I think it's interesting, but I don't really care for the practical application. In the end, models are models. They're used to help us understand why things are the way they are, and they help a lot to make educated predictions, but we shouldn't really consider them to represent what's really going on. Maybe that's a plea for better models, but I'll leave that to the engineers, my interest is just in the intuition.
Looking back, it's pretty interesting how far that kind of thought got me into areas I had no business. I got pretty far into math without ever really learning how to compute integrals. Since most of our classes were proof based, I just kind of pushed on because I was able to prove things about integrals and stochastic models without ever really being able to tell you what they evaluated too. Eventually I hit a brick wall though, since you just can't analyze things in a reasonable amount of time unless you're solid at computation.
My own personal recommendation is to consider how much it's going to cost you to study and adjust your goals accordingly. I had spent 4 years studying pretty much whatever I wanted, and it was pretty terrifying in the last year having a degree in economics and a minor in philosophy, and knowing that I absolutely didn't want anything to do with finance. By not focusing on practical matters, I really just left the direction of my life to chance, and given the current state of the economy...not a very good idea if you can avoid it.
On the other hand, I wasn't leaving school with a large amount of debt because I was mostly on grants. The situation you really don't want to be in is not being able to find a job, and having large amounts of student loans on top of that. The concept behind the student loan is that by borrowing money now, you are gaining the education necessary to get a job that will allow you to pay it off in the future. Sadly that is not the case, and education is deceptively subsidized. In an ideal world, education would be about making yourself a better person; I think it would be swell if everyone studied philosophy. In the real world, you need to pay bills. College does give you the opportunity to explore all sorts of cool things--once you have a job, you just don't have time to just learn. So the trick is to find that balance, get what you NEED out of your education, but try as hard as you can to fit in what you WANT.
Here's what I think about Computer Science. You probably have not had enough exposure to remotely know if this is something you want to pursue. It's more than just wanting to make games, I'm sure many of us have had some sort of dream of making a game at some point, and for most of us computer science wasn't the right path for us.
My suggestion is to start learning a serious programming language like C. If you find yourself really interested in finding out why things work the way they do, than Computer Science might be a good match for you. If you find yourself really interested in using your knowledge to do useful things, than Computer Engineering might be a better match. Naturally you're more likely to have a mixture of the two. But in either case, you have to find a real passion for it, that's the difference between having the drive to finish the program, and just thinking "it would be cool if I could make this cool video game." And honestly, there's nothing wrong with you if you aren't seriously interested in the theory of computation.
