Toponym Search by Figure-Eight-Knots

by Ashok Khosla, Di Hi, and Kylie Quave - November 2024

1. Toponym Search

In the article:

Information Control in the Palace of Puruchuco: An Accounting Hierarchy in a Khipu Archive from Coastal Peru,

by Gary Urton and Carrie J. Brezine. There is a short section describing “Toponyms” - indicators of a particular place. In the article, Brezine and Urton divide the Puruchuco khipus into three levels of hierarchy - Level 1 being “ground level” and Level 2 and 3 being summations of their lower levels.

To quote:

Introductory Segments

We assume that the accounting hierarchy shown in figure 5 was a set of records for use both within and outside Puruchuco. The use of this information at a wider level, perhaps regional or provincial, would have been connected with the reporting function of some or all of these khipus. For example, khipus on level III could represent either a set of instructions issued to the lord of Puruchuco from the provincial governor, or reports on local Puruchuco resources to be sent to the provincial governor. In either of these scenarios, one of the requirements would have been that the khipus bear an indication of their destination or origination. … If numerous khipus were coming into a central archive for storage or were being dispersed from that archive to disparate places, it would have been helpful, if not essential, to have place identifiers encoded within each khipu. We suggest that the introductory segments on level II and III khipus represented just such identity labels (see Pärssinen, 1992:39–43)… The numerical values knotted onto strings within the introductory segments on level II and III khipus all contain arrangements of just three figure-Eight-Knots (denoted E) tied onto three separate strings (see fig. 8). Figure-Eight-Knots normally signify the numerical value one (1), however it is important to note that the numeric values on these introductory segments are neither derived from nor implicated in the summation/ partition relationship.

The introductory segments in all cases occur near the short, doubled end of the primary cord, which is usually taken to be the beginning of a khipu account. We hypothesize that the arrangement of three figure-Eight-Knots at the start of these khipus represented the place identifier, or toponym, “Puruchuco.” Three figure-Eight-Knots tied onto a few of the dozen or so strings is not a lot of information by which to signal a toponym. It is difficult for us to explain otherwise, however, the purpose of these parallel sets of strings, which do not figure in any discernible way into the summation/partition relations. We suggest that any khipu moving within the state administrative system bearing an initial arrangement of three figure-Eight-Knots would have been immediately recognizable to Inka administrators as an account pertaining to the palace of Puruchuco. This implies that there ought to be place identifiers relating to khipus from other archives as well, though we are not prepared to suggest other such labels at this time.

Why don’t level I khipus bear introductory segments? Perhaps UR63 and UR73 were not intended to travel away from Puruchuco; instead they were local accounts, drawn up by the resident khipukamayuq for accounting purposes within the palace. If the seven khipus register demands for service received from outside Puruchuco, meaning that if the relationship among them is one of partition, then the level I khipus would have represented the reorganization of the mandate from outside in relation to the availability of resources at the local level. In this scheme, level I khipus would have pertained only to local accounting matters and it would have been unnecessary to attach the place identifier. However, if the overall relationship is one of summation, and these khipus were prepared as a report on local conditions for dispatch outside Puruchuco, then level I khipus would represent the “raw” tables of local information that served as the foundation for constructing level II and III khipus. Level III khipus, the summary reports, would have been sent to a distant administrative center.

On this page, we will search for “toponymic” features as suggested by Brezine and Urton.

The authors note that the higher level khipus, start with a three cord sequence that has Figure-Eight-Knots in a seriated pattern. The actual data/images for these khipu show a 4 or 5 cord seriated starting sequence. The khipus are:

Intermediate Level - KH0301/UR064
Intermediate Level - CM009
Intermediate Level - KH0305/UR068
High Level - KH0306/UR067
High Level - KH0303/UR066

Intermediate Level - KH0301/UR064

Intermediate Level - CM009

Intermediate Level - KH0305/UR068

High Level - KH0306/UR067

High Level - KH0303/UR066

2. Search Criteria:

Based on the examples in the Puruchuco hierarchy, let’s first look for all khipus containing

