About Ashok Khosla

“Throughout the day, I explore the remnants of civilizations long gone, piecing together their stories & secrets. In the absence of life, these vestiges of the past are my only companions, whispering their tales of triumph & tragedy. As the sun begins to set, I return to the Ark of Apocalypse, my collection of artifacts growing ever larger. I study each relic, meticulously documenting its properties & potential uses, ever aware of the responsibility I carry.”

Graphic Novelist Awet Moges

Inka khipus remain one of the world’s last undeciphered historical mediums. Are they writing? or just record-keeping? What do they mean? We admire the Arabs who brought us the concepts of 0 and base 10, and replaced Roman mathematics. The Inkas did that also. We admire the Romans who conquered a continent. The Inkas did that also. I could keep going but you get the idea. As an American immigrant, I am painfully aware, how notably blind “western civilization” is to the accomplishments of our South American neighbors.

The Inka’s unique approach to communication, using cloth as a medium, has fascinated me for much of my adult life. As a child I loved to read books about scripts and symbols’s - I reveled in The Glass Bead Game (see below), and could easily transport myself into the role of a novitiate monk - building universes on symbols represented by glass beads. The patterns of chess became my first “glass bead game.” and then the delightful inventions of algebra and calculus. As a young unemployed architect, I read with fascination, and a little bit of envy, the story of British architect Michael Ventris. Ventris built on the work of Alice Kober to decipher the Mycenaean Greek script Linear B. As an adult, I have been amazed at how rapidly 2000 years of Mayan writing have became understood in a mere 50 years. It is an incredibly moving thing to hear Linda Schele recite the history of a people from a thousand years ago, in their own language.

Twenty years ago, I picked up Ascher’s Mathematics of the Incas - Code of the Quipu in a Berkeley California bookstore. After a quick read, it sat on my bookshelf waiting to inspire me again. For the last thirty years I have worked in the field of Natural Language Processing (NLP). We used to call it Computational Linguistics, but frankly we were never very good linguists, and Natural Language Processing is a humbler and more accurate term. We’re the idiot savants that provide the 21st century equivalent of the secretarial pool. Every once in a while, I’d think, gee - could I apply everything I’m learning in NLP to khipu decipherment? Then a few years ago I met a professor in Ecuador, and I started learning Quechua, and before I knew it … I had become a knot-head.

In the last 70 years, decipherment has become a community activity. Everyone contributes some little tiny thing, and then all of a sudden - !!!WHAM!!! a key synthesis emerges from all those little things. Any language dreamer dreams that they might be The One, who after enough hard work, gains an insight that changes directions. But the truth is, we dreamers… (yes, I’m one)…, we dreamers are content if we are able to contribute one tiny thing. This, perhaps, is my one tiny thing.

I am indebted to three scholars who have aided my education and the creation of this Field Guide.

Project Scope

This is a large project. As such it is divided into three phases:

Phase 1 - Reading and Writing (Completed)

In phase 1 a basic understanding of khipu was achieved. This involves five steps.

  1. Yak Shaving - All data science projects start by yak-shaving, the affectionate name for the process of cleaning data, checking for integrity, etc. This project was no different - Sadly, integrity checks led to a loss of one-sixth of the khipus from the database. After removing the khipus that failed integrity checks, the Harvard Khipu Database SQL tables were transformed into CSV spreadsheets capable of being viewed in a variety of applications. The current database, now the largest well-formed khipu database in the world, has taken over 3 years to build.

  2. Exploratory Data Analysis - What kinds of knots are there, how are knots, cords, cord colors and clusters distributed. What are likely spreadsheet khipus, and what are possibly something else such as a narrative khipu? What things do we want to emphasize in rendering?

  3. Class Building - Simple Python functions and the Python Pandas Dataframe library will not easily provide the type of functionality and interface we need to draw khipus and do more sophisticated data analysis. A Python class object has been built built for each Khipu component, knot, cord, cord color, cord cluster, primary cord etc. This class library then supports the rendering of Khipu and of more tailored types of data inquiry and output.

  4. Khipu Rendering - Many khipu scholars regard khipu as a “tactile medium” (think of khipu reading as a kind of braille for example). Understanding them from CSV tables, is the farthest thing from tactile. Rendering is needed. Producing the code to satisfactorily render khipu has taken four months. As the Russians say, “It’s not a miracle the bear dances well. It’s a miracle the bear dances at all.”

