In the lightning-fast span of 10 years, Google (GOOG), which started as a search algorithm at Stanford Univesity, became the Internet's most successful company. Asking where co-founders Larry Page and Sergey Brin’s brainchild will be 10 years from now is like asking how far twice the distance to infinity is.

Of course, that doesn’t mean we can’t try.

And try, we do. All over the internet, blogs like Google System predict what new products the company will roll out next. Like GDrive, the online "hard drive" that will purportedly provide users with 20 GB of storage. Or the full release of Gears, an application which, when integrated into the Google Apps suite, will allow users to work offline on all of Google’s products.

But it gets bigger. Facial recognition has been on the radar of futurists ever since Google acquired Neven Vision in 2006. And with its embrace of open-source technology, some believe it’s only a matter of time before the G1 surpasses Apple’s (AAPL) tightly controlled iPhone.

And did we mention Google Health - your one-stop shop for keeping track of your entire medical existence? Check it out; it’s already in beta.

The point is, Google has consistently demonstrated rhythmic grace when it comes to expanding itself. Search gave way to Gmail - and AdSense redefined the online-advertising industry. With deceptive ease, Google outpaced MapQuest with Google Maps and put the kibosh on video competitors when it bought YouTube.

But you’ve heard all this before: In the future, Google will be everywhere - on your desk, on your TV, on your phone and in your head. Google will cross-reference your name with your favorite peanut butter and sell it to you before you even knew you wanted it.

Larry Page is now Google’s products president, and there appears to be no limit to his desire for innovation: “The Star Trek computer doesn't seem that interesting,” he once said. “They ask it random questions, it thinks for a while. I think we can do better than that.”

What then? Google transport? Google food? Entire conversations composed only of slightly modified inflections of the word Google?

“Google.”

“Google, google?”

“Google!”

And to think, it all began with this: