Glimpses of Dozenalism in Tlon

On Borges' reference to a failed movement to remake the world in one of his most well-known stories.

A while ago, I wrote a commentary on one of the stories from “Fictions” by Borges and promised to follow up with some others. After much delay I have finally begun fulfilling my promise. Furthermore, the story I shall write about is one of Borges’ most famous works, “Tlon, uqbar, Orbis Tertius”.

For those who unfortunately have no idea of what this story is about, it is essentially a tale of a man, the narrator, who learns of a mysterious land called “Uqbar” from a friend who claims to have read about it in an Encyclopedia. When they both fail to find the entry for this country in a different copy of the same Encyclopedia the Narrator and his friend go on a quest to find anything about the mysterious land of “Uqbar”. Eventually it is revealed that the country of “Uqbar”, and the alien world of “Tlon” that it exists in, is the fictional work of a secret society of intellectuals who were founded by a rich Atheist who wanted to prove to “God” that humanity was just as capable of making a world as diverse and complex as the real one. The plot twist that makes this short story of Borges so memorable is that as awareness of this great work of fiction spreads people become so fascinated by it that they begin to forsake the “Real” world for “Tlon”, to the point that they begin teaching and studying this fictional world in school.

This classic tale of Borges is usually interpreted as being an exaggerated metaphor of how not only fiction, but works of ideology and philosophy, can figuratively “change the world”, or more precisely cause us to radically (mis?)interpret how we perceive it, alter our memory of its history to the point that it may as well have been truly rewritten, and forsake reality for the imaginary in general¹. I have no qualms with this view as I agree with this interpretation of the story. Rather, the purpose of this essay is to bring attention to an allusion about an obscure intellectual movement that I noticed within the story that develops its message in an interesting way.

Now, at this point any Borges scholars who are expecting me to talk about the Rosicrucians will be surprised to learn that this is not the case. The Rosicrucians, who are mentioned a few times in the story and are clearly something of an inspiration for it, are a group of Christian esoteric philosophers who's entire society and philosophy was originated by a book that was written as a parody of the kind of Christian-mystic books that were popular in the 17th century, that was so well written that it inspired some of its readers to make its fictional society a reality.² This reference is explicit enough that it is already well known to most readers of Borges, and thus needs no commentary. It is another society less explicit in the story and less successful in reality that is the subject of this essay. This society, or rather intellectual movement, is Dozenalism.

Dozenalism is the name given to a certain belief popular amongst a few intellectuals, especially mathematicians, that we should replace the common decimal/Base 10 system of mathematics with a Duodecimal/base 12 system instead. Any readers confused as to what a “Base” is, or why some believe that one base is superior to others should probably read the Dozenal societies’ own explanations about these things as they do a better job of it than I could. My only goal here is to explain the interesting way Borges references Dozenalism in his story and its relevance to the story’s central theme.

It is in the second part of “Tlon, Uqbar, Orbis Tertius” that the Duodecimal number system is first mentioned, in the conversation the narrator has with a friend and engineer named Herbert Ashe. Herbert Ashe apparently has been entrusted by some Norwegian man with the task of creating a conversion table for translating duodecimal numbers into Base 60/Sexagesimal numbers, presumably (I theorise, as it is never explained in the story) for some obscure purpose involving Astronomical instruments and calculations since the Sexagesimal number system was often used for such purposes since classical times. The duodecimal system is mentioned a second time, as a footnote, where the narrator explains that a century would last 144 years in a duodecimal system of time-reckoning. These two references of the Duodecimal number system are the only explicit and obvious ones in the story. But after some meditation I realised that there were also two other hidden and implied references as well, which are only perceivable if you are acquainted with how the Duodecimal number system works.

(If you haven’t yet, I suggest reading through the Dozenal society’s introduction material, as it will make this explanation easier to grasp.)

The Duodecimal number system is composed of eleven digits, rather than nine as in the Decimal system. Just as we write “10” after counting past nine, the Dozenalist writes “10” after counting past eleven for exactly the same reason. Once this is grasped a seemingly trivial detail in the story becomes quite significant, which is the prevalence of the number eleven.

There are eleven volumes of “The encyclopedia of Tlon”, and it is the 11th volume that is first discovered by the narrator. Furthermore, the name of the man who introduced the readers to the Duodecimal number system, Herbert Ashe, is composed of eleven letters.

Now that I have revealed these subtle references to Dozenalism, I must now explain their relevance. To do this, let us briefly return to Rosicrucianism.

Rosicrucianism, despite originating in the 17th century, is still a living spiritual tradition in the modern world that, unlike many others, is fairly common and dominant in the modern world. So much so that, against modern expectations, up to the 20th century advertisements for this society were a common thing to find in “Popular mechanics” and other science-themed magazines. I shall not go into too much detail about its beliefs and rituals, but it should be clear that a spiritual movement only attains such success when it fulfills the various needs of its adherents, such as explaining certain aspects of life and offering ways to improve the self, while also attracting a constant stream of newcomers due to wide appeal to many different demographics, along with the obvious enjoyment current members display in participating in it. Rosicrucianism clearly fulfills these requirements.

Now, let’s compare Rosicrucianism with Dozenalism. Dozenalism focuses purely on the improvement of a narrow area of day-to-day life, Arithmetic. It doesn’t offer much else beyond this. And not only does it focus on a rather uninspiring aspect of human existence, its contributions to improving our relation to it is at best moderate in its effects. It also appeals to a very narrow slice of the world’s population, intellectuals with mathematical inclinations or mathematicians with revolutionary inclinations. It appeals largely to one’s intellectual curiosity rather than anything more enduring and appealing to one’s passions. All in all, it is clear why Rosicrucianism succeeds and Dozenalism fails.

Returning to the story, one realises the reason for Borges’ subtle inclusion of this obscure movement in a story about how great works of mind and imagination, invented and propagated by a small group of individuals, can entrance the world. It is a hidden example of the kind of contrast between two related yet opposite concepts he was so fond of.

One society, Rosicrucianism, appeals to the many. One society, Dozenalism, appeals to the few. The former succeeded in gaining power in the world, while the latter failed. The former answers the many questions of life, the latter offers an answer to one. The former focuses on the greater world of spirit, the former on some minor island in the world of the mind. And finally, while the former is mentioned explicitly by name, with the latter only the object of its devotion is mentioned at all.

1. One only needs to look at ideologies such as Communism or Ethno-nationalism, Philosophies such as Scientific materialism, and the fandoms of LOTR and Disney to see the process Borges described in action.

2. Any Rosicrucians reading this must not assume that I am denigrating them, by mentioning this historical fact. Very often some of the best and most profound works were inspired by what many would call trivial or crass reasons.