Karen writes, "I met someone for the first time in a meeting the other day. A few hours later, she showed up on my Facebook page as 'someone I might know.' I've also noticed that people sometimes pop up in this feed shortly after sending me emails. How does Facebook know about these interactions? Or am I just being paranoid?"
You're not being paranoid, Karen. From what we can tell, Facebook has someone spying on you at all times. That secret spy is [insert dramatic music here]: your smartphone!
We would bet dollars to donuts that you not only have an iPhone or an Android phone, but that you also have the Facebook app installed and that you have location services enabled on your phone. If that is the case, your phone is allowing the Facebook app to occasionally check your location, which the app does to see if you’re near any other Facebook users. This is one way Facebook knows to suggest people you've come into contact with.
However, this doesn’t mean that the app will suggest you be friends with every random person you pass on the street. Facebook is smarter than that. Even though you met this person for the first time the other day, the two of you presumably have things in common: you have similar jobs, you work in the same industry, you know some of the same people, etc. You are in what Facebook considers to be a "network."
Your colleague probably also had the app installed on her smartphone. When Facebook saw that the two of you, who are in the same network, spent an hour in the same location, it thought, "These people know each other! They should be Facebook friends!" And so she popped us as "someone you may know."
You mentioned that Facebook also seems to know when you've emailed someone, and will suggest that you be friends with that person. You'll be happy to know that Facebook isn't reading your emails. What it is reading is your smartphone's contact list, another thing the app has access to. You most likely have your contacts synced with your email, so when you email a new person they are added to your phone's list. Facebook sees this, and again thinks that person is "someone you may know."
These aren't the only methods Facebook uses to suggest new friends. According to Facebook's website, they "show you people based on mutual friends, work and education information, networks you're part of, contacts you've imported and many other factors."
If you don't want Facebook to have access to this information on your smartphone, your best bet is to just uninstall the app. In fact, that is your only option if you have an Android phone. If you have an iPhone, though, you can change what the Facebook app has permission to see.
We have instructions for how to revoke the Facebook app's permissions on iOS on Deemable.com.
