Cord Value Hierarchy

In general, we believe:

Non-solid cords tend to have lower cord values than solid cords.
Seriated clusters tend to have higher cord values than banded clusters.
Ascher sum clusters tend to have higher cord values than seriated clusters.

Let’s just take a look at those distributions to verify….

Code

import numpy as np
import pandas as pd
import khipu_kamayuq as kamayuq  # A Khipu Maker is known (in Quechua) as a Khipu Kamayuq
import khipu_qollqa as kq
from pandas import Series, DataFrame

# 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)

(khipu_dict, all_khipus) = kamayuq.fetch_khipus()

1. Belief 1. Non-solid cords tend to have lower cord values than solid cords.

We performed this study in Appendix 04. Here’s a copy of the code:

Code

khipu_colors = []
for aKhipu in all_khipus:
    khipu_colors += [(cord.longest_ascher_color(), cord.knotted_value()) for cord in aKhipu.cc_cords()]
    
def is_solid(aColor):
    return len({':','%','-','*'} & set(aColor)) == 0
def is_mottled(aColor):
    return aColor.count(":") > 0
def is_barberpole(aColor):
    return aColor.count("-") > 0
def is_double_mottled(aColor):
    return aColor.count(":") > 1
def is_double_barberpoled(aColor):
    return aColor.count("-") > 1
def is_mottled_barberpoled(aColor):
    return is_barberpole(aColor) and is_mottled(aColor)

solid_colors = [aColor for aColor in khipu_colors if is_solid(aColor[0])]
mottled_colors = [aColor for aColor in khipu_colors if is_mottled(aColor[0])]
barberpole_colors = [aColor for aColor in khipu_colors if is_barberpole(aColor[0])]
double_mottled_colors = [aColor for aColor in khipu_colors if is_double_mottled(aColor[0])]
mottled_barberpoled_colors = [aColor for aColor in khipu_colors if is_mottled_barberpoled(aColor[0])]
double_barberpoled_colors = [aColor for aColor in khipu_colors if is_double_barberpoled(aColor[0])]

solid_cord_values = [aColor[1] for aColor in solid_colors]
mottled_cord_values = [aColor[1] for aColor in mottled_colors]
barberpole_cord_values = [aColor[1] for aColor in barberpole_colors]
double_mottled_cord_values = [aColor[1] for aColor in double_mottled_colors]
mottled_barberpoled_cord_values = [aColor[1] for aColor in mottled_barberpoled_colors]
double_barberpoled_cord_values = [aColor[1] for aColor in double_barberpoled_colors]

num_solids = len(solid_colors)
num_mottled =  len(mottled_colors)
num_barberpoles =  len(barberpole_colors)
num_double_mottled =  len(double_mottled_colors)
num_mottled_barberpoled =  len(mottled_barberpoled_colors)
num_double_barberpoled =  len(double_barberpoled_colors)

from statistics import mean, stdev

print(f"             {num_solids=: 6.0f} - Average cord value={mean(solid_cord_values): 4.0f} with Std_dev={stdev(solid_cord_values): 5.0f}")
print(f"            {num_mottled=: 6.0f} - Average cord value={mean(mottled_cord_values): 4.0f} with Std_dev={stdev(mottled_cord_values): 5.0f}")
print(f"        {num_barberpoles=: 6.0f} - Average cord value={mean(barberpole_cord_values): 4.0f} with Std_dev={stdev(barberpole_cord_values): 5.0f}")
print(f"     {num_double_mottled=: 6.0f} - Average cord value={mean(double_mottled_cord_values): 4.0f} with Std_dev={stdev(double_mottled_cord_values): 5.0f}")
print(f"{num_mottled_barberpoled=: 6.0f} - Average cord value={mean(mottled_barberpoled_cord_values): 4.0f} with Std_dev={stdev(mottled_barberpoled_cord_values): 5.0f}")
print(f" {num_double_barberpoled=: 6.0f} - Average cord value={mean(double_barberpoled_cord_values): 4.0f} with Std_dev={stdev(double_barberpoled_cord_values): 5.0f}")

             num_solids= 42316 - Average cord value= 169 with Std_dev= 2540
            num_mottled= 10951 - Average cord value= 103 with Std_dev=  892
        num_barberpoles=  2267 - Average cord value= 120 with Std_dev=  758
     num_double_mottled=   390 - Average cord value= 100 with Std_dev=  393
num_mottled_barberpoled=    52 - Average cord value=  41 with Std_dev=  139
 num_double_barberpoled=    27 - Average cord value=  27 with Std_dev=   74

