The Garden of Forking Paths

This article is a transcript of a lecture given at BorgesConf 2014 in Viterbo, Italy.

Hi, everybody!

Before getting to my topic I would like to thank Alvaro for organizing this awesome event. I think that he deserves three huzzas. So here we go: Huzza! Huzza! Huzza!

I was also asked to mention that Medioera festival begins here in Viterbo in just few days. Those of you who are interested in digital culture may consider prolonging your stay here.

Finally, there's an Alfajor stand beneath the stairs in the main hall. Go and try it. It's delicious!

[Some barely audible mumbling about the length of the microphone cable.]

Hi, again!

Recounting the story of illustrious Ts'ui Pen to this audience would be carrying coals to Newcastle. However, for the sake of strangers who may have strayed here from the street, let me mention that when Ts'ui Pen retired from the government service he claimed it was so that he can write a book. Others have reported that he said that he wanted to build a labyrinth. But when he died, the labyrinth was never found and instead of the book there was just a shapeless mass of contradictory rough drafts.

Many years later English sinologist named Stephen Albert realized that when saying those two different things to different people, Ts'ui Pen was actually referring a single thing. A book that was, at the same time, a labyrinth.

Let me read you the quote… Uhm, let me see: "In all fiction, when a man [the writer] is faced with alternatives he chooses one at the expense of the others. In the almost unfathomable Ts'ui Pen, he chooses - simultaneously - all of them. He thus creates various futures, various times which start others that will in their turn branch out and bifurcate in other times. This is the cause of the contradictions in the novel."

But as always, Borges is Herbert Quain in disguise. His stories are like Quain's "Statements", short, cryptic, intentionally unfinished, left for less talented writers to use as a starting point for their own five hundred page long novels. I believe that a substantial portion of this gathering has, at one time or another, fallen into that trap.

Similarly, the story of Ts'ui Pen postulates the existence of the book, that Everett monster, where all possible story lines are explored in parallel, but it remains conspicuously silent about how exactly was this chimaeric cross between a novel and a maze constructed.

The only example it gives are two story lines that merge into a single one. In one case an army marches to battle over a desolate mountain pass. The bleak rocky landscape makes soldiers feel the unimportance of their life and they win the battle easily. In the other case the warriors march through a palace where banquet is being held. The battle seems to them to be just a continuation of the feast and the easy victory follows.

Is short, if you want to write a book that is a labyrinth yourself and when you wonder how to do it, the original story is not very helpful.

However, when sifting through other Borges' stories you can find couple of other hints.

One that comes readily to mind is "April March" by Herbert Quain. Quote. The work is made up of thirteen chapters. The first reports the ambiguous dialogue of certain strangers on a railway platform. The second narrates the events on the eve of the first act. The third, also retrograde, describes the events of another possible eve to the first day; the fourth, still another. Each one of these three eves (each of which rigorously excludes the other) is divided into three other eves, each of a very different kind. The entire work, thus, constitutes nine novels; each novel contains three long chapters. Unquote.

It's the same trick again. Multiple story lines converging into a single story.

You can think of it as of children's "choose your own adventure" books, where, at the end of each chapter, the child can decide what action should be taken by the protagonist.

Except that it's done in reverse. And so a joyful children's story with a single beginning and many possible endings in transformed into a fatalistic nightmare where every possible beginning leads to the same ending.

But here's another quote: "I also recalled that night at the center of the Thousand Nights and a Night [it's the night 602, for those who are curious but too lazy to find out for themselves], when the queen Scheherazade (through some magical distractedness on the part of the copyist) begins to retell, verbatim, the story of the Thousand Nights and a Night, with the risk of returning once again to the night on which she is telling it - and so on, ad infinitum."

Now I bet you are thinking: "Oh my, yes! There can be actual loops in a book!" But hold your horses! Borges is being subtle here, as ever. The bait of looping books is used only to distract you from the reference to the Book of the Thousand Nights and a Night which happens to be a labyrinth itself!

Putting the night 602 aside, the narrative structure of the book is based on embedding — which, if you look at it from a different perspective, may be called branching. Scheherazade entertains the king by a story of a poor fisherman who pulls our a copper jar in his net. There's a jinni inside. Jinni begs the fisherman to let him out. When the fisherman hesitates the jinni tells him a cautionary tale of a raven and a fox. In that story the fox recounts the history of Harun al-Rashid and his wife Zubaydah. And so on and so forth. When reading the book you feel like falling into an abyss, frightened that you'll be trapped inside the nested stories forever, never able to make it back to the surface again.

