I was thinking about that Samsung's phone and the other which folds like a newspaper with screen out, can't remember its name.
At first I was convinced the Samsung's approach is MUCH better and that there is absolutely no value in folding the other way around. After all, you are protecting the poor screen which needs to fold and you are exposing something that can be much more rigid and whatnot. Plus, having it fold like a newspaper looks very weird and unnatural, while the book folding makes sense in every single way.
However, now I believe newspaper folding is a much better idea. Folding like a book looks great on first sight, but it doesn't age well if you think about it longer. (but I believe Samsung's implementation of this inferior concept will be superior to the implementation of that other company I can't even recall, so in the end inherent advantages of the approach won't really matter. So, I would like to focus only on the concept itself and its potential, not on the two devices coming out):
Now, for the advantages of the newspaper folding.
1. Internal bend radius is MUCH smaller than external. Additionally, it compresses the screen. This is likely going to cause tons of problems by pixels smashing into each other, ruining the screen much faster than folding the other way around - where you first stretch the pixels (generally easier) and you have a much larger radius of bending = there is less stretching.
1b. This also leads to possibly much smaller gap when folded as you can have rear side that suitably slides to eliminate the gap. Much harder to do the same on active screen.
1c. Or, if you keep the gap, you could put pen there. Nicely packed pen when the device is in the pocket, get it out and extend to tablet size and pen is available, without taking precious internal space in the device like Samsung's current implementation on Note.
2. The thing is flexible plastic anyway. It isn't a solid glass that breaks when it hits the floor. Plus it doesn't matter much on new phones whether the front or rear glass gets shattered, both are insanely expensive to repair (though you can easily opt to not repair the rear one).
3. Having a single screen that folds costs less than having one extra screen. Not that anyone would notice with stuff cosing 1k+, but still.
Thinking about the benefits of the book-like folding again - I can't think of a single actual advantage. It SEEMS much better in every way, but those advantages are skin-deep. Or did I miss any huge drawback of newspaper-like approach or some viable advantage of book-folding approach?