First cord group/cluster is seriated
First cord contains a figure-eight-knot

Code

import os
import numpy as np
import pandas as pd
from pandas import Series, DataFrame
from collections import Counter

import qollqa_chuspa as qc  # A Khipu Maker is known (in Quechua) as a Khipu Kamayuq
import utils_loom as uloom
import utils_khipu as ukhipu
import utils_pandas as upanda
    
# Plotly
import plotly
from plotly.offline import iplot, init_notebook_mode
import plotly.graph_objs as go
import plotly.express as px
import plotly.figure_factory as ff
plotly.offline.init_notebook_mode(connected = False)

# Load all khipus
(khipu_dict, all_khipus) = qc.fetch_khipus()
khipu_names = ukhipu.kfg_order(khipu_dict.keys())

Code

def is_potential_toponym(aKhipu):
    """Returns True if the khipu has a toponym, False otherwise."""
    first_cord_group = aKhipu[0]
    first_cord = first_cord_group[0]
    is_possible_toponym = first_cord.has_eight_knot(include_subsidiaries=False) and first_cord_group.is_seriated_group() and (aKhipu.num_top_cords()== 0)
    return is_possible_toponym

potential_toponym_khipus = [aKhipu for aKhipu in all_khipus if is_potential_toponym(aKhipu)]
potential_toponym_khipu_names = uloom.multiline(", ".join([akhipu.kfg_name() for akhipu in potential_toponym_khipus]), split_char = ", ", continuation_char=",\n\t")
print(f"There are {len(potential_toponym_khipus)} potential toponym khipus.")
print(f"\t{potential_toponym_khipu_names}")

There are 62 potential toponym khipus.
    CM009, KH0006, KH0010, KH0017, KH0037, KH0054, KH0066, KH0076, KH0077, KH0078,
    KH0090, KH0091, KH0092, KH0134, KH0141, KH0162, KH0166, KH0168, KH0175, KH0190,
    KH0226, KH0227, KH0231, KH0243, KH0285, KH0286, KH0297, KH0301, KH0303, KH0304,
    KH0305, KH0315, KH0328, KH0352, KH0360, KH0374, KH0406, KH0419, KH0434, KH0441,
    KH0480, KH0481, KH0496, KH0514, KH0521, KH0523, KH0527, KH0542, KH0551, KH0563,
    KH0565, KH0570, KH0595, KH0599, KH0657, KH0663, KH0664, KH0673, KH0689, KH0692,
    KH0702, RA001

We can still do some culling:

A quick glance at AS004, shows that the first 8 knot is part of a sum, followed by a top cord. Let’s eliminate all khipus with top cords, knowing that top cords are generally a hallmark of banded khipus. Since banded khipus are considered to be local, by Urton and Brezine’s definition, local they are unlikely to be toponymic (see Medrano and Khosla’s article How Can Data Science Contribute to Understanding the Khipu Code?).

Code

def is_potential_toponym(aKhipu):
    """Returns True if the khipu has a toponym, False otherwise."""
    first_cord_group = aKhipu[0]
    first_cord = first_cord_group[0]
    is_possible_toponym = first_cord.has_eight_knot(include_subsidiaries=False) and first_cord_group.is_seriated_group() and (aKhipu.num_top_cords()== 0)
    return is_possible_toponym

potential_toponym_khipus = [aKhipu for aKhipu in all_khipus if is_potential_toponym(aKhipu)]
potential_toponym_khipu_names = uloom.multiline(", ".join([akhipu.kfg_name() for akhipu in potential_toponym_khipus]), split_char = ", ", continuation_char=",\n\t")
print(f"There are {len(potential_toponym_khipus)} potential toponym khipus.")
print(f"\t{potential_toponym_khipu_names}")

There are 62 potential toponym khipus.
    CM009, KH0006, KH0010, KH0017, KH0037, KH0054, KH0066, KH0076, KH0077, KH0078,
    KH0090, KH0091, KH0092, KH0134, KH0141, KH0162, KH0166, KH0168, KH0175, KH0190,
    KH0226, KH0227, KH0231, KH0243, KH0285, KH0286, KH0297, KH0301, KH0303, KH0304,
    KH0305, KH0315, KH0328, KH0352, KH0360, KH0374, KH0406, KH0419, KH0434, KH0441,
    KH0480, KH0481, KH0496, KH0514, KH0521, KH0523, KH0527, KH0542, KH0551, KH0563,
    KH0565, KH0570, KH0595, KH0599, KH0657, KH0663, KH0664, KH0673, KH0689, KH0692,
    KH0702, RA001

Next let’s elimate any khipus where the first cord is a sum marker.