2. Belief 2. Seriated clusters tend to have higher cord values than banded clusters.

Code

seriated_khipu_cluster_vals = []
banded_khipu_cluster_vals = []
for aKhipu in all_khipus:
    seriated_clusters = [aCluster for aCluster in aKhipu[:] if aCluster.is_seriated_cluster() and aCluster.num_pendant_cords()>1]
    seriated_cluster_means =  [aCluster.mean_cord_value() for aCluster in seriated_clusters]
    banded_clusters = [aCluster for aCluster in aKhipu[:] if aCluster.is_banded_cluster() and aCluster.num_pendant_cords()>1]
    banded_cluster_means = [aCluster.mean_cord_value() for aCluster in banded_clusters if aCluster]
    seriated_khipu_cluster_vals.append(mean(seriated_cluster_means) if seriated_cluster_means else 0)
    banded_khipu_cluster_vals.append(mean(banded_cluster_means) if banded_cluster_means else 0)

def source_color(index): return 0.0 if seriated_khipu_cluster_vals[index] <= banded_khipu_cluster_vals[index] else 1.0
seriated_exceeds_banded = [source_color(i) for i in range(len(all_khipus))]
khipu_names = [aKhipu.name() for aKhipu in all_khipus]
banded_vs_seriated_df = pd.DataFrame(zip(khipu_names, banded_khipu_cluster_vals, seriated_khipu_cluster_vals, seriated_exceeds_banded), columns=["name", "mean_banded_cluster_value", "mean_seriated_cluster_value", "seriated_exceeds_banded"])
banded_vs_seriated_df

	name	mean_banded_cluster_value	mean_seriated_cluster_value	seriated_exceeds_banded
0	AS010	11.500000	5.000000	0.0
1	AS011	104.500000	0.000000	0.0
2	AS012	1.750000	1.000000	0.0
3	AS013	6.333333	2.500000	0.0
4	AS014	0.000000	53.000000	1.0
...	...	...	...	...
646	UR193	14.500000	31.000000	1.0
647	UR221	0.000000	66.500000	1.0
648	UR253	1.000000	9.555556	1.0
649	UR280	51.000000	70.000000	1.0
650	UR292A	0.000000	1.625000	1.0

Code


legend_text = "<b>Seriated vs Banded Mean Cluster Cord Values:</b><i style=\"font-size:10pt;\"> Blue-Banded >=, Red-Seriated >=</i>"
fig = (px.scatter(banded_vs_seriated_df, x="mean_banded_cluster_value", y="mean_seriated_cluster_value", #log_y=True,log_x=True,
                 #size="mean_num_summands",
                 opacity=.4, 
                 color='seriated_exceeds_banded', color_continuous_scale=['#3c3fff', '#ff3030',],
                 labels={"name": f"Khipu Name"},
                 hover_data=['name'], title=legend_text,
                 width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

3. Belief 3. Ascher Sum Relationships > …. what exactly?

Code

#=======================================================
# INITIALIZE
# Read in the Fieldmark and its associated dataframes
#=======================================================
from fieldmark_ascher_pendant_pendant_sum import Fieldmark_Pendant_Pendant_Sum
aFieldmark = Fieldmark_Pendant_Pendant_Sum()
khipu_df = aFieldmark.dataframes[0].dataframe
sum_cord_df = aFieldmark.dataframes[1].dataframe

