Khipus with DecaDecimal Cords

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Appendix 5 - Analysis of Khipus with DecaDecimal Cords

Many khipus have cord values that are multiples of 10. Are these khipus “intentionally planned” to be this way? For example, could they be top-down khipus that reflect a taxation scheme? This idea, proposed by Manual Medrano, investigates the mean cord values of these khipus, and looks at their distribution.

Code

(khipu_dict, all_khipus) = kamayuq.fetch_khipus()

Code

(khipu_dict, all_khipus) = kamayuq.fetch_khipus()

# Analysis is done for pendant cords only:
# Build a dictionary of all cord values for each khipu
khipu_names = [khipu.name() for khipu in all_khipus]
cord_values_dict = {khipu.name():[cord.knotted_value() for cord in khipu[:,:]] for khipu in all_khipus}

Code

from scipy.stats import entropy
import warnings
warnings.simplefilter("ignore")     

def is_decadecimal(aValue): return (aValue != 0) and (aValue%10==0)
def num_decadecimals(cord_values): return sum([is_decadecimal(aValue) for aValue in cord_values])
decadecimal_table = [(khipu_name, 
                      num_decadecimals(cord_values_dict[khipu_name]),
                      float(num_decadecimals(cord_values_dict[khipu_name]))/float(len(cord_values_dict[khipu_name])),
                      entropy(cord_values_dict[khipu_name]),
                      mean(cord_values_dict[khipu_name]),
                      len(cord_values_dict[khipu_name])) for khipu_name in khipu_names]         
decadecimal_df = pd.DataFrame(decadecimal_table, columns=["Khipu_Name", "Num_Decadecimals", "Decadecimal_Proportion", "Entropy", "Mean_Cord_Value", "Num_Cords"])
decadecimal_df

See Full Dataframe in Mito

	Khipu_Name	Num_Decadecimals	Decadecimal_Proportion	Entropy	Mean_Cord_Value	Num_Cords
0	AS010	2	0.074074	2.650825	8	27
1	AS011	2	0.133333	1.624489	92	15
2	AS012	1	0.011765	2.765642	2	85
3	AS013	5	0.055556	2.807698	4	90
4	AS014	10	0.238095	3.478898	53	42
...	...	...	...	...	...	...
646	UR193	10	0.101010	4.274406	30	99
647	UR221	6	0.600000	1.733907	70	10
648	UR253	3	0.050847	3.219005	10	59
649	UR280	7	0.189189	2.808857	60	37
650	UR292A	1	0.018868	3.031936	2	53

Now that we have a dataframe of relationships, let’s plot them:

Code

# Initialize plotly
import warnings
warnings.filterwarnings("ignore")
plotly.offline.init_notebook_mode(connected = False);

fig = (px.scatter(decadecimal_df, x="Num_Cords", y="Decadecimal_Proportion", 
                  hover_data=['Khipu_Name'], 
                  title=f"<b>Relationship between Decadecimal Proportion, and Num Cords</b>",
                  width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

Code

# Initialize plotly
import warnings
warnings.filterwarnings("ignore")
plotly.offline.init_notebook_mode(connected = False);

fig = (px.scatter(decadecimal_df, x="Mean_Cord_Value", y="Decadecimal_Proportion", 
                  hover_data=['Khipu_Name'], 
                  title=f"<b>Relationship between Decadecimal Proportion, and Mean Cord Value</b>",
                  width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

Code

# Initialize plotly
import warnings
warnings.filterwarnings("ignore")
plotly.offline.init_notebook_mode(connected = False);

fig = (px.scatter(decadecimal_df, x="Num_Cords", y="Entropy", 
                  hover_data=['Khipu_Name'], 
                  title=f"<b>Relationship between Entropy, and Num Cords</b>",
                  width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )

Code

# Initialize plotly
import warnings
warnings.filterwarnings("ignore")
plotly.offline.init_notebook_mode(connected = False);

fig = (px.scatter(decadecimal_df, x="Mean_Cord_Value", y="Entropy", 
                  hover_data=['Khipu_Name'], 
                  title=f"<b>Relationship between Entropy, and Mean Cord Value</b>",
                  width=944, height=944)
        .update_layout(showlegend=False).update(layout_coloraxis_showscale=False).show()
      )