To this we build a concatenated dataframe of pendant_pendant_sums, indexed_pendant_sums, and colored_pendant_sums, and see if p1 occurs in any of the khipus sums

Code

# Ascher sums for a khipu
from fieldmark_ascher_pendant_pendant_sum import FieldmarkPendantPendantSum
from fieldmark_ascher_indexed_pendant_sum import FieldmarkIndexedPendantSum
from fieldmark_ascher_colored_pendant_sum import FieldmarkColoredPendantSum
pendant_pendant_sums_df = FieldmarkPendantPendantSum().relations_df()
indexed_pendant_sums_df = FieldmarkIndexedPendantSum().relations_df()
colored_pendant_sums_df = FieldmarkColoredPendantSum().relations_df()
potential_toponym_df = pd.concat([pendant_pendant_sums_df.copy(deep=True),
                                 indexed_pendant_sums_df.copy(deep=True),# .drop(columns=['summand_group_positions']),
                                 colored_pendant_sums_df.copy(deep=True)]) #.drop(columns=['Unnamed: 0'])
potential_toponym_df['sum_type'] = ['pendant_pendant_sum']*len(pendant_pendant_sums_df) + ['indexed_pendant_sum']*len(indexed_pendant_sums_df) + ['colored_pendant_sum']*len(colored_pendant_sums_df)
print(f"figure-eight-knots Sums Dataframe:")
# potential_toponym_df.drop(columns=['Unnamed: 0'], inplace=True)

# First cull is for khipus that have a potential toponym as noted above
potential_toponym_khipu_names = [akhipu.kfg_name() for akhipu in potential_toponym_khipus]
potential_toponym_df = potential_toponym_df[potential_toponym_df['kfg_name'].isin(potential_toponym_khipu_names)]
print(f"After first cull we have {potential_toponym_df['kfg_name'].nunique()} potential toponyms.")


potential_toponym_df.columns
# # Second cull is for khipus that don't have p1 in 'leading_exact_pendant_cord_name' or 'leading_close_pendant_cord_names' 
potential_toponym_df = potential_toponym_df[potential_toponym_df['left_exact_pendant_8knot_cord_name'].str.contains('p1') == False]
potential_toponym_df = potential_toponym_df[potential_toponym_df['left_close_pendant_cord_names'].str.contains('p1') == False]
print(f"After second cull we have {potential_toponym_df['kfg_name'].nunique()} potential toponyms.")

potential_toponym_kfg_names = potential_toponym_df['kfg_name'].unique().tolist()
potential_toponym_khipu_strrep = ", ".join(potential_toponym_kfg_names)
print(f"\nThere are {len(potential_toponym_kfg_names)} potential toponym khipus")
print(f"\t{potential_toponym_khipu_strrep}")

figure-eight-knots Sums Dataframe:
After first cull we have 39 potential toponyms.
After second cull we have 17 potential toponyms.

There are 17 potential toponym khipus
    CM009, KH0090, KH0141, KH0175, KH0297, KH0301, KH0305, KH0360, KH0406, KH0441, KH0595, KH0702, KH0162, KH0434, KH0480, KH0496, KH0521

Let’s build a table of these khipus with information about the first cord group:

KFG_Name
Number of cords (pendants and subsidiaries)
Cord names
Values for each cord
Knot sequence for each cord
Colors for each cord

