Not necessarily. It all depends on the geometry you're using. Classical Euclidean geometry, the stuff people learned in high school, allows for spheres. The thing to remember is that the sphere is a three-dimensional object with a surface and an interior volume. Within those three dimensions, all of Euclid's laws of geometry apply as normal. Parallel lines don't meet, the interior angles of a triangle add up to 180 degrees, and so on. We think of this geometry as flat because the axes are either going to be straight lines or a planar figure if you're using polar coordinates.

In *Riemannian* geometry those laws don't necessarily hold true. The basic geometric shapes that we find so intuitive exist, but they're warped by the fact that the geometry itself is curved. For instance, the surface of a sphere is a perfectly good *two-dimensional* Riemannian space. Lines that are parallel in one region of the surface are not necessarily parallel elsewhere (like lines of longitude being parallel at the Equator but intersecting at the poles) and the interior angles of a triangle don't have to add up to 180 degrees (you can get 270 on the surface of the Earth). Granted a sphere is the simplest possible geometry here, but more complex spaces are possible. Also, you can have curvature *without* wrapping the space around another dimension. In fact, you *only* need that extra dimension if you're trying to use Euclidean geometry to model the space.

The problem is that the human brain is not wired to visualize anything more than a two-dimensional curved space and it can only understand that by embedding it in a three-dimensional flat space. Current theory holds that the universe is a four-dimensionnal hypersurface whose curvature (gravity) is determined by the presence of matter and energy. We can model this as a surface in a five-dimensional Euclidean space, but I don't think that's inappropriate because that fifth dimension does not exist in any form we can experience. As such, it's best to invoke Ockham's Razor and discard the idea. Also, remember that the fourth dimension is *time* and, for whatever reason, time seems to be quite different from space. You can't embed time in a spatial dimension - it just doesn't work. (For the sake of argument, I'm ignoring the higher-dimensional theories floating around. If the universe has more dimensions, they may also be curved so the argument holds generally. Also, at least for now it seems that we can only directly interact with four of those dimensions - space and time - so my basic premise here should hold).

Which should be easy if the Big Bang was an explosive event. That would necessitate that the universe is essentially a huge, three-dimensional spherical cloud of matter that expands with time. We should, in theory, be able to find a point from which all galaxies are receeding, based on their redshifts.

Well, why does the amount of matter in the universe have to be finite? In fact, if the universe is a four-dimensional hypersurface it must have an infinite amount of matter to preserve the idea that it has no center and no edge. Otherwise, you could come to a point where you'd see lots of galaxies one direction and none in another. That violates the restriction that the universe must be uniform throughout its entirety. As long as matter and energy aren't being continuously created, there is no violation of energy and matter conservation. (Granted, spontaneous pair creation is an exception, but the Uncertainty Principle covers it).

No, the discussion is out there. The problem is that understanding the very early universe will eventually require us to finally get general relativity on the same page as quantum mechanics. Right now, those two theories are incompatible as there is still no way to get gravity to work on a quantum level. There is no experimental evidence of gravitons - or even gravity waves - and no generally accepted theory that bridges the gap.

Perhaps more importantly, the very early universe, by which I mean the Big Bang and the time shortly thereafter, poses a couple of huge questions that theorists find baffling, but intriguing. For instance, why is there no evidence of large amounts of anti-matter in the universe? If, as has been suggested, that some galaxies are made of anti-matter, why aren't they mixed within galaxies? Why didn't the galaxies and anti-galaxies annihiliate each other in the first place? Why do galaxies exist at all if the universe should be completely uniform? What is causing spacetime expansion to change speeds? What - and where - are dark matter and dark energy? I don't think I'm alone in thinking (and hoping) that the answers to these questions will help us understand the baby universe.