>> I will admit I don't know much about the geometry of our galaxy, but I 
>> was under the impression that the disk is hundreds of billions of 
>> light years "thick",
> 
> It's much smaller than you think:
> 
> http://en.wikipedia.org/wiki/Milky_way

Heh, "only" 100,000 light years across and 1,000 light years thick. 
Well, that's the trouble when you start dealing with Really Huge 
Numbers, see?

There's a reason why would talk about 4 Terabytes rather than 
4,000,000,000,000 bytes - it's frighteningly easy to get the number of 
digits wrong! ;-)

Obligatory XKCD:

http://xkcd.com/558/

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