Code

def build_toponym_record(aKhipu):
    kfg_name = aKhipu.kfg_name()
    first_group = aKhipu[0]
    group_cords = first_group.all_cords(include_subsidiaries=True)
    return {'KFG Name':kfg_name,
            '# Cords':len(group_cords),
            '# Pendants':len([aCord for aCord in group_cords if aCord.is_pendant_cord()]),
            '# Subsidiaries':len([aCord for aCord in group_cords if aCord.is_subsidiary_cord()]),
            'Cord Names':", ".join([aCord.pendant_name for aCord in group_cords]),
            'Cord Values':", ".join([str(aCord.knotted_value) for aCord in group_cords]),
            'Knot Sequence':" - ".join([aCord.knot_sequence() for aCord in group_cords]),
            'Cord Colors':", ".join([aCord.main_color() for aCord in group_cords]),
    }

the_topo_records = [build_toponym_record(khipu_dict[topo_khipu_name]) for topo_khipu_name in potential_toponym_kfg_names]
the_topo_df = pd.DataFrame(the_topo_records)
the_topo_df.head(20)

	KFG Name	# Cords	# Pendants	# Subsidiaries	Cord Names	Cord Values	Knot Sequence	Cord Colors
0	CM009	5	5	0	p1, p2, p3, p4, p5	1, 1, 1, 0, 0	E - S - S - -	W, GG, W, AB, W:KB
1	KH0090	4	4	0	p1, p2, p3, p4	1, 3, 2, 6	E - E,L - E,E - L	B, W, AB, W
2	KH0141	21	10	11	p1, p1s1, p2, p2s1, p3, p3s1, p4, p4s1, p5, p5...	21, 1, 20, 1, 21, 1, 12, 0, 20, 0, 12, 0, 20, ...	S,E - E - S - E - S,E - E - S,L - - S - - S,...	W-CB, CB, W-CB, W, B-CB, W, W-CB, B, B-CB, W, ...
3	KH0175	8	7	1	p1, p1s1, p2, p3, p4, p5, p6, p7	1, 20, 17, 16, 16, 18, 12, 16	E - S,L,L - S,L,E - S,L - S,L - S,L - S,L - S,L	W, W, W:B, W:B, W:B, W:B, B, W:B
4	KH0297	5	5	0	p1, p2, p3, p4, p5	1, 1, 1, 1, 2	E - E - E - E - L	MB, AB, MB, MB, GG:MB
5	KH0301	5	5	0	p1, p2, p3, p4, p5	1, 0, 0, 0, 0	E - - - -	AB, W, MB, GG, W:CB
6	KH0305	5	5	0	p1, p2, p3, p4, p5	1, 0, 0, 0, 0	E - - - -	AB, GG, W, AB, W:KB
7	KH0360	3	3	0	p1, p2, p3	1, 0, 5	E - - L	W, AB, W
8	KH0406	7	4	3	p1, p2, p2s1, p3, p3s1, p4, p4s1	35, 20, 15, 11, 7, 11, 6	S,L,E - S,L,E - S,L - S,E - L - S,E - L	AB, AB, MB:KB, AB, MB, AB, MB
9	KH0441	12	6	6	p1, p1s1, p1s2, p2, p2s1, p2s2, p3, p4, p5, p6...	18, 11, 17, 11, 10, 21, 28, 22, 32, 13, 41, 9	S,L,E - L,E,SP,U - L,E,L - E,S - L,E - E,S,S -...	W, W, W, W, W, W, W, W, W, 0K, MB, W
10	KH0595	7	4	3	p1, p2, p2s1, p3, p3s1, p3s2, p4	1, 2, 2, 24, 0, 14, 1	E - L - L - S,L - - S,L - E	YB:B, YB:B, YB:B, YB:B, KB, B, YB:B
11	KH0702	11	8	3	p1, p2, p3, p3s1, p4, p5, p5m1, p6, p6m1, p7, p8	1, 0, 0, 2, 2, 1, 0, 1, 0, 0, 1	E - - - L - L - E - - E - - - E	W, W, AB, GL, PK:GL, W:AB, W:KB, W:AB, PG, AB, W
12	KH0162	81	72	9	p1, p2, p3, p4, p5, p6, p7, p7s1, p8, p9, p10,...	11, 10, 11, 11, 8, 9, 64, 11, 0, 0, 0, 0, 0, 6...	S,E - S - S,E - S,E - L - L - S,L - S,E - - ...	YB, YB, YB, YB, YB, YB, B, BB, B, B, B, B, B, ...
13	KH0434	11	9	2	p1, p1s1, p2, p3, p4, p5, p5s1, p6, p7, p8, p9	61, 4, 16, 0, 13, 43, 2, 10, 21, 13, 16	S,E - L - S,L - - S,L - S,L - L - L - S,E - S...	W, MB, AB:MB, KB, AB, AB, MB, AB, AB, KB, AB
14	KH0480	8	8	0	p1, p2, p3, p4, p5, p6, p7, p8	1, 21, 4, 5, 20, 4, 2, 5	E - S,E - L - L - S - L - L - L	W:AB, W:AB, W:AB, W:AB, W:MB, W:AB, W:AB, W:AB
15	KH0496	16	12	4	p1, p2, p3, p3s1, p4, p5, p6, p7, p7s1, p8, p9...	1, 2, 1, 0, 1, 1, 2, 3, 1, 1, 1, 1, 2, 1, 3, 1	E - L - E - - E - E - L - L - E - E - E - E -...	AB, AB, AB, PK, AB, AB, W:AB, W:AB, AB-KB, W:A...
16	KH0521	18	18	0	p1, p2, p3, p4, p5, p6, p7, p8, p9, p10, p11, ...	7, 7, 12, 4, 2, 2, 10, 2, 3, 2, 2, 2, 2, 0, 5,...	E,E,L,L,E - E,L,L,L - S,L - L - L - L - S - L ...	W, AB, HB, AB, W-YY, W-MB, AB-GG, W-MB, BG-HB,...

