Yes, they can. There are a couple of interesting ways that they gather this information.
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Your digital fingerprint
When you access any website, whether it’s a search engine or even Ask Leo!, the server gets a fair amount of information from your connection to that server and from your browser. This could be the IP address that you’re at, the type of browser you’re using and its settings, any cookies set by prior visits to that site, and possibly some other information.
The combination of information sent turns out to be almost, but not quite, unique. Even if you’re using an almost identical system to another user that combination of information still has enough differences that make it unique to you.
That creates what you might consider a digital fingerprint.
Even if it doesn’t identify you specifically (which we’ll talk about that in a minute), a site uses your visit to determine that the person who was here yesterday looking for this is here today looking for something else.
Identifying you from information that doesn’t identify you
The idea of a digital fingerprint gets interesting when you start talking about searches. We naturally reveal a lot about ourselves by what we look for when we search.
Some years ago, a search engine made search information available to researchers. The company believed they filtered and anonymized the data to remove every possible personally identifiable piece of information (like IP addresses and cookies) from the results before they gave it to the researchers.
Nonetheless, the researchers used the actual phrases that people were searching for to identify a few specific individuals who had performed those searches.
Should I be worried?
That is as interesting as it may be scary. Personally, I don’t worry about anything like that. I say it often, but regular users like us are just not that interesting.
These days, it feels like true anonymity is almost impossible.
Using a browser and a search engine – even one without the concept of an “account” to associate specifically with you – you’re almost always leaving a fairly interesting trail of information that can be analyzed and cross referenced in interesting ways.
So, yes, search engines absolutely can and probably do “track” you, in the sense that they have the information to say that “this person is doing that”. What they may or may not have is enough information to say “this person is YOU”.