However, I also discover that I really definitely do have an Erdős number of three, which is the mathematical world's equivalent - I authored a paper with someone who authored a paper with someone who authored a paper with Paul Erdős. As a result, if my Bacon Number were legitimate, which it's not, I could lay claim to an Erdős-Bacon number of 6, which would be one better than Natalie Portman.
As is already well known, it's a small world. What's most obvious to me is that some people, whom I'll probably never meet or know, have sufficiently large personal networks that it's pretty easy for other people to find links to them. If you're a politician or an actor, that's probably pretty useful to you - always nice for people to feel they have a personal connection with you, even if it's almost entirely bogus.
What's new and interesting is that social or business networking sites are making these relationships just a little more visible and easy to discover.