Knots, twists, and meaning

One of the most curious relics of the past, and one which is a persistent mystery, is the quipu (also spelled khipu) of Andean South America.

A quipu is a linked series of knotted, dyed cotton strings, and were apparently some kind of meaningful device -- but what their meaning was is uncertain, thanks to the thoroughness and determination of Spanish priests in the sixteenth century to destroy whatever they could of the "pagan" Inca culture.  The result is, there are only 751 of them left, which is a pretty small sample if you're interested in decipherment.

An Incan quipu in the Larco Museum, Lima, Peru [Image licensed under the Creative Commons Claus Ableiter nur hochgeladen aus enWiki, Inca Quipu, CC BY-SA 3.0]

A number of attempts have been made to understand what the patterns of knots meant, but none of them have really panned out.  Some of the possibilities are that they were devices for enumeration, perhaps something like an abacus; a literary device for recording history, stories, or genealogies; or census data.

In fact, the jury's still out on whether they encode linguistic information at all.  An anthropologist named Sabine Hyland has suggested that they do; the color, position of knots, and even the ply of the string combine in 95 different ways to represent a syllabic writing system, she says, and claims that they were intricate family records.  If she's right, the burning of the Incan quipus represents a horrific eradication of the entire cultural history of a people -- something the invading Europeans were pretty good at.

The reason the topic comes up is because of a paper that came out last week in Nature Communications that has a striking parallel to the quipu.  The paper, titled "Optical Framed Knots as Information Carriers," by Hugo Larocque, Alessio d'Errico, Manuel Ferrer-Garcia, and Ebrahim Karimi (of the University of Ottawa), Avishy Carmi (of Ben-Gurion University), and Eliahu Cohen (of Bar Ilan University), describes a way of creating knots in laser light that could be used to encode information.  The authors write:

Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots.  However, unlike simpler types of structured light, the topological properties of these optical fields have hitherto remained more of a fundamental curiosity as opposed to a feature that can be applied in modern technologies.  Due to their robustness against external perturbations, topological invariants in physical systems are increasingly being considered as a means to encode information.  Hence, structured light with topological properties could potentially be used for such purposes.  Here, we introduce the experimental realization of structures known as framed knots within optical polarization fields.  We further develop a protocol in which the topological properties of framed knots are used in conjunction with prime factorization to encode information.

"The structural features of these objects can be used to specify quantum information processing programs," said study lead author Hugo Larocque, in an interview in Science Daily.  "In a situation where this program would want to be kept secret while disseminating it between various parties, one would need a means of encrypting this 'braid' and later deciphering it.  Our work addresses this issue by proposing to use our optical framed knot as an encryption object for these programs which can later be recovered by the braid extraction method that we also introduced.  For the first time, these complicated 3D structures have been exploited to develop new methods for the distribution of secret cryptographic keys.  Moreover, there is a wide and strong interest in exploiting topological concepts in quantum computation, communication and dissipation-free electronics.  Knots are described by specific topological properties too, which were not considered so far for cryptographic protocols."

A few of the research team's knotted beams of light

I have to admit that even given my B.S. in physics, most of the technical details in this paper went over my head so fast they didn't even ruffle my hair.  And I know that any similarity between optical framed knots and the knots on quipus is superficial at best, but even so, the parallel jumped out at me immediately.  Just as the Incas (probably) used color, knot position and shape, and ply of the string to encode information, these scientists have figured out how to encode information using intensity, phase, wavelength, polarization, and topological form to do the same thing.

Which is pretty amazing.  I know the phrase "reinventing the wheel" is supposed to be a bad thing, but here we have two groups independently (at least, as far as I know) coming up with analogous solutions for the same problem -- how to render information without recourse to ordinary symbology and typography.

Leaving me awestruck, as always, by the inventiveness and creativity of the human mind.

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Have any scientifically-minded friends who like to cook?  Or maybe, you've wondered why some recipes are so flexible, and others have to be followed to the letter?

Do I have the book for you.

In Science and Cooking: Physics Meets Food, from Homemade to Haute Cuisine, by Michael Brenner, Pia Sörensen, and David Weitz, you find out why recipes work the way they do -- and not only how altering them (such as using oil versus margarine versus butter in cookies) will affect the outcome, but what's going on that makes it happen that way.

