It's not what you know, it's what you can find out. The Internet has put at the forefront resourcefulness and critical-thinking and relegated memorization of rote facts to mental exercise or enjoyment. Because of the abundance of information and this new emphasis on resourcefulness, the Internet creates a sense that anything is knowable or findable — as long as you can construct the right search, find the right tool, or connect to the right people. The Internet empowers better decision-making and a more efficient use of time.
Simultaneously, it also leads to a sense of frustration when the information doesn't exist online. What do you mean that the store hours aren't anywhere? Why can't I see a particular page of this book? And, if not verbatim, no one has quoted it even in part? What do you mean that page isn't available? Page not found?
The Internet can facilitate an incredible persistence and availability of information, but given the Internet's adolescence, all of the information simply isn't there yet. I find that in some ways my mind has evolved to this new way of the thinking, relying on the information's existence and availability, so much so that it's almost impossible to conclude that the information isn't findable because it just isn't online.
The Web has also enabled amazing dynamic visualizations, where an ideal presentation of information is constructed — a table of comparisons or a data-enhanced map, for example. These visualizations — be it news from around the world displayed on a globe or a sortable table of airfares — can greatly enhance our understanding of the world or our sense of opportunity. We can understand in an instant what would have taken months to create just a few short years ago. Yet, the Internet's lack of structure means that it is not possible to construct these types of visualizations over any or all data. To achieve true automated, general understanding and visualization, we will need much better machine learning, entity extraction, and semantics capable of operating at vast scale.
On that note — and in terms of future Internet innovation, the important question may not be how the Internet is changing how we think but instead how the Internet is teaching itself to think.