For example I use [email protected] to send emails to [email protected], [email protected] and [email protected]. Google now have a profile for [email protected] with a graph that includes nodes for alice@, bob@ and charlie@ and edges for the relationships between the four people, and links to anything we've discussed. If [email protected] then sends an email to [email protected] Google know that david@ has a second order link to alice@, bob@ and charlie@ despite the fact that they have never communicated or informed Google of this relationship, because Google have a profile based on [email protected] - an address that Google might not have a justifiable reason to be building a profile on.
Whether or not you believe that is a reasonable use of data is up to you. Some people think it's not.
I'm not sure at all that it is clear what the nature of that link is. I have no insight into the gmail's email relationship modeling but I suspect that it doesn't automatically build a relationship between [email protected] and other people that onion2k contacted. For one thing, it would be impractical to do this across all possible relationships -- there would be polynomial growth of the adjacency matrix with no information gain to justify it. Ask yourself, what does it mean that david contacted onion2k and onion2k, at some point in time, contacted alice, bob, and charlie? Unless you already know something nontrivial about these people, you assume they are independent.
I guess my point is that data analysis can be very costly; it is reason that humans have a hard time dealing with meaningful relationships spanning more than about 150 people[1]. Even a company with Google's resources would be overwhelmed if it had to store and take into account a large number of mostly (I mean, vastly mostly) meaningless relationships. At the least, it takes away resources from the relationship graphs that do matter and which are actionable, such as the graphs of spammers.
But does Google profiles it?
There's nothing implied in sending an email beyond "I want you to read the contents". If there's more I want you to do, those wishes would be in the email itself.
30 years ago, if I wrote a paper letter to a company, I was not implying that I want them to build up a profile of me based on my stated info compared to the stated info of other people, where my letter came from, type of stationary, quality of my grammar, etc., then send me coupons that match the behavior they expect of people of my profile. I am implying that I want them to read my letter and take care of my request.
Yeah, but it essentially always happened. You know those warranty cards you get with new products? They have always been used to build marketing databases.
http://www.nytimes.com/2003/12/25/technology/do-you-really-n...
Meanwhile, no, you have no right to dictate how I contract out how I handle my mail by sending me a letter. You gave me that letter, and you'd have a difficult time making a case even if I then proceeded to make thousands of physical copies of it and distributed it at a street corner.
I guess what I'm saying is... what's your point?
edit:
You appear to be misreading your parent comment. The parallel situation they describe is precisely that the recipient engages a company to process their mail (read the description: "you hire some company to sort and collate your mail (and toss out your junk mail for you), and in exchange they slip in some coupons [for] people who get the kind of mail that you do". All of that applies to receiving mail, not sending it.)
And this is precisely what's happening with Google: if you send mail to my gmail address, I've engaged Google to process it on my behalf. You have no say in the matter, nor can you.