Phase 2 - Reproduction of Existing Studies (Ongoing)

Phase 2 of this project (now underway) is an exploration of existing work in khipu analysis. In this phase, I will attempt to identify and reproduce studies of existing khipu, such as Lockes UR166, or Urton’s Calendar Khipu UR006, the Ascher’s analyses of the Ascher khipus, Manny Medrano’s analyses of the Santa River khipus, the Pleiades star chart, etc. This journey will provide the smorgasboard of analyses types and analytical tools needed to do more decipherment.

Phase 3 - Using Data Science and Natural Language Processing (NLP) Techniques (Ongoing)

In Phase 3 modern Data Science and NLP techniques are being applied to Khipu.

The great bird educator and ornithologist, Roger Tory Peterson, produced the first bird “field-guide” of the modern age. Rather than simply showing a picture of a duck, Peterson had arrows that pointed out key features of a particular duck to look for in identification. The increased curve (the 2nd derivative in mathematical terms) of a bill of an avocet allowed you to identify it as female or male; the presence of a white rump patch allowed you to confirm that the raptor was in fact a northern harrier, etc. Now known as Fieldmarks, these key identification traits will be the outcome of Phase 3.

What types of Fieldmarks will we look for? As examples, we can examine verso/recto cord attachments, or the presence of Z vs S knots (i.e. Urton’s studies), or we could look for color and patterns (i.e. Sabine Hyland’s work), or cord distribution and summation patterns (i.e. Marcia Ascher’s detailed studies). Whenever I see something intriguing (as in it stands out), and at a higher level than a simple knot or cord characteristic, it will be noted as a potential Fieldmark. The goal of Phase 3 then, is to finish with a set of Fieldmarks that allow us to categorize khipu by “Family” - hence the name of this site - the Khipu Field Guide.

There is an old joke. Stupid scientist does an experiment with a frog.
    Jump Froggy! he says. Frog jumps. Stupid scientist cuts off one leg.
    Jump Froggy! Jump he says. Frog jumps. Another leg. Another jump.

    Finally he cuts off the last leg.
    Jump Froggy! Jump! Nothing happens. He yells louder
    JUMP FROGGY!!!! JUMP!!!! Nothing happens.

He writes in his lab notebook, “After cutting off fourth leg, frog became deaf.

So it is with khipu analysis. The decoding of unknown “languages” is fraught with stupid science. The goal is to use modern data science to tease out more information about khipus. Like Pygmalion, I want khipus to speak. I suspect, however, at the end of the day, I will be ecstatic, if I simply get them to mumble, squeak, or even make the sound of a punctured balloon.

Magister Ludi - The Glass Bead Game, by Herman Hesse

“Let no one, therefore, expect from us a complete history and theory of the Glass Bead Game. Even authors of higher rank and competence than ourself would not be capable of providing that at the present time.

That task must remain reserved to later ages, if the sources and the intellectual prerequisites for the task have not previously been lost. Still less is our essay intended as a textbook of the Glass Bead Game; indeed, no such thing will ever be written. The only way to learn the rules of this Game of games is to take the usual prescribed course, which requires many years; and none of the initiates could ever possibly have any interest in making these rules easier to learn.

These rules, the sign language and grammar of the Game, constitute a kind of highly developed secret language drawing upon several sciences and arts, but especially mathematics and music (and/or musicology), and capable of expressing and establishing interrelationships between the content and conclusions of nearly all scholarly disciplines. The Glass Bead Game is thus a mode of playing with the total contents and values of our culture; it plays with them as, say, in the great age of the arts a painter might have played with the colors on his palette. All the insights, noble thoughts, and works of art that the human race has produced in its creative eras, all that subsequent periods of scholarly study have reduced to concepts and converted into intellectual property – on all this immense body of intellectual values the Glass Bead Game player plays like the organist on an organ. And this organ has attained an almost unimaginable perfection; its manuals and pedals range over the entire intellectual cosmos; its stops are almost beyond number. Theoretically this instrument is capable of reproducing in the Game the entire intellectual content of the universe. These manuals, pedals, and stops are now fixed. Changes in their number and order, and attempts at perfecting them, are actually no longer feasible except in theory. Any enrichment of the language of the Game by addition of new contents is subject to the strictest conceivable control by the directorate of the Game. On the other hand, within this fixed structure, or to abide by our image, within the complicated mechanism of this giant organ, a whole universe of possibilities and combinations is available to the individual player. For even two out of a thousand stringently played games to resemble each other more than superficially is hardly possible. Even if it should so happen that two players by chance were to choose precisely the same small assortment of themes for the content of their Game, these two Games could present an entirely different appearance and run an entirely different course, depending on the qualities of mind, character, mood, and virtuosity of the players.

