Statistical Overview

But just as Yunpacha and his mother left with the Vicha to the place of the stone. There was no moon, but no clouds, and they could be guided by the light of the stars so as not to fall into the abyss that opened on their side, and in which they could hear well below, as if coming from the very entrails of the Pachamama, the murmur of the river.

“Five hundred and forty-six,” Yunpacha said. (counting)



They reached the slope, passed the place of the stone, and continued climbing. His mother was ahead of him, stepping firmly and without slipping on the loose stones despite the weight of the bag in which she carried her offerings, and with the Vicha at her side as if showing her the way.

“Do you know who this Pururauca is ?” Rampac asked him when they were at the top, in front of Warrior’s Rock.


“He’s a Chanka warrior. He survived the battle of Ichupampa, in which the Inca Pachacutec defeated our ancestors, made drums from their skins and glasses of chicha from their skulls. He became stone from crying so much, like all the warriors who survived the defeat and went to spread out on the hills from the Pampas River to the Pachachaca River. There they are, waiting for the Flow of Return to resume their human form and end our submission.”

His mother was silent: she was looking up at the peaks of the neighboring apus.

“Why the Pururauca has given you that power, (to count) I don’t know, Yunpacha. But we have to thank you.”

Excerpt From: Rafael Dumett - El Espía del Inka (The Spy of the Inka)

For more information about how the Inka’s viewed stone (hint - they regarded large stone boulders as numinous - having a strong religious or spiritual quality; indicating or suggesting the presence of a divinity. “the strange, numinous beauty of this ancient landmark”) see Carolyn Dean’s awe-instilling book “A Culture of Stone - Inka Perspectives on Rock”

1. Statistical Fieldmarks

What is a Statistical Fieldmark? Features such as mean cord counts per group, or number of top cords per khipu where we can directly count on the khipu without any additional computation or indirection are considered Statistical Fieldmarks.

When is a khipu’s statistical fieldmark useful? When it is significant! Map the distribution of a statistic and decide what is significant (ie. in the top 1st standard deviation, or existence at all, etc.). Then the process for deciding whether or not to present a statistical fieldmark is to view it’s distribution, look at it’s impact overall in the khipu database, and then decide what constitutes a significant presence or absence of that fieldmark.

In the Khipu Fieldmark Browser, the default test for significance for statistical fieldmarks, is to see if a khipu’s particular value for that mean lies above significantly above the mean or significantly below the mean. An example is Benford Match. For many statistical fieldmarks, however, the mean is close to zero. For example, the mean cord value for most cords lies close to 0, since so many cords are of 0 or 1 value. Consequently, for many statistical fieldmarks, “significance” may lie well above the mean. For some fieldmarks, whose presence is rare (top cords are an example), simply the presence of the fieldmark means it’s significant. These fieldmark-specific significances are a part of the Khipu Fieldmark Browser’s implementation, when it decides which values for a given fieldmark deserve a box’ed/detailed representation.


  • Click on the Fieldmark Name to see the in-depth page about that fieldmark.
  • Click on the # (Number) of Significant Khipus link to see an image quilt of khipus with significant quantity of that fieldmark.
Fieldmark Name Description Num Significant Khipus
Number of Cord Groups The number of cord groups or groups residing on the primary cord. 67 (10%)
Mean Number of Cords Per Group What is the average number of cords per group for the khipu. Some return 28. What could be 28 I wonder? :-) 121 (19%)
Number of Cords The total number of cords for the khipu, including top cords, subsidiary cords, etc. 121 (19%)
Mean Cord Value The mean cord value of all the cords in the khipu. Khipus with really large cord values are in a class all their own. 24 (4%)
Number of Color Bands The number of color bands of length 4 or more, in a khipu. 258 (40%)
Number of Ascher Colors Each cord is assembled from various colors and then woven and tied in a solid, or barberpole, or mottled, etc … manner. This is described by an Ascher Color Operator. This metric returns the number of unique Ascher Color Operators for the khipu. 202 (31%)
Recto/Verso-attached Cords Khipus with verso attached cords. 325/291 (50%)/(45%)
Number of Z Cords Khipus with Z-twisted cords. 80 (12%)
S Knotted Khipus Khipus with S knots in their cords. 310 (48%)
Z Knotted Khipus Khipus with Z knots in their cords. 387 (60%)
Number of Top Cords The number of khipus with top cords. 47 (07%)
Deepest Branch Level Khipus with at least one level of subsidiaries. 382 (59%)

2. Conclusions:

At the beginning the introductory page on fieldmarks, I noted how fieldmarks can be used as identification traits. With that in mind, let’s look at these noteworthy statistical fieldmarks.

  • Small Cord Value Khipus
    The data confirms a hypothesis by Manuel Medrano, that khipus that have had knots that were tied, and then untied, should have a lower value range of knot values, since they are “working khipus”. Of the few samples we have, those khipu’s cord’s untied knots are on the low end of the range for mean cord values.

  • Large Cord Value Khipus
    The large (by cord value) khipus UR188, UR1143, UR1104, UR1119, UR1120, and to some extant UR247 and UR161 are clearly in a field of their own, as is evident in viewing them in the Khipu Fieldmark Browser, when viewing them as a connected graph, or as when examining their low summation counts. When you are measuring something in the waranqa scale of 1000’s, those are unusual numbers. Large cord-value khipus appear to be more of an “executive summary” and less of a working man’s khipu.

  • Top Cords
    A look at the graph of Top cords vs Banded groups/Seriated Groups, along with an examination of the individual khipus with top cords reveals that Manuel Medrano’s hypothesis that top cords are associated with banded groups appears to be true in the KFG data.

  • Recto vs Verso Cord Attachments
    A look at the graph of Recto vs Verso cord attachments says it all. The relationship between these two is lovely to look at.

  • S vs Z Knots
    A match made in heaven, a look at the graph of S vz Z Knot percentage also says it all. The relationship between these two is also lovely to look at. S and Z knots are arranged in a spatial fashion in astronomical khipus, and we can use this fieldmark to identify likely astronomical khipus.

  • Colors
    • Of the 651 colors, the top 200 colors cumulate to 98% of the cords. As expected, the majority of the cords are solid colors - with close to 30% being white!. Mottled colors follow, with barberpoles eventually showing up.
    • White is the most prevalent color, followed by browns of various shades, and mottled colors made from browns and white.
    • Barberpoles may be visually arresting, but the frequency count tells us they seldom (< 0.32%) show up in the khipu record.
    • Cord color frequency distribution rapidly declines, with a very very long tail. In fact this distribution appears to be a power law, something that often appears in linguistic contexts. A classic example of a linguistic power law distribution is Zipf’s Law whose first use by linguist Herman Zipf was to note that a word’s length in characters was inversely proportional to it’s use in language. In light of Sabine Hyland’s Collata khipu discovery that 17th-18th Century Collata khipus/khipu boards’ colors implied a phonetic letter scheme, this power law distribution makes sense and adds to her argument. However, the jury remains deadlocked. When we look at the actual Zipfian distribution, we see that while it is a power curve, it is not a natural Zipfian distribution. Furthermore, cord colors lack the conventional amounts of hapax legomena the only-once-occuring “words” that comprise 40-60% of the words in natural language. Color, whether, alone or in group sequence, lacks the correct proportions of uniquity to ubiquity.
    • While white cords comprise a third of all pendant cords, and of cord groups of white, we don’t yet know what their color significance is. One theory, that they are grammatical markers for addition, appears disproved. However, they do show interesting levels of positional significance, appearing at the end or beginning of cord groups that contain many sums (sum groups), and in certain spikes in larger groups (i.e. in odd positions more than even ones).