The answers from benihana and cromulent are correct, but the following may possibly be a useful thought experiment.
Imagine a balloon (our universe) with lots of ants crawling on it (photons moving at the speed of light). The ants can't walk any faster than 2mm/s. They can't take a message from any part of the balloon to any other faster than that. (And, let's suppose, there's nothing living on the balloon that moves faster than an ant.)
Now someone blows up the balloon; it gets much bigger. Its expansion moves the ants apart much faster than 2mm/s. But it's still true that if you have two points 10mm apart, no ant can get from one to the other in less than 5s.
Suppose the balloon starts off rather small, and then is blown up very rapidly: perhaps it grows abruptly from 100mm across to 1000mm across in less than a second. (The corresponding phenomenon for the universe is called "inflation"; it explains many otherwise puzzling things but no one knows for sure whether it really happened.) Then it may happen that the only ants that have been able to reach one particular place on the balloon (our observatories) have come from a smallish fraction of the balloon (the observable universe).
This is what I cant wrap my head around... into what is the universe expanding?
What if the universe is not a balloon - but a doghnut where the outer edges fold back into itself, the overall space it is in can be finite yet the surface is curved away. The light would travel along the curved surface of space-time and thus travel a greater distance than is linear.
It's not expanding into anything (so far as we know), just expanding. A curved spacetime doesn't need to be, and so far as we know isn't, embedded inside a higher-dimensional not-curved thing in the way that a balloon is embedded in (more or less) flat three-dimensional space. (That sort of embedded picture is useful for the intuition, though.)
So, you might be asking, whatever does it mean to say that space, or spacetime, is curved? It means, e.g., that if you measure the radius and circumference of a small circle very very very accurately, the relationship isn't C = 2 pi r. If the circumference is "too small" then space is positively curved there, like a balloon. If it's "too large" then space is negatively curved there, like a saddle. The curvature might actually be different depending on the orientation of the circle, but if space is the kind of thing we think it is then you basically only need six numbers to tell the whole story at each point of space. (In two dimensions -- the surface of that balloon -- there's only one possible orientation for the circle, so you only need one number to describe the curvature at each point.) Note that you can measure this thing without needing to go "outside" space: the radius and circumference are measured within the space. Distances along the surface of the balloon.
Yup, the universe could be curved and topologically nontrivial in all kinds of interesting ways: it doesn't have to be like the surface of a balloon. (There's some intriguing but inconclusive evidence suggesting that the large-scale geometry of the universe is a "Poincare dodecahedral space": take a dodecahedron, and apply some magic to its faces so that when you try to leave it by one face you come back in by the opposite face.) And yes, light travels along the shortest paths it can within the universe, and doesn't take out-of-the-universe short cuts even if there are any.
Most experiments (usually regarding density of the universe, but also some looking at light from really far pulsars) points to the universe being flat. A flat universe also allows for the total energy of the universe to be zero, which is nice from a physicists standpoint, since then the big bang still obeys conservation of energy.
And on that note, the creator has made the common mistake of performing the calculation speed_of_light * age_of_universe to determine the radius of the observable universe.
Space has expanded during the lifetime of the universe so the objects that emitted light at the edge of the observable universe have moved further away since emitting the light. The estimated distance to the edge of the observable universe is more like 47 billion light-years: http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN
According to general relativity, space can expand faster than the speed of light. So while what we can see is limited by the speed of light, the size of the universe is not.
If there is a minimum physical length, that is a planck length, does that mean that nothing is technically continuous? Or, is it possible to imagine 'half a planck length'?
That's a great question. I'm not sure how motion (and thus transfer of information) would be possible in a discrete universe. A somewhat related question is whether the universe is the result of computation. Many thinkers have chimed in about the physics and philosophy of this sort of thing:
I think of it as: Newtonian physics makes down to a certain scale where it is no longer accurate. Quantum makes sense down to a Planck length where beyond that, we may need different theories.
They don't really -- in particular, the picture you might have from high-school physics lessons of electrons orbiting a nucleus like planets orbit a star is really wrong. And it's not really the same forces; the way an atom looks is mostly down to the electromagnetic force, whereas the way a solar system looks is mostly because of gravity.
On the other hand, it is true that Newtonian gravity and the electrostatic force (i.e., what the electromagnetic force becomes when you make the approximation that there are no moving charges) have very similar mathematical forms, with the same sort of differential equation governing them. What Newtonian gravity and electrostatics have in common is mostly that they are convenient simplified approximations; you could say that they're so similar because there's a limited repertoire of differential equations simple enough to make good approximations. (There's a bit more to it than that; for instance, inverse square laws fall naturally out of the geometry of a 3-dimensional world.)
Indeed, some patterns in nature might look familiar. For instance, stellar matter in novae seem a lot like clouds but only because human psychology is really good at pattern recognition.
As for Newtonian physics versus relativity Brian Green’s Elegant Universe TV show (and book) does a great job illustrating the differences in an entertaining way.
No: not the same forces. The structure (and motion) of the macro-verse is governed entirely by gravity. The structure of the micro-verse is governed by the EM, weak and strong forces. Gravity, being about 10^25 times weaker than the next weakest force (the weak) has no influence at quantum scales. And as gjm11 points out below, the "solar system" model of the atom is a old classical model of convenience, hypothesised before the work of bohr, fermi, dirac et al worked out the quantum model. It's still taught in schools because the QM model requires fairly advanced math.
Some people get depressed when they find out how huge the universe is... What is the big deal about bigness? A cow is much bigger than you, but it is a ridiculous animal and you are a valuable person. You know it's a cow. It doesn't know anything. it just stands there eating grass (grass!) and mooing. And if it were bigger, that would only make it more ridiculous.
Actually thinking about it, viewed in terms of quantum mechanics the universe from our scale looks more like a bitmap image than a vector image. (Note that I have no actual knowledge of quantum physics for the purposes of this meandering nonsense of a comment.)
I ask because initially I tended to look at the universe as a really large bitmap - what is the smallest observable particle - thats our bit, everything else is a bitmap.
As I looked at the original post however I keep thinking that the purpose of physics is to determine standard rules and definitions that work across the entire scale.
That uniformity, comforting as it is, would make the entire thing vector-like (I think).
Assuming the Big Bang, doesn't that imply the 'outer matter' must have an average velocity of about 3.3 times the speed of light?