Potential academic career in very different fields There's this question about doing research in two very different fields, but my question is somewhat different. I have serious academic interests in two very different fields: one in computer science/mathematics, but the other would be considered comparative literature/cultural studies. I could hardly think of any way to combine those two academic interests (well, I know of digital humanities, but that is not what I exactly want to do).

Nevertheless, I wish to continue research in both areas as an academic, although not necessarily at the same time. Clearly, a possible route is to go one way and then do another PhD and switch mid-career, but I am not sure if this is a good idea. But on the other hand, I am not sure if this is even possible without a mid-career career change.
This isn't impossible, but would be very difficult to manage. Trying to earn degrees in two disparate fields at the same time would not really be possible for anyone unless they have an exceptional mind and drive to match. This might be you, of course. 

However, assuming that you have the credentials it might not be very possible to actually pursue matching positions in academia. Academic couples usually have a problem finding work at the same institution just due to a mismatch in the needs of various departments over time. One member of a couple might find a great offer while the other can't find anything at the same or nearby institution. That won't be exactly your issue, of course, and you might be able to get one good position in either of your fields and then use that position to make contacts to get something in the other. But I think that depends a lot on individual circumstances. 

Your suggestion to pursue one now and the other later seems like a good one. Hopefully you can choose one that (a) is feasible to enter now and (b) will satisfy you if the other options fail. 

All that doesn't imply, of course, that you don't have a worthy goal. People who know a lot of things and can write and do on a lot of topics are worth having, though the academic establishment in most places isn't especially well set up to reward them properly. There are a few exceptions, perhaps. Oxford (UK) comes to mind with their college system rewarding diversity of thought. 

Perhaps a way to think about it is this. Which of these fields cannot be done without a credential? Can I pursue the other, independently for now, uncredentialed? If that is the situation, it might be a solution. Similarly, in which of these is it more important that I build a reputation? There are plenty of academics in various fields who are also novelists, for example. Not the same thing, I realize, but different mind sets for the two activities.