Now, I hope you agree, we are finally getting somewhere. The Book of the Thousand Nights and a Night, unlike any Borges' story, is an actual full-blown labyrinth. You can even examine its topology. It turns out that — if we disregard the night 602 — it's a mannerist labyrinth, one that, if stretched out, resembles a tree. There are many dead ends but there are no cycles.

Which begs for a question: Are there any labyrinthine books that are modernistic in their topology? Books that can't be really disentangled because they are, by their nature, generic graphs?

Enter Milorad Pavić and his "Dictionary of the Khazars". I am aware that a lot of you here are not familiar with literature of the Balkans, so I'll spend a little… [inaudible] …a dictionary, or encyclopoedia if you will, and therefore, as the preface suggest, you can read it in different ways. You can read one entry at a time. You can read it in alphabetic order. You can follow the cross-references.

You may be tempted to think that every book has exactly one authoritative ordering, namely the ordering of the text on the pages, but with the Dictionary of the Khazars you should reconsider: If the book is translated into a different language, the order of entries and thus the ordering of the text on the pages changes.

Moreover, the Dictionary of the Khazars is not a single dictionary, but rather three distinct dictionaries plus the preface and the appendices. Many entries exists in all three of the lexicons and thus you can explore the same thing from the point of view of Christian, Islamic and Judaistic scholars. The narratives are at times delightfully inconsistent. To give just the most striking example, each dictionary claims that it was their own religion that won the Khazar dispute.

It is also said that the book exists in two editions. A male one and a female one. I cannot comment on that. I own only the male edition…

Yes, I hear you. Paul down here is saying that Pavić has basically re-invented hypertext… Well, you should keep in mind that the book was published in 1984, well before World Wide Web was invented in 1989.

But the remark is a good one. If you want to explore an actual modernistic labyrinth, open your laptop and start browsing. The web is even more labyrinthine than Pavić's book because it has an additional dimension of time. The content appears, changes and disappears all the time. To borrow a metaphor from the popular culture, the labyrinth of the web is castle Hogwarts with its ever shifting corridors and staircases.

Now that we briefly reviewed the literature let me move to the actual science (or art, if you will) of the construction of labyrinths.

I've already mentioned the difference between classical, mannerist and modernist labyrinths, but there's a different classification of labyrinths that will be more useful in our inquiry. Namely, there are "god's perspective" labyrinths and "human perspective" labyrinths.

There's no topological difference between the two. The difference is in how the labyrinth is interacted with.

In god's perspective labyrinth the player is kind of omniscient. He sees the entire labyrinth from the above. These are the labyrinths in children's magazines: "Help Fluffy find the bone." If the goal is to find a man, a lion or a slave in the labyrinth, player can point at them immediately. No walls block his vision. There's no way he can get lost. The complexity emerges from player's limited cognitive or computational capabilities. Although he sees the entire labyrinth, he has no idea how to connect the entry and the exit other than trying out different paths.

Now, you may think that an actual god would have no problem with that. After all, all that it takes to solve a manneristic labyrinth is to make it out of threads, then hold it by the entry and the exit and pull them apart. The straight thread between your hands will be the solution. And if the physics can do that, so can the God, right?

But check out what Scott Aaronson has to say about computational phenomena in physics and you may end up less sure about it. It may be that everything in our universe, maybe even God himself, is bound by computational complexity. Go figure!

Anyway, the other kind of the labyrinth is the human-perspective one. These labyrinths are made of bricks, dwarf box or common hornbeam. The player is inside the labyrinth. He has no idea what's behind the next corner. If there are any items hidden in the labyrinth, or Asterion lurking around, he has no way to know.

Now, if we apply this classification to the labyrinthine books we've reviewed so far it turns out that all of them are god-perspective labyrinths. The reader is free to start reading from any place, jump between the chapters and so on. She's limited only by her ability to consume and process the text.

And I am finally getting to the core of my lecture, which is this: Can we make a human-perspective labyrinth that is a book? Is it possible to get lost in a book as you get lost in Hampton Court Maze or in Masone Labyrinth?