How far back the historian wishes to place the origins and antecedents of the Glass Bead Game is, ultimately, a matter of his personal choice. For like every great idea it has no real beginning; rather, it has always been, at least the idea of it. We find it foreshadowed, as a dim anticipation and hope, in a good many earlier ages. There are hints of it in Pythagoras, for example, and then among Hellenistic Gnostic circles in the late period of classical civilization. We find it equally among the ancient Chinese, then again at the several pinnacles of Arabic-Moorish culture; and the path of its prehistory leads on through Scholasticism and Humanism to the academies of mathematicians of the seventeenth and eighteenth centuries and on to the Romantic philosophies and the runes of Novalis’s hallucinatory visions. This same eternal idea, which for us has been embodied in the Glass Bead Game, has underlain every movement of Mind toward the ideal goal of a universitas litterarum, every Platonic academy, every league of an intellectual elite, every rapprochement between the exact and the more liberal disciplines, every effort toward reconciliation between science and art or science and religion. Men like Abelard, Leibniz, and Hegel unquestionably were familiar with the dream of capturing the universe of the intellect in concentric systems, and pairing the living beauty of thought and art with the magical expressiveness of the exact sciences. In that age in which music and mathematics almost simultaneously attained classical heights, approaches and cross-fertilizations between the two disciplines occurred frequently. And two centuries earlier we find in Nicholas of Cues sentences of the same tenor, such as this:”The mind adapts itself to potentiality in order to measure everything in the mode of potentiality, and to absolute necessity in order to measure everything in the mode of unity and simplicity as God does, and to the necessity of nexus in order to measure everything with respect to its peculiar nature; finally, it adapts itself to determinate potentiality in order to measure everything with respect to its existence. But furthermore the mind also measures symbolically, by comparison, as when it employs numerals and geometric figures and equates other things with them.”

Incidentally, this is not the only one of Nicholas’s ideas that almost seems to suggest our Glass Bead Game, or corresponds to and springs from a similar branch of the imagination as the play of thought which occurs in the Game. Many similar echoes can be found in his writings. His pleasure in mathematics also, and his delight and skill in using constructions and axioms of Euclidean geometry as similes to clarify theological and philosophical concepts, likewise appear to be very close to the mentality of the Game. At times even his peculiar Latin (abounding in words of his own coinage, whose meaning, however, was perfectly plain to any Latin scholar) calls to mind the improvisatory agility of the Game’s language.As the epigraph of our treatise may already have suggested, Albertus Secundus deserves an equal place among the ancestors of the Glass Bead Game. And we suspect, although we cannot prove this by citations, that the idea of the Game also dominated the minds of those learned musicians of the sixteenth, seventeenth, and eighteenth centuries who based their musical compositions on mathematical speculations. Here and there in the ancient literatures we encounter legends of wise and mysterious games that were conceived and played by scholars, monks, or the courtiers of cultured princes. These might take the form of chess games in which the pieces and squares had secret meanings in addition to their usual functions. And of course everyone has heard those fables and legends from the formative years of all civilizations which ascribe to music powers far greater than those of any mere art: the capacity to control men and nations. These accounts make of music a kind of secret regent, or a lawbook for men and their governments. From the most ancient days of China to the myths of the Greeks we find the concept of an ideal, heavenly life for men under the hegemony of music. The Glass Bead Game is intimately bound up with this cult of music (“in eternal transmutations the secret power of song greets us here below,” says Novalis).

Although we thus recognize the idea of the Game as eternally present, and therefore existent in vague stirrings long before it became a reality, its realization in the form we know it nevertheless has its specific history. We shall now attempt to give a brief account of the most important stages in that history.”

Magister Ludi (The Glass Bead Game)Herman Hesse