Animal Counting Game

I heard this story from a Mexican friend, whose great grandfather moved to Northern California long before the land got transferred to United States. Prior to discovery of gold in the hills of Sierra Nevada and arrival of 49ers, California was sparsely populated and two Spanish farmers lived in the area currently known as Menlo Park. Juan and Estevan raised avestruz (ostrich), cerdo (pig), ganso (goose) and toro (bulls) in their huge farm.

Life was quite easy and a bit too boring at times. To make their daily routine interesting, Juan invented a new game. Every once in a while, he took all animals to a small pond and let them drink water one at a time. When an animal was at the pond, he raised a flag – red for avestruz, green for cerdo, yellow for ganso and blue for toro. Estevan sat far away on top of a redwood tree and marked the colors of flags on a piece of paper. Juan also kept his own notes. After all animals drank water, they sat together for lunch and compared their markings. On some other days, Juan climbed the tree and Estevan took the animals to the ponds. What a silly game, don’t you think? Let me remind you that they were farmers and not chess grand-masters. If they were happy with it, what can we say?

When I visited Mexico, my friend showed me the pieces of papers that their family preserved for generations to remember the lives of their ancestors. It was quite an amazing feeling to sit with the papers, close my eyes and try to imagine what life was like in the completely desolate ‘Silicon valley’. I even attempted some ‘data science’ on their notes and noticed a puzzling pattern. Day after day, the guy on the tree got the correct animal from flag signal about 85% of times and made errors for another 15% of cases. I checked several papers and found the split to be always 85% correct and 15% incorrect. Not only that, most errors were of the form of marking an extra animal (11% of times), or missing an animal (4% of times). Only 1% of times, Juan or Estevan mistook red for blue or made other mistake in color.

Here is what I found rather odd. No matter whether Juan or Estevan sat on the tree, different types of errors continued to accumulate at the same rate and manner day after day. I have no idea, whether that observation says anything about human nature, Mexican farmers or farms built in redwood forests around Menlo Park. I wish I had a time machine to go back to 1830s and watch those farmers.