The Internet has not changed the way I think nor has it changed the way anyone else thinks. Thinking has always been the same. To simplify: the thinking process starts with an expectation or hypothesis; thinking requires one to find (or make up) evidence that explains where that expectation went wrong; and thinking involves deciding upon explanations of one's initial misunderstanding. Thinking is about attempting to understand how an aspect of the world works, and the process hasn't changed since caveman times. The important questions in this process are these: What constitutes evidence? How do you find it? How do you know if what you found is true? We construct explanations based on the evidence we have found.
This process was in place long before the Internet existed. Thinking hasn't changed. What has changed is how we find evidence, how we interpret the evidence we have found, and how we find available explanations from which to choose.
I went into AI to deal with exactly this issue. I was irritated that people would argue about what was true. They would get into fights about Babe Ruth's lifetime batting average. That doesn't happen much any more. Someone can quickly find it. Argument over.
Finding evidence and interpreting evidence has not, unfortunately, changed that much either. At first glance, we might think that the Internet has radically changed the way look for and accept evidence. And, I am sure this is true for the intellectuals who write Edge response essays. I am able to find evidence more quickly, to find explanations that others have offered more easily. I can think about a complex issue with more information and with the help of others who have thought about that issue before. Of course, I could always do this in a University environment, but now I can do it while sitting at home, and I can do it more quickly. This is nice, but less important than people realize.
Throughout human history, evidence to help thinking has been gathered by consulting others, typically the village elder who might very well have gotten his knowledge by talking to a puff of smoke. Today, people make decisions based on evidence that they get from the Internet all right, but that evidence often is no better than the evidence the village elder may have supplied. In fact, that evidence may well have been posted by the modern day version of the village elder.
The intelligentsia may well be getting smarter because they have easy access to a wider range of good thinking, but the rest of the world may easily be getting dumber because they have easy access to nonsense.
I don't believe the Internet has changed the way I or anyone else thinks. It has changed the arbiters of truth however. Now everyone is an expert.