Should we cull khipus with greater than 5 pendants? The color sequences, or knot values for groups with more than 5 seems to not fit the classic seriated pattern proposed by Brezine/Urton.

Code

the_topo_records = [build_toponym_record(khipu_dict[topo_khipu_name]) for topo_khipu_name in potential_toponym_kfg_names \
                        if khipu_dict[topo_khipu_name][0].num_pendant_cords() <= 5]
the_topo_df = pd.DataFrame(the_topo_records)
the_topo_df.head(20)

	KFG Name	# Cords	# Pendants	# Subsidiaries	Cord Names	Cord Values	Knot Sequence	Cord Colors
0	AS005	4	4	0	p1, p2, p3, p4	11, 1, 5, 0	E,E - E - L -	MB, MB, MB, W:KB
1	AS077	4	4	0	p1, p2, p3, p4	1, 3, 2, 6	E - E,L - E,E - L	B, W, AB, W
2	CM009	5	5	0	p1, p2, p3, p4, p5	1, 1, 1, 0, 0	E - S - S - -	W, GG, W, AB, W:KB
3	QU007	7	4	3	p1, p2, p2s1, p3, p3s1, p3s2, p4	1, 2, 20, 24, 0, 14, 1	E - L - L - S,L - - S,L - E	YB:B, YB:B, YB:B, YB:B, KB, B, YB:B
4	UR060	5	5	0	p1, p2, p3, p4, p5	1, 1, 1, 1, 2	E - E - E - E - L	MB, AB, MB, MB, GG:MB
5	UR064	5	5	0	p1, p2, p3, p4, p5	1, 0, 0, 0, 0	E - - - -	AB, W, MB, GG, W:CB
6	UR068	5	5	0	p1, p2, p3, p4, p5	1, 0, 0, 0, 0	E - - - -	AB, GG, W, AB, W:KB
7	UR120	3	3	0	p1, p2, p3	1, 0, 5	E - - L	W, AB, W
8	UR167	7	4	3	p1, p2, p2s1, p3, p3s1, p4, p4s1	35, 20, 15, 11, 7, 11, 6	S,L,E - S,L,E - S,L - S,E - L - S,E - L	AB, AB, MB:KB, AB, MB, AB, MB

3. Conclusion

There is an old science joke that goes like this:

A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.
“Aha,” says the engineer, “I see that Scottish sheep are black.”
“Hmm,” says the physicist, “You mean that some Scottish sheep are black.”
“No,” says the mathematician, “All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black.”

In the case of the Puruchuco khipus, I suspect that one side of one sheep is black.