I'm especially interested in hearing from other parents, so please highlight that fact in your responses.
(Posting anonymously to preserve my and my son's privacy)
I am also thinking about ways to develop abstract thinking in my baby. I plan to work on cards / minibooks to teach him some abstract concepts in a basic way: like transformations, combinations, logic, sets, etc.
I think it's very important not to force it on children, do not burden them with your expectations - they will rebel or build low self-esteem. It should be a delicate support, encouragement for them to follow their natural curiosity deeper, like Paul Graham described in his recent essay http://www.paulgraham.com/genius.html
Some people I know in childhood psychology and education basically say, that early on, these specific topics in STEM are beyond the human mind at that age. For example, you can give them a programming toy or game, and they will learn the game, but not the ideas behind programming.
It takes time for the young mind to develop the capacities we take for granted as adults.
Another thing to keep in mind is that kids eventually resent the pressure parents put on them for career choices. Would you have a problem if they chose to be an artist or musician?
Kids who go to day care talk to other kids so they learn social skills.
Kids who hang out with adults learn better verbal skills. A kid who grows up with adults with high verbal skills will sound more intelligent whether or not they really are.
Also, train sets and marble maze blocks can be an early exposure to a very abstract take on branching logic.