If you could see the future, how would such an ability manifest itself? How would you describe "seeing" the future, especially given that the future is much less one image as a superposition of an infinite number of probable images? How do we take into account the "observer" effect -- where the future of some events drastically depends on what the one seeing it decides to do in the next few seconds?

I imagine that seeing the future would be just like seeing in a classical sense, with a few exceptions. First, you could focus on some time in the future (just like you focus on a particular element in your field of vision) and that would reveal the state of reality in that point in the future. It would be pinpoint-, but not distance-accurate (just like focusing is): you can focus on a particular existing element well and almost instantaneously, no matter how close or far it is, but you couldn't focus on an element at a particular distance. Similarly, when seeing the future, you would be able to focus on a particular event, but not necessarily on a particular point in time (and you would only know by and large what time this event is going to happen).

Moreover--and more importantly--possibilities in the future would manifest themselves as blurry spots. If something was a certainty, you would see it as sharp and distinct. If something was a possibility, it would blur with the other possible outcomes. For example, the sun rising tomorrow is a certainty so as you focus on the event of the run rising tomorrow you would see it sharp and distinct. But, say, your dog might be hit by a car in a week so it would appear in your visions of the subsequent future as blurry. The further out you "focus", the more blurry it will be.

This model comes to a beautiful conclusion in the case of the above mentioned "observer" effect. As you focus on the future event that depends heavily on a decision you make, the details in the event will shift from blurry to more defined as you think more or less heavily of making one decision relative to the other. In a way, you will be able to "focus" your vision of the future by committing to certain decisions.