

It's pretty mind blowing to imagine things like the moon going through a donut planet.  But it probably shouldn't be so outrageous to think about because sending through donuts was what brought us to the moon in the first place.  Hank is going to tell the story of how little old ladies knitted us to the moon. 

Back in the 1960s and 70s, the Apollo missions blasted their way from Earth to the moon.  And they carried two of the smallest, most sophisticated guidance computers ever invented, which were running on software knitted by little old ladies.  I'm not kidding, the software running on Apollo's guidance computers was literally woven by hand out of wires and magnetic rings that looked like tiny donuts.  It was called core rope memory. 

The Apollo missions were a huge hurtle for both navigation and portable computing.  The orbital mechanics were complicated and they needed guidance, especially while they were on the far side of the moon, unable to communicate with Earth.  Navigating there and back was a serious problem, and NASA needed computers to solve it.  A team at MIT invented the navigation software to run on these computers.  Programmers wrote it from scratch, and tested it on huge mainframe computers using paper punch cards to input programs.  Running any given program could take an entire night.  And of course the software had to be bug free because once the programs were loaded onto the hardware of Apollo computers, they couldn't be changed, so they had to be perfect. 

Why couldn't they be changed?  Because the program was hardware, essentially.  There were a few different forms of storage that existed in the 1960s that could hold a computer program.  One involved paper punch cards with holes in them read in a giant reader.  There were also disc drives that were so big they had to be pushed on wheeled steel carts and magnetic steel tape on reels.  But these options were all way too heavy to fly into space, or in engineer speak, they weren't flight-weight.  Even if they were light enough to fly they'd still need to be able to withstand the shock, vibration and g-forces of launch, temperature changes, and cosmic radiation.  And if they couldn't withstand all that, the astronauts could die, so memory storage had to be small, lightweight, safe, strong and robust enough that even if you lost power, you didn't lose the program.  

The only technology at the time that met these specs was core rope memory, which coded ones and zeros, the fundamental language of programming, into wires and magnets.  It was woven on a type of loom by threading individual wires through various holes with large needs, kind of like knitting needles.  Engineers at the time called it LOL memory, a not very nice acronym for "Little Old Lady" memory because it took highly skilled garment workers, often older women, to weave it. 

To represent a 1, a seamstress wove a wire through a little magnetic donut, called a core.  The donut acted like a transformer, a device that changes the voltage of an electrical current running through it.  If the computer saw a voltage change at the other end of the wire, it assigned it the number one.  To get a 0, they'd weave the wire outside of the core; electrical current through it wouldn't change.  The computer would interpret that lack of voltage change as a zero.  They'd weave the entire program out of wires going through or around cores. 

There were lots of wires and donuts which meant that core rope memory was incredibly hard to manufacture.  It came out looking a lot like rope, but it was really a program made out of woven electrical pathways.  It also provided the most storage per cubic centimeter at the time.  The Apollo guidance computer came with a whopping 36KB of memory.  This tiny microSD card has almost a million times that.  But core rope memory is read only memory.  You can't write to it which is really good if you don't want to accidentally record the 1960s equivalent of a podcast over what would be steering you to the moon. 

But it also meant the programs had to be perfect the first time around.  When each core rope was finished, the program was run and compared with the program stored on magnetic tape from MIT, they actually had a defense contractor build a machine to do this automatically.  If they found a mistake, the program could be rewired before it left the factory, though fixing it was an enormous pain.  So there's a lot more to knitting than scarf patterns.  It can also take you to the moon and back.

So, none of these space donuts are the sugary treats we know and love, but if you want real space sugar, you can check out our video all about the sweet stuff hiding in space rocks.