Long-range dependance
How many days make your year worth living?
It's a sunny day. You pick up a book someone abandoned on a park bench. It's an intricate crime novel. You read through the book passionately. Every page builds up the intrigue with suspense. You arrive to the end, ready for mystery's solution, only to realise with dismay that the last page is missing. Someone tore it out.
They left a quirky ransom note. They demand the full price of the book just for that one missing page. What do you do? It feels extortionate, but you decide to pay. After all, it's just the fair price marked on the back cover and you had not payed for the book.
Now, imagine that instead of a crime novel it was a (possibly infinite) dictionary. Would you ever pay for the final page or any other missing page?
No, you probably would not even notice. In these cases, paying is harder to justify . The marginal contribution of any random page is close to zero, especially as the dictionary size grows. Without the missing page, you'd have a perfectly functioning dictionary 99.99% of the time.
You could ask the reverse question for any story:
How many pages do you have to take out of a book, so that they'd be worth as much as the entire novel?
You'd end up with a metric of the global long-term dependence in a story.
In the dictionary the contribution of the individual pages is (marginally) null. On the other end, the crime novel has a fat-tail distribution, where some pages have a value (exponentially!) greater the mean value of any other page.
What kind of distribution does our daily experience follow?
Never trust a random book you pick up, it might be poisoned!
David