Imagine a row of books on a shelf numbered 1, 2, 3, ...
Chapters in each book could be similarly numbered, so that Chapter Five in Volume Three would be represented as 3.5. This could be extended arbitrarily, so that 188.8.131.52 represents Volume Three, Chapter Five, Section Ten, Paragraph Six.
If you had Volume Three open to the place mentioned above, and were told to move forward two volumes, sixteen chapters, and three sections, you would doubtless put Volume Three back, take down Volume Five, then count forward sixteen chapters and three sections. This may be represented as a non-commutative arithmetic operation:
A similar case, but with an offset remaining within the first volume, is shown in this example:
* The first non-zero offset element is added to the corresponding element of the initial position.
* The remaining elements of the final position are equal to the remaining elements of the offset.
This sort of numbering system is widely used in military documents, to permit insertion of material at any point without renumbering subsequent parts. Note that if one does not identify particular parts of a tumbler with any particular level of text, then one can insert a book's worth of material (with appropriately numbered chapters, etc.) between any two characters. This merely involves appending to the number for the first character a "." followed by a "1" (for the first item inserted between those two characters). The body of the book could be numbered by appending further tumbler elements.