Short-range dependance
Tell me something about a story without telling me anything about the story
Alice and Bob are cousins. Alice loves reading. Bob does not but likes to spend time with Alice. Since she passes all her days assorted in her books, he misses her attention. So, one day, he comes up with a mischievous plan: every time Alice starts a new novel, he’ll pick it up as well from the library. Then, he’ll begin reading it, but starting a few pages ahead. This way, he can spoil her reading and she can hear the story told by him.
Assume they read exactly at same speed: one page every night (Alice is a keen reader, but Bob is a little older). Assume Bob cannot browse through the book, but only choose one page (a certain lag) continue reading from that point onwards.
So, here's a question.
How many pages in advance should Bob start reading? What's Bob's optimal lead?
Many would say: it really depends on the story! What kind of novels does Alice like to read? What kinds of stories?
Bob has a general intuition. Start from too far (last pages) and the new information may be irrelevant to her current point in the story. Start from too close (1-2 pages) and most of the days he might have just mundane anticipations and nothing good to share… unless the story is so well written!
- “Wouldn’t be amazing if Alice only read page-turners!”, Bob sights. Informationally dense novels are hard to predict, but easy for Bob’s anticipation game. The next page, by definition of a page-turner, is already worth spoilering!
In some sense, we can say that, correlation functions (Alice and Bob narrative points-of-view entangling) showcase the story’s time-structure.
Short-range dependent process, the coupling between values at different times decreases rapidly as the time difference (lag) increases. Either the auto-covariance drops to zero after a certain time-lag, or it eventually has an exponential decay. In the case of Long-range dependence, there is much stronger coupling. (Wikipedia)
Alice is smart. One day she figures out Bob's game and decide to only read dictionaries.
Until the next one,