sum_cord_df

	Unnamed: 0	khipu_id	name	cord_id	cord_name	cord_position	cord_position_index	cord_value	cord_color	num_summands	sum_string	handedness
0	0	1000166	AS010	3016349	p13	[3, 2]	2	20	LB	4	[2, 0]:4 +[2, 1]:1 +[2, 2]:12 +[3, 0]:3	-1
1	1	1000166	AS010	3016360	p24	[9, 2]	2	38	W	6	[3, 0]:3 +[3, 1]:3 +[3, 2]:20 +[4, 0]:3 +[5, 0]:0 +[6, 0]:9	-5
2	2	1000166	AS010	3016340	p4	[1, 2]	2	23	W:RG	3	[1, 5]:18 +[2, 0]:4 +[2, 1]:1	1
3	3	1000166	AS010	3016343	p7	[1, 5]	5	18	W:LB	3	[2, 2]:12 +[3, 0]:3 +[3, 1]:3	2
4	4	1000166	AS010	3016346	p10	[2, 2]	2	12	LB	3	[4, 0]:3 +[5, 0]:0 +[6, 0]:9	3
...	...	...	...	...	...	...	...	...	...	...	...	...
8084	8084	6000085	UR253	6010389	p36	[6, 11]	11	106	MB	21	[7, 1]:17 +[8, 0]:0 +[8, 1]:0 +[8, 2]:2 +[8, 3]:0 +[8, 4]:0 +[8, 5]:0 +[8, 6]:0 +[8, 7]:4 +[8, 8]:0 +[9, 0]:1 +[9, 1]:0 +[9, 2]:3 +[9, 3]:0 +[10, 0]:2 +[10, 1]:4 +[10, 2]:5 +[10, 3]:30 +[10, 4]:11 +[10, 5]:21 +[11, 0]:6	3
8085	8085	6000085	UR253	6010410	p57	[10, 5]	5	21	0D	2	[11, 0]:6 +[11, 1]:15	1
8086	8086	6000086	UR280	6010448	p3	[0, 2]	2	87	NB	4	[5, 2]:52 +[5, 3]:3 +[5, 4]:28 +[5, 5]:4	5
8087	8087	6000086	UR280	6010468	p23	[4, 5]	5	150	NB	4	[5, 1]:67 +[5, 2]:52 +[5, 3]:3 +[5, 4]:28	1
8088	8088	6000087	UR292A	6010719	p24	[3, 0]	0	20	W	6	[4, 2]:7 +[4, 3]:6 +[5, 0]:1 +[5, 1]:0 +[5, 2]:0 +[5, 3]:6	2

Code

khipu_names = sum_cord_df.name.to_list()
cord_names = sum_cord_df.cord_name.to_list()
sum_cords = [khipu_dict[khipu_name][level_name] for khipu_name, level_name in zip(khipu_names, cord_names)]
sum_clusters = [aCord.parent_cluster for aCord in sum_cords]
sum_clusters_by_khipu = {name:[aCluster for aCluster in sum_clusters if aCluster.khipu_name == name] for name in khipu_names}
def calc_mean_sum_cluster(name):
    clusters = sum_clusters_by_khipu[name]
    return mean([cluster.mean_cord_value() for cluster in clusters]) if clusters else 0.0

mean_sum_clusters_by_khipu = {name: calc_mean_sum_cluster(name) for name in khipu_names}

Code

def source_color(index): 
    name = all_khipus[index].name()
    ascher_sum_mean = mean_sum_clusters_by_khipu[all_khipus[index].name()] if name in mean_sum_clusters_by_khipu else 0.0
    seriated_cluster_mean = seriated_khipu_cluster_vals[index]
    return 0.0 if ascher_sum_mean <= seriated_cluster_mean else 1.0
sum_exceeds_seriated = [source_color(i) for i in range(len(all_khipus))]
khipu_names = [aKhipu.name() for aKhipu in all_khipus]
sum_cluster_means = [(mean_sum_clusters_by_khipu[name] if name in mean_sum_clusters_by_khipu else 0.0) for name in khipu_names]
ascher_vs_seriated_df = pd.DataFrame(zip(khipu_names, sum_cluster_means, seriated_khipu_cluster_vals, sum_exceeds_seriated), columns=["name", "sum_cluster_mean", "seriated_cluster_mean", "sum_exceeds_seriated"])
ascher_vs_seriated_df

	name	sum_cluster_mean	seriated_cluster_mean	sum_exceeds_seriated
0	AS010	9.200000	5.000000	1.0
1	AS011	0.000000	0.000000	0.0
2	AS012	3.285714	1.000000	1.0
3	AS013	10.000000	2.500000	1.0
4	AS014	53.000000	53.000000	0.0
...	...	...	...	...
646	UR193	31.777778	31.000000	1.0
647	UR221	0.000000	66.500000	0.0
648	UR253	16.807692	9.555556	1.0
649	UR280	129.500000	70.000000	1.0
650	UR292A	20.000000	1.625000	1.0

Code

legend_text = "<b>Ascher Sum vs Seriated Mean Cluster Cord Values:</b><i style=\"font-size:10pt;\"> Blue-Seriated >=, Red-Ascher_Sum >=</i>"
fig = (px.scatter(ascher_vs_seriated_df, x="seriated_cluster_mean", y="sum_cluster_mean", #log_y=True,log_x=True,
                 #size="mean_num_summands",
                 opacity=.4, 
                 color='sum_exceeds_seriated', color_continuous_scale=['#3c3fff', '#ff3030',],
                 labels={"name": f"Khipu Name"},
                 hover_data=['name'], title=legend_text,
                 width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

