Neal Stephenson, The Confusion
If you have ever attempted to shelve your own books in an organized way, you know the problem. Some books can be extremely difficult to categorize.I touched on the problem a year ago (Sept. 28, 2015) in a post called "Staying put" about Vivian Swift's book When Wanderers Cease to Roam. Is this, I asked, a travel book, a memoir, a journal, an art book or a book about natural history? Well, yes. And it's about many other things as well. So on what shelf so you place it so you can find it again? This explains why I now have no idea where the book is in my library.
According to his example, Plato's number is 2, Aristotle's number is 3, trees are assigned the number 5 and turtles get the number 7. Thus, if Plato writes a book about trees, it would be assigned the number 10, and if Aristotle writes about turtles, it would get the number 21. Obvious problems present themselves, in addition to those of assigning numbers to every writer and every subject and the requirement that every librarian also be a mathematician. If Plato then writes about turtles (14) and Aristotle writes about trees (15), the two turtle books would not be side by side on the shelf, nor would the two books about trees. Furthermore, what do you do if either Plato or Aristotle writes a book about turtles under trees? Or what number would you assign to Vivian Swift's book about so many different subjects?
The Dewey Decimal System, created by Melvil Dewey in 1876, did in fact find a way to assign a number to every book. These numbers had the advantage of grouping books about turtles on one shelf and books about trees on another shelf. As for books about turtles resting under trees, assuming that turtles ever prefer trees to direct sunlight, there was a card catalog for cross-referencing.
Now, thanks to computers, it is possible to do the kind of things Leibniz, early inventor of mechanical calculators, could only dream of. Feed into a computer what you are looking for, and it will tell you where to find relevant books on library shelves. Those of us who do not have our home libraries computerized, however, may still experience the kind of confusion Leibniz and Fatio share in The Confusion.