Approaches for Discerning Narrative in Khipus - II - Encoding Decisions that Occur Before the Knots
If Marcia Ascher suggests that the numerical data encoded in the knots of khipus can be enough to assemble a meaningful narrative from them, so long as one came to understand the format of the data encoded in these knots, others point out that the making of the knots on the khipu pendant strings is actually one of the last steps in the making of the khipu. Other decisions are made before the making of the knots that hold the potential of encoding a great deal of information.
In William J. Conklin's contribution A Khipu Information String Theory in Narrative Threads, he notes the number, color composition, material and clockwise or counterclockwise (S or Z) plying of the strands making up the primary chord as well as the knot characteristics of both its ends, already have the potential for encoding a great deal of information about the contents of a khipu.
Further, pendant chords, again of varying material and color composition are generally attached to the primary chord halving the chord and attaching by means of a loop. The halved strands would then be plied (twisted) together again in an S or Z direction and knotted in some way at the chord's end free end. Further the loop by which the pendant is attached to the primary chord may be clockwise or counterclockwise (D or R) from the pendant chord's plied strands extending from its point of attachment to the primary chord.
These are all decisions made by the chord makers, quipocamayos, even before a single numerical knot (of types S, L or E as discussed in a previous post) is made on the pendant chord, and all these decisions have the potential to encode further information beyond that simply encoded in the pendant chord's knots.
Further, subsidiary chords with further encoded information are often attached to the pendant chords, and various special classes of pendant chords, such as top chords (which seem to have a sumation role, giving the sum total of the information present in the pendant chords preceeding them).
So how much information can be stored on a khipu?
At the end of his article in Narrative Threads (p 82-83), Conklin calculates that a single pendant chord, has a "knot represenational capacity of 10,000 [represented in up to four sets of knots each set encoding a numerical value between 0-9], [multiplied by] the knot altar egos (knots made in the opposite directions) say 2, by the possible colors, say 8, by the plying types, say 12, by the possible plying directions, 2, by incidental variables such as accessory threads and basic materials, say 2. Each such secondary chord could theoretically hold a grand possibility of some 8 million differing combinations of states [or infons]. Attaching a [subsidiary] chord then being a modifier of all the information on the [pendant] chord would theoretically square that information capacity. Fourth order chords attached to and used as modifiers of [subsidiary] chords could, each time they occur, square even that number. But certainly only a tiny portion of that vast theoretical information capacity of a khipu was ever in use at one time.
"To compare the information capacity of a khipu with the bit capacity of a computer, one must take the logarith to the base 2 of the number of khipu infons. In the example, 8,000,000 is the estimated possible number of infons in a single pendant chord, whose log produces some 23 bits, comparable to the number of bits in a single word written in the ASCII alphanumeric code used to store information in computers. A single encoded ASCII character of 7 bits covers numbers, capitals, lower case, and afew dozen other characters."
Conklin notes however, "Since there was no written language or alphabet in use when khipu were created, this attempt at the measurement of khipu in bits and as ASCII code is perhaps only a curiosity."
However, as the reader will see in subsequent posts, when the characteristics of the Quechua language are taken into account, both consonant-based and syllabatic interpretations of the information encoded on khipus become possible and perhaps even probable.
Dennis (moderator)
In William J. Conklin's contribution A Khipu Information String Theory in Narrative Threads, he notes the number, color composition, material and clockwise or counterclockwise (S or Z) plying of the strands making up the primary chord as well as the knot characteristics of both its ends, already have the potential for encoding a great deal of information about the contents of a khipu.
Further, pendant chords, again of varying material and color composition are generally attached to the primary chord halving the chord and attaching by means of a loop. The halved strands would then be plied (twisted) together again in an S or Z direction and knotted in some way at the chord's end free end. Further the loop by which the pendant is attached to the primary chord may be clockwise or counterclockwise (D or R) from the pendant chord's plied strands extending from its point of attachment to the primary chord.
These are all decisions made by the chord makers, quipocamayos, even before a single numerical knot (of types S, L or E as discussed in a previous post) is made on the pendant chord, and all these decisions have the potential to encode further information beyond that simply encoded in the pendant chord's knots.
Further, subsidiary chords with further encoded information are often attached to the pendant chords, and various special classes of pendant chords, such as top chords (which seem to have a sumation role, giving the sum total of the information present in the pendant chords preceeding them).
So how much information can be stored on a khipu?
At the end of his article in Narrative Threads (p 82-83), Conklin calculates that a single pendant chord, has a "knot represenational capacity of 10,000 [represented in up to four sets of knots each set encoding a numerical value between 0-9], [multiplied by] the knot altar egos (knots made in the opposite directions) say 2, by the possible colors, say 8, by the plying types, say 12, by the possible plying directions, 2, by incidental variables such as accessory threads and basic materials, say 2. Each such secondary chord could theoretically hold a grand possibility of some 8 million differing combinations of states [or infons]. Attaching a [subsidiary] chord then being a modifier of all the information on the [pendant] chord would theoretically square that information capacity. Fourth order chords attached to and used as modifiers of [subsidiary] chords could, each time they occur, square even that number. But certainly only a tiny portion of that vast theoretical information capacity of a khipu was ever in use at one time.
"To compare the information capacity of a khipu with the bit capacity of a computer, one must take the logarith to the base 2 of the number of khipu infons. In the example, 8,000,000 is the estimated possible number of infons in a single pendant chord, whose log produces some 23 bits, comparable to the number of bits in a single word written in the ASCII alphanumeric code used to store information in computers. A single encoded ASCII character of 7 bits covers numbers, capitals, lower case, and afew dozen other characters."
Conklin notes however, "Since there was no written language or alphabet in use when khipu were created, this attempt at the measurement of khipu in bits and as ASCII code is perhaps only a curiosity."
However, as the reader will see in subsequent posts, when the characteristics of the Quechua language are taken into account, both consonant-based and syllabatic interpretations of the information encoded on khipus become possible and perhaps even probable.
Dennis (moderator)
posted by Dennis Kriz at 8:31 PM
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