If the universe is infinite, how big is what it is expanding into? (Strange Universe 2011)

We can observe data that tell us the Universe appears to be at least 46 to 70 billion light years in radius. Even though that is much further than light could travel in the 13.7 billion years since the Big Bang, the accelerating expansion rate of the Universe means that the light we see from the most distant objects left the location they were in 13.5 billion years ago or so, and just got here, but they have since moved much, much further away from us. Some theorize that the Universe is actually infinite. If it is, how can it expand when it is already everywhere there is and fills everything there could ever be?

One might think that the Big Bang was like a stick of dynamite exploding inside a bolder, blowing everything outwards at great speed. This is a flawed concept. Such human-bound physics could not account for pieces of the boulder accelerating. Nor is it necessarily true that the Big Bang occurred at a single point. So an infinite Universe is possible.

Do you think the Universe is infinite? If it is, what is it expanding into? Do you think this conundrum proves the Universe is finite, or that it shows we cannot grasp the morphology of all its dimensionality?
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Here are the previous questions in the Strange Universe Series for 2011.
1: —How do you envision space in more than 3 dimensions, then rotate it to see what happens?

The 2010 list of 20 questions in the series is shown here.