Here's the rub - for a given query there is no such thing as the list of link that are "most relevant". Different people will have (potentially widely) divergent opinions on what the most relevant set of links are for the exact same query.
The goal Google web-search [1] is to show you the links from the whole web that are most relevant to you. Knowing more about you allows a search engine to make better decisions about what links are relevant to you.
You would be hard pressed to find an engineer at Google that thinks search is remotely close to a "solved" problem.
([1] for the cynics - yes, Google makes a lot of money from showing ads on search result pages. That is a nice effect of having a great search engine. Making money isn't the goal of web-search. Showing relevant results is. That was true when Larry and Sergey were cobbling together machines in their dorm room. It is still true today)
But your own example implies that you could've achieved the same results by simply using the "and" operator: ring AND mathematics. No reason to give up privacy.
I'm actually surprised that your friends didn't get the Wikipedia entry on "ring" among their top results. When I ran the search on both Google and Bing, it came up second.
> The goal Google web-search [1] is to show you the links from the whole web that are most relevant to you.
But my point is: there is no such thing as "me". Now I do this (programming) and an hour later I do that (cooking). Then my daughter comes along and she wants to see pictures of puppies -- but I personally could not care less about puppies.
If Google thinks I'm into puppies and tries to infer something from that, then they will have broken search for me.
> Different people will have (potentially widely) divergent opinions on what the most relevant set of links are for the exact same query.
I really (really) don't think that's true.
What is true is that the "exact same query" could be about different things (domains), such as java the programming language, the island, or coffee.
But given a query and a domain, the most relevant links are obtained by consensus (PageRank). An interesting evolution would be to have PageRanks evaluated per topic.
But my point is: there is no such thing as "me". Now I do this (programming) and an hour later I do that (cooking). Then my daughter comes along and she wants to see pictures of puppies -- but I personally could not care less about puppies.
False problem. For one, your daughter can (and eventually will) either get her own Google account, or she will get her own computer.
But most importantly: ok, so you're not just "you", but your whole family uses the computer.
You still, as a person, get better results by Google using its knowledge of your family search habits --which include yours--, than just blindly guessing.
I agree 100% that various levels of opting out should always be possible.
Some of that is available now - e.g. incognito mode in Chrome (or the equivalent) or simply not being logged in, Search+ has the toggle for whether or not to include personalized results are the examples that come to my mind first. One could imagine other controls that might be useful or desirable.
"But I don't want it to take my entire online life into account when I am doing a search"
Personally I think that over time, the difference in the quality of the results provided by search engines that don't know anything about it's users will so much behind those from search engines that do that we will look back and wonder how we ever found anything.
Here's the rub - for a given query there is no such thing as the list of link that are "most relevant". Different people will have (potentially widely) divergent opinions on what the most relevant set of links are for the exact same query.
The goal Google web-search [1] is to show you the links from the whole web that are most relevant to you. Knowing more about you allows a search engine to make better decisions about what links are relevant to you.
You would be hard pressed to find an engineer at Google that thinks search is remotely close to a "solved" problem.
([1] for the cynics - yes, Google makes a lot of money from showing ads on search result pages. That is a nice effect of having a great search engine. Making money isn't the goal of web-search. Showing relevant results is. That was true when Larry and Sergey were cobbling together machines in their dorm room. It is still true today)