Along the way, you get to read interviews with today's top chefs, and to find out some of their favorite recipes for you to try out in your own kitchen.  Full-color (and mouth-watering) illustrations are an added filigree, but the text by itself makes this book a must-have for anyone who enjoys cooking -- and wants to learn more about why it works the way it does.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Knotty problem

As a language geek, the loss of our ability to understand communication from past civilizations always strikes me as tragic.

It's worse when that loss was the deliberate work of people trying to silence a culture.  This is the case with the strange and fascinating khipus (also spelled quipus), a set of strings with knots that the Incas used to encode something -- we're not sure what -- and which were systematically destroyed in the 17th century by the Spanish, who were suspicious of a system of communication they couldn't understand, and worried about how it might be used against them.

It's probable that they served more than one purpose -- as most written languages do -- one of which was enumeration.  There are current Andean societies that make at least limited use of khipus for keeping track of numbers of livestock,  But it's far from clear that this was their only use; after all, the Latin alphabet and Arabic numerals can be used for everything from shopping lists to censuses to history texts to telling a story.

[Image licensed under the Creative Commons Claus Ableiter nur hochgeladen aus enWiki, Inca Quipu, CC BY-SA 3.0]

Part of the problem with decoding them, however, is the same difficulty faced by anyone trying to decipher the Plougastel-Daoulas inscription that I wrote about a few days ago; there simply aren't many of them left.  The Spanish priests who gathered up and burned every khipu they could find simply did their job too well.

The other problem is the one I referenced in the same post, in connection to Linear B and the Voynich Manuscript; we don't even know how the knots correspond to units of language.  The type of knot seems as significant as the spacing, as does the color of the thread, but what any of those features mean is at this point speculation at best.

Another piece of the puzzle was added this week, however, in a paper authored by Alejandro Chu and Gary Urton in the journal Latin American Antiquity.  Chu has discovered 29 khipus at a site called Qolqawasi, and each one was found with quantities of edibles -- chili peppers, peanuts, and other regional crops.  This has led Chu and Urton to theorize that the khipus represented quantities of produce -- and, perhaps, the amount of taxes to be collected on it.  The authors write:

These khipus contain a formulaic arrangement of numerical values not encountered on khipus from elsewhere in Tawantinsuyu (the Inka Empire).  The formula includes first, a large number, hypothesized to record the sum total of produce included in a deposit, followed by a “fixed number,” and then one or more additional numbers.  The fixed number plus the additional number(s) sum to the original large number.  It is hypothesized that the fixed number represents an amount deducted from the deposit to support storage facility personnel.  As such, it represented a tax assessed on deposits, the first evidence we have for a system of taxation on goods in the Inka Empire.  It is proposed that the size and complexity of the storage facility at Inkawasi prompted the “invention” of a kind of financing instrument—taxation—not known previously from Inka administration. 

Their interpretation is not certain -- witness the number of times they use the word "hypothesized" and "proposed" -- but it's an intriguing possibility.  Whether the khipus were used for other purposes, such as in place of a written language, is still worth considering.  It's to be hoped that there will be additional discoveries of these odd artifacts, and that at some point the work of archaeologists such as Chu and Urton will lead to a complete decipherment -- and these voices from the past won't turn out to have been silenced completely.

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Aptly enough, considering Monday's post about deciphering scripts, this week's Skeptophilia book recommendation is Steven Pinker's brilliant The Stuff of Thought.  Here, experimental psychologist Pinker looks at what our use of language tells us about our behavior and neural wiring -- what, in fact, our choice of words has to do with human nature as a whole.

Along the way, he throws out some fascinating examples -- my favorite of which is his section on the syntax of swearing.  I have to admit, the question, "Just what does the 'fuck' in 'fuck you' actually mean?" is something I've never thought about before, although it probably should have given that I'm guilty of using the f-word a lot more than is generally considered acceptable.

So if you're interested in language, the human mind, or both, this is a must-read.  Although I'll warn you -- if you're like me, it'll leave you thinking, "Why did I just say that?" several times a day.