Code

def source_color(index): 
    name = all_khipus[index].name()
    ascher_sum_mean = mean_sum_clusters_by_khipu[all_khipus[index].name()] if name in mean_sum_clusters_by_khipu else 0.0
    banded_cluster_mean = banded_khipu_cluster_vals[index]
    return 0.0 if ascher_sum_mean <= banded_cluster_mean else 1.0
    
sum_exceeds_banded = [source_color(i) for i in range(len(all_khipus))]
khipu_names = [aKhipu.name() for aKhipu in all_khipus]
def calc_sum_cluster_mean(name):
    return mean_sum_clusters_by_khipu[name] if name in mean_sum_clusters_by_khipu.keys() else 0.0

sum_cluster_means = [calc_sum_cluster_mean(name) for name in khipu_names]
ascher_vs_banded_df = pd.DataFrame(zip(khipu_names, sum_cluster_means, banded_khipu_cluster_vals, sum_exceeds_banded), columns=["name", "sum_cluster_mean", "banded_cluster_mean", "sum_exceeds_banded"])
ascher_vs_banded_df

	name	sum_cluster_mean	banded_cluster_mean	sum_exceeds_banded
0	AS010	9.200000	11.500000	0.0
1	AS011	0.000000	104.500000	0.0
2	AS012	3.285714	1.750000	1.0
3	AS013	10.000000	6.333333	1.0
4	AS014	53.000000	0.000000	1.0
...	...	...	...	...
646	UR193	31.777778	14.500000	1.0
647	UR221	0.000000	0.000000	0.0
648	UR253	16.807692	1.000000	1.0
649	UR280	129.500000	51.000000	1.0
650	UR292A	20.000000	0.000000	1.0

Code

legend_text = "<b>Ascher Sum vs Banded Mean Cluster Cord Values:</b><i style=\"font-size:10pt;\"> Blue-Banded >=, Red-Ascher_Sum >=</i>"
fig = (px.scatter(ascher_vs_banded_df, x="banded_cluster_mean", y="sum_cluster_mean", #log_y=True,log_x=True,
                 #size="mean_num_summands",
                 opacity=.4, 
                 color='sum_exceeds_banded', color_continuous_scale=['#3c3fff', '#ff3030',],
                 labels={"name": f"Khipu Name"},
                 hover_data=['name'], title=legend_text,
                 width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

Code

def band_seriated(index): 
    num = banded_khipu_cluster_vals[index]
    den = (banded_khipu_cluster_vals[index] + seriated_khipu_cluster_vals[index])
    return num/den if den > 0 else 0.0
    
band_seriated_color = [band_seriated(i) for i in range(len(all_khipus))]
khipu_names = [aKhipu.name() for aKhipu in all_khipus]
def calc_sum_cluster_mean(name):
    return mean_sum_clusters_by_khipu[name] if name in mean_sum_clusters_by_khipu.keys() else 0.0

cluster_means = [max(banded_khipu_cluster_vals[i], seriated_khipu_cluster_vals[i]) for i in range(len(all_khipus))]  

sum_cluster_means = [calc_sum_cluster_mean(name) for name in khipu_names]
ascher_vs_band_seriated_df = pd.DataFrame(zip(khipu_names, sum_cluster_means, cluster_means, band_seriated_color), columns=["name", "sum_cluster_mean", "cluster_mean", "band_seriated_color"])
ascher_vs_band_seriated_df

	name	sum_cluster_mean	cluster_mean	band_seriated_color
0	AS010	9.200000	11.500000	0.696970
1	AS011	0.000000	104.500000	1.000000
2	AS012	3.285714	1.750000	0.636364
3	AS013	10.000000	6.333333	0.716981
4	AS014	53.000000	53.000000	0.000000
...	...	...	...	...
646	UR193	31.777778	31.000000	0.318681
647	UR221	0.000000	66.500000	0.000000
648	UR253	16.807692	9.555556	0.094737
649	UR280	129.500000	70.000000	0.421488
650	UR292A	20.000000	1.625000	0.000000

Code

legend_text = "<b>Ascher Sum vs Mean Cluster Cord Values:</b><i style=\"font-size:10pt;\"> Blue-Banded >=, Red-Ascher_Sum >=</i>"
fig = (px.scatter(ascher_vs_band_seriated_df, x="cluster_mean", y="sum_cluster_mean", #log_y=True,log_x=True,
                 #size="mean_num_summands",
                 opacity=.4, 
                 color='band_seriated_color', 
                 labels={"name": f"Khipu Name"},
                 hover_data=['name'], title=legend_text,
                 width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )