Subsidiary cords that are Sums of similarly indexed (by color not position) cords in contiguous groups to the right or left of the cord.
Ascher khipu AS038 (KH0049), is the first of the many khipus that use subsidiary position indexing for summing. In AS038, Ascher notes:
\(P_{2,i°sub_j}=P_{3,i°sub_j}+P_{4,i°sub_j}+P_{5,i°sub_j}+P_{6,i°sub_j}\;for\;i=(1,2,3...,18)\;\;\;j=(B,W,B,W,GG,RL,BD,BS)\)
Interestingly, this is a search by color as index, not by position, as sometimes certain colors are missing, or the colors are in a different order than the sum group. As in indexed-pendant sums, we limit the search to contiguous groups, whose sum is > 5. The code is largely the same as Pendant Indexing, except for the fact that we are using Ascher color as the index instead of cord position in it’s parent group.
Occurrences must exceed 1 (1 deemed to be possibly accidental), to be marked as significant. 24 khipu have 2 or more subsidiary sums, resulting in this pattern occuring 173 times in the KFG (Khipu Field Guide).
| Measure | Result |
|---|---|
| Number of Khipus That Match | 41 (6%) |
| Number of Significant Khipus | 22 (3%) |
| Five most Significant Khipu | UR1175, KH0049, UR1136, AS069, UR119 |
| Database View | Click here |
# Initialize plotly
import plotly
import plotly.express as px
import pandas as pd
plotly.offline.init_notebook_mode(connected = False);
# Read in the Fieldmark and its associated dataframe and match dictionary
from fieldmark_ascher_indexed_subsidiary_sum import FieldmarkIndexedSubsidiarySum
aFieldmark = FieldmarkIndexedSubsidiarySum()
fieldmark_dataframe = aFieldmark.dataframes[0].dataframe
raw_match_dict = aFieldmark.raw_match_dict()# Plot Matching khipu
matching_khipus = aFieldmark.matching_khipus()
matching_values = [raw_match_dict[aKhipuName] for aKhipuName in matching_khipus]
matching_df = pd.DataFrame(list(zip(matching_khipus, matching_values)), columns =['KhipuName', 'Value'])
fig = px.bar(matching_df, x='KhipuName', y='Value', labels={"KhipuName": "Khipu Name", "Value": "Number of Indexed Subsidiary Sum Cords", },
title=f"Matching Khipu ({len(matching_khipus)}) for Number of Indexed Subsidiary Sum Cords", width=944, height=450).update_layout(showlegend=True).show()# Plot Significant khipu
significant_khipus = aFieldmark.significant_khipus()
significant_values = [raw_match_dict[aKhipuName] for aKhipuName in significant_khipus]
significant_df = pd.DataFrame(list(zip(significant_khipus, significant_values)), columns =['KhipuName', 'Value'])
fig = px.bar(significant_df, x='KhipuName', y='Value', labels={"KhipuName": "Khipu Name", "Value": "Number of Indexed Subsidiary Sum Cords", },
title=f"Significant Khipu ({len(significant_khipus)}) for Number of Indexed Subsidiary Sum Cords", width=944, height=450).update_layout(showlegend=True).show()AS069 once again shows just how much summing is going on inside of it! It and UR1175 both show significant pendant index summing and subsidiary index summing by color. KH0083 stands out for an astounding 19 summands.
sum_cord_df = aFieldmark.dataframes[1].dataframe
fig = (px.scatter(sum_cord_df, x="cord_index", y="cord_value", log_y=True,
size="num_summands", color="num_summands",
labels={"cord_index": "Sum Cord Position Index", "cord_value": "Cord Value (Log(y) scale)"},
hover_data=['kfg_name','cord_index', 'summand_string'], title="<b>Color Indexed Subsidiary Sums</b> - <i>Hover Over Circles to View Khipu/Cord Info</i>",
width=944, height=944)
.update_layout(showlegend=True)
.show()
)right_sum_cord_position_df = sum_cord_df[sum_cord_df.handedness >= 0]
left_sum_cord_position_df = sum_cord_df[sum_cord_df.handedness < 0]
num_left_sums = len(left_sum_cord_position_df) # sum(fieldmark_dataframe.num_right_sums.values.tolist())
num_right_sums = len(right_sum_cord_position_df) # sum(fieldmark_dataframe.num_left_sums.values.tolist())
num_total_sums = num_left_sums + num_right_sums
right_pct = round(100.0*float(num_left_sums)/float(num_total_sums))
left_pct = round(100.0*float(num_right_sums)/float(num_total_sums))
print(f"Out of {num_total_sums} indexed sums, there are {num_right_sums}({right_pct}%) right_handed sums and {num_left_sums}({left_pct}%) left-handed sums")Out of 193 indexed sums, there are 114(41%) right_handed sums and 79(59%) left-handed sumsfrom statistics import mean
def handed_color(x): return "#F00" if x < 0 else "#00F"
handness_color = [handed_color(x) for x in sum_cord_df.handedness.values]
handedness_mean = mean(list(sum_cord_df.handedness.values))
fig = (px.scatter(sum_cord_df, x="handedness", y="cord_value", log_y=True,
size="num_summands",
color=handness_color,
labels={"handedness": f"Handedness - Mean({handedness_mean})", "cord_value": "Cord Value (Log(y) scale)", },
hover_data=['kfg_name'], title="<b>Handeness of Indexed Subsidiary Sums</b> - <i>Hover Over Circles to View Khipu/Cord Info</i>",
width=944, height=944)
.add_vline(x=-2)
.update_layout(showlegend=False)
.show()
)Along with pendant index subsidiaries, this is an interestingly different fieldmark. Like Pendant-Color-Sum indexing, this fieldmark uses color indexing instead of position indexing. Is the use of color-indexing a user-interface issue - it’s just harder to pick a cord and run your thumbs on it, if it’s a subsidiary? Is it’s use a result of an “options” grammar (only include the color if the condition occurs)?
These relations occur in only 8% of the khipu. Additionally only 173 such relations occur - compare that to the 8,091 pendant pendant sum relationships (just 2% of those). So is this just a statistical fluke? The presence of a subsidiary at all renders that argument unlikely. This is a known technique, not a statistical fluke - the bar chart for matching/significant khipu adds to that argument, but it seems a sign/signature of some sort, rather than a common technique. AS038 pendant 19 seems to be the poster child for this relationship.
Due to the scarcity of occurrence, as well as the fact that it’s a subsidiary relationship, I’m going to pass on further investigation of this fieldmark at this time.