Applications are now open for Omidyar Fellowships at the Santa Fe Institute. It's a three-year gig with complete academic freedom. You work on whatever questions you find most interesting, using whatever tools you deem appropriate. And you get to hang out with a bunch of like-minded individuals from all sorts of different fields.
The Santa Fe Institute is highly interdisciplinary. Typically, there are people there doing physics, and biology, and anthropology, and computer science, and linguistics, and on and on. Most of the individual people you would meet there would be actively engaged in more than one of these areas. So, if you're an interdisciplinary type of person, you should definitely apply.
You should especially apply if you feel that your work is constrained by disciplinary / departmental boundaries in a traditional academic setting, and you want to forge your own path.
The only sort-of constraint is that most of the work that happens there is mathematical / theoretical / computational. There's no wet-lab space, and math tends to be the lingua franca that allows all of these people with different backgrounds to communicate and work together. That being said, there are people who have successfully managed to do some combination of theoretical and empirical / lab work by spending some of their time at a University or field site.
The major caveat I would raise is that you only want to take one of these positions if you are really ready to function as an independent researcher. You won't have a traditional advisor, and no one will be looking over your shoulder -- although you will have excellent and supportive colleagues and peers.
Here's a snippet from Galway Kinnel's The Book of Nightmares, which to me sums up the essence of this fellowship, and the ideals of the Santa Fe Institute:
I long for the mantle
of the great wanderers, who lighted
their steps by the lamp
of pure hunger and pure thirst,
and whichever way they lurched was the way.If that resonates with you, submit your application by November 1. Here's the official flyer. I ran the postdoc program at SFI for about three years, and would by happy to try to answer any questions, but if you want answers that are actually correct, your best best is to contact the program directly.