Is there a compelling reason (besides convention) why a user's typical default view of a long sorted list is always the beginning of the list and not the middle? Assuming a random distribution of selection targets, it would be more efficient to start in the middle and scroll up or down to find the target selection. For example, when I open my contacts, starting in the median position would halve the average distance I need to scroll. The idea came to me when reading about recursive binary search algorithms. Is there something different in the way that humans perform searching a sorted list that would make the beginning a better place to start than the middle?
The human brain and a computer algorithm work quite differently.
Your assumption that it should be easier to start in the middle of a list is wrong.
In those cases you would first need to figure out what the middle point of your list was. Then you would need to figure out whether the item you are searching for would be above or below this middle point. Then you could start scrolling in the right direction. If the thing you're looking for would be above the middle, then you would have to search backwards - a pretty complicated mental operation.
I'm not even sure if I know the alphabet backwards... :-P
A few reasons:
If you have a long sorted list, you shouldn't have to swipe to your destination anyways. There should be some way to accelerate the scrolling. For example in contacts, you usually have a scroller on the side with letters so you can jump to a specific letter.
It's a bit hard to substantiate this claim, but I think starting at the top feels cleaner. It's hard to describe; it may even be a bit of OCD. I would be quite annoyed by an app that starts me off mid-list. Maybe it's that I've come to expect them. When I look at lists in general, I start at the top. I don't binary search my lists. I don't binary search my way to page 248 of a book. I jump to roughly the right spot then linearly make my way to 248.
I think you dismiss convention a little bit in your question; I think its valuable. Convention ensures that skills learned in one situation (one app's list view) transfer to a different situation (another app's list view). This decreases the amount of time people spend learning new things that don't significantly improve their lives.
Putting my personal feelings aside though you bring an interesting problem up though. You made the assumption of a random distribution for selection targets. But in reality people look certain folks more than others in a contact directory. People look up some words more than others in a dictionary, and they look up some recipes in a book more than others when cooking dinner.
So what about putting you in a place in the list with the minimum cost of scrolling using a cost function that takes into account the probability distribution of you wanting to select each list item.