I am assuming the word "Google" used in the question is in relation to the search optimization engine technology. In relation to Nicholas Carr's suggestion that our brains are adapting to shorter attention spans and higher stimulation, I question what type of tool Google truly is (is Google similar to a calculator since we do not memorize as much information?). In order to assess whether or not Google is making us stupid, we must assess the construction of knowledge in relation to Google's business model
Google's mission statement is, "...to organize the world's information and make it universally accessible and useful." In other words, Google's search engine is a tool to utilize by curious folks who want to search a particular subject. In return, Google is able to collect hundreds of bytes of data, which is commodified as currency for the company. This transaction can be similar to a library, where you learn how to effectively search the information you seek (but does not mean you necessarily retain what you learned, nor does the library release your data back to you).
Therefore, I think Google is a consolidation of tools that we have used in the past and present, and we are simply interacting with the tool in exchange for our data to be sold to advertisers. Dr. Maria Wimber from the University of Birmingham's School of Psychology believes, "...the internet simply changes the way we handle and store information, so the Google Effect 'makes us good at remembering where to find a given bit of information, but not necessarily what the information was.'"
It is on a personal level that we must understand that hardware or cloud space is where our information can be held since some people claim that the internet knows everything. I believe we are becoming smarter since we are able to effectively manage a tool that gives us access to any type of information.
Although we may have an advantage of searching anything we like, we must not be complacent in our views when searching information. Google's model for making money relies on our attention spans to be quick so we continue clicking through different links. Our digital traces leaves data, which can create personalization thus reinforcing our ideas/ideals (and making it easier for capitalism to infiltrate its way through the co-construction of a collective knowledge).