Let's see.

We've already mentioned the web and, apparently, it's easy to create a human-perspective labyrinth there. All it takes is to make each chapter a separate web page and to connect them via hyperlinks. Each URL, of course, has to be a Babelic letter soup, so that players can't guess the URLs in advance.

But there was no Internet at Ts'ui Pen's time and if there were, I think he would disapprove of it. The labyrinth has to be drawn on a hand-made paper with a fine brush. It has to be done properly, by kindling black fire on top of white fire.

So again, can we do this in a printed book?

First, we would need to duplicate the hypertext structure in a printed book. But, as we know from Pavić, that's a pretty easy thing to do. We can use Pavić's lexicon model, or, alternatively, we can just number the chapters and link them via comments like "Continue reading at chapter 108."

It we want to fork paths, we can have two or more such links in a chapter. If we want to join paths we have to… well, noting really, you just have to [inaudible]. This way we can turn the text into an arbitrary directed graph.

Second, we have to enforce the human-perspectiveness by preventing the reader from jumping around in the text. At the first glance it seems that that's not possible. There is no way to prevent the reader from opening the book at random page and reading whatever there is. But once you try to think outside the box, more than one option arises.

You can, for example, hide the real content of the book among irrelevant stuff, Where's-Waldo-style. If the book is full of old news articles, letters, accounting statements, fragments of boring novels, and nonsensical diagrams it means that reader who randomly opens the book will, with a high probability, end up reading the fluff. For added fun, you can make the fluff contradict the actual content on the book.

Then there's a different kind of book that cannot be read from a random place. Namely a language textbook. Good luck with opening your Chinese textbook at chapter 52 and trying to understand what's going on there. In this particular case the ability to read a chapter depends on reading the previous chapters which, in turn, imposes linear order of reading.

Finally, we can relax the no-jumping requirement. We can acknowledge that preventing the reader from reading a random text in the book is hard, but we can require that if she does so she won't be able to proceed in any meaningful way.

Let's first consider the case of finding the previous chapter. Given that the graph is directed, there's no easy way to do that. If you are into cryptography you may think of it as an one-way function. Chapter 12 may say "continue reading at chapter 93" but if the first chapter of the book that you have read was chapter 93, you have no easy way to find out that chapter 12 points to it. Unless it's an e-book, that is. Is such case you can search for the string "93". Problem solved, right? But not so fast! What if chapter 12 says "continue reading at chapter ninety three", the number spelled out? Searching for digits nine and three won't help. And what if it says "continue reading at chapter 90 + 3"? Your e-reader device would eventually need a human-level intelligence to solve these kinds of puzzles.

What about finding the next chapter? Can we prevent that? Surely, if the current chapter says "continue reading at chapter 93" there's no way to prevent the reader from finding out that she should continue reading at chapter 93?

Well, remember the trick with the Chinese textbook! If Chinese numeral characters are introduced in chapter 108, which has a link to chapter 12, which in turn says "continue reading at chapter 九十三" the reader who have started reading at chapter 12 has no idea where to go next.

As can be seen, while a true human-perspective labyrinth may not be doable without making it prohibitively hard for the readers — such as expecting them to learn Chinese or to decrypt encoded text — we can get pretty close with rather humble means.

I originally wanted to end the lecture here but I see I have two minutes left before the Q&A… Correct? … Good. Let me explore one more topic then.

Specifically, I can create dynamic content on the web. I can make a link point to a different chapter on the nights when moon is full. But can we do something similar in a printed book? Any ideas, anyone?


Well that would work for a magazine, but not for a book…


Anyway, here's an idea: We already have these small puzzles at the end of each chapter. Stuff like "continue reading at chapter 90 + 3" or "continue reading at chapter 九十三". What if we had a Sudoku there instead? The text would say "solve this Sudoku and whatever number appears in the top right corner is the next chapter to read".

But, unbeknownst to the reader, the Sudoku will have two possible solutions, sending different readers along different narrative lines. Generally speaking, you could expect half of the reader population to read one story and the other half to read a different story. If two such people ever met they would have to compare their notes and do some literary debugging to find out what actually happened.

And yes, we are definitely out of time now.

Any questions?

[the recording ends at this point]

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