Here is terrible paintbrush image showing 3 images each one with more zoom.
http://imgur.com/JX0qQfO
The idea is basically
1) in the "street view" mode you are just opening a pdf text like usual
2) in the map mode you are (in the very basic definition) in an improved table of contents mode
In an stantard table of contents you see the hierarchical division of the book and the page where each division starts. The program would transform the table of contents in a map.
In the picture I linked, the first image (top left) is assumed to show the topic industrial revolution. Unless it is a book about industrial revolution that image would just be a part of bigger map. But for a moment lets ignore we could zoom out and focus only on the part of the map that talks about industrial revolution. As you can see, there is a division of the map in pieces. I took that division from wikipedia entry for Industrial Revolution. The area of each division should be a representation of how much is written about it (number of pages). So we can immediately see that etymology of industrial revolution will not take as long to read as the causes of industrial revolution will.
At first we could suppose all subdivisions are independent so you can read any part in any order. That is not always the case, sometimes you are supposed to read one topic before reading another. For those cases you would not be able to open the pdf of those topics unless you read the pre-requisite topics or mark those topics as already read or disable the pre-requisite watch.
As you zoom in more and more you are going deeper in the book you will end up in bottom of the structure, as you see in the botton part of the picture. Each zone size is still a reference of the number of pages and now each one is a clickable link to a pdf file (short 1,2,3 pages max).
The variation of the square sizes would be continuous (like in google maps), not discrete zoom values (like in the picture I linked). Changing the font size and making them disappear when they are too big or too small is the part of the challenge.
So in a more formal definition
book is a tree node with no parents
each node has children nodes (chapters)
each chapter has children nodes (sub-chapters)
and so on.
at scale 1x (no zoom in no zoom out)
each node size = sum of size of all its direct children
if a node has no children the the node is a pdf file and its size is the number of pages of the file.
for the visualization it would required an algorithm with entry
1) rectangle (height,width) --where height x width = number of pages under that rectangle
2) a partition of k values (p1,p2,p3,....,pk) where p1+p2+p3+...+pk = p = height x width
and the output would be a division of the rectagle into k rectagles.
I don't know if such an algorithm exists, I will check it out, but I think there are infinite solutions and finding a solution should not be that hard, but it is just a supposition.
You asked why this would be useful, lets say you is reading a lot of details about the causes of the industrial revolution. But you must also keep track all the time where industrial revolution belongs in humanity history, how long it last, the other events that happened near it. So maybe it would be good from time to time to zoom out to see where what you are reading belongs in the time line. I lose track all the time in a book but with a tool like this where I can just mouse wheel down and see the big picture, it would be much easier to not lose contextualization. Remember I am considering you are reading something very detailed so you may be reading about industrial revolution for several days. You will need to step back to see the whole picture quite a few times otherwise you get lost in detail with no contextualization.