What's the purpose of the deep indentation under a bottle of Champagne?
There are many theories to explain that feature – known as a punt or kick – but none is conclusive. One of the more likely purposes is strength.
I'm no materials scientist, but I believe the added glass, moulded at a diagonal, renders the base stronger. This is especially critical in the case of Champagne, which is bottled under substantial pressure. A flat bottom would pop out more easily if the bottle were jostled or plunked down too hard, especially at room temperature. That's why sparkling-wine bottles are thicker in the first place.
It's not just Champagne that comes with indentations, of course. You'll notice punts on still wines, too. Some people have speculated all sorts of other purposes for the cavity. The groove helps collect and concentrate sediment when the bottle's placed upright, for example. Others claim the purpose has to do with stability. Back in the hand-blown-glass days, it could not have been easy to craft a perfectly flat base. By indenting the centre, you created a hollow circle, and that created a more solid footprint. But this doesn't explain why the punt, especially on Champagne bottles, has to be so deep; there are plenty of white wines with very shallow indentations that achieve every bit as much stability.
Another good theory: It was (and is) a marketing ploy, helping to create the appearance of a larger and more "important" vessel. Certainly this is the case with some red wines today that come with absurdly deep punts. And ever notice the cleverly disguised punt on a plastic bottle of Orville Redenbacher popcorn? I'll bet that was inspired by the larger-volume optics; it bothers me every time I reach the bottom of the container sooner than expected.
Whatever the original purpose, traditions die hard in the wine world. But the fact that only Champagne bottles invariably come with pretty deep punts (whereas, say, many still whites have flat bases) leads me to conclude that all other theories, besides strength, are secondary if they apply at all. You don't want to aggressively handle a punt-less Champagne bottle, at least not unless it's made of plastic or carbon fibre.