The epic of Glagalbagal the shepherd - Part 1
Glagalbagal was a very intelligent shepherd who lived thousands of years ago - when dinosaurs and humans roamed the world together. He had a herd of sheep and cows and had enclosed them in a fenced-off area. During the day, he would let them out to graze, and his sheep-dinosaur, Blortz, would herd them back in the evening. After a while, he realized that something was going wrong.
The herd seemed a lot smaller than it used to be. Blortz insisted that there was no change in the size of the herd. However, Glagalbagal was suspicious. Due to his bad knee, he was unable to follow the herd around all day. So, he tried to think of a way to keep track of what was going on. Unlike most people today, Glagalbagal did not know about numbers. So, he couldn’t count the sheep and cows. What else could he do?
Assuming you were in Glagalbagal’s position, how would you know whether every animal that leaves the enclosed area returns after grazing? Remember that you cannot count them. Spend some time thinking about this before reading on. The solution is not obvious, so don’t worry if you can’t think of something.
Glagalbagal hit upon a very simple but ingenious solution. He gathered up a large number of pebbles in a box. Then, as each animal left the enclosure in the morning, he took a pebble from the box and dropped it into a basket. When they came back in the evening, he took a pebble out of the basket for each animal. If there were no pebbles left, that would mean that all the animals who had left had also returned.
At the end of the week, a number of the sheep and cows had not returned. So he hired a velociraptor to spy on the herd. In just a few days of hiding behind bushes, the velociraptor confirmed that Blortz had been snacking while on duty.
Glagalbagal confronted Blortz, who confessed and apologized. Blortz had been with him for many years. So, Glagalbagal forgave him. However, he decided to continue keeping track of the herd’s entry and exit from the enclosure.
Glagalbagal’s fortunes changed after that day. Owing to his strict accounting, he barely lost any animals. Soon, he had the largest herd in all the land. As a result, he had to collect lots and lots of pebbles, and the entire exercise got very cumbersome. So he decided that he needed something better.
Can you think of something better so that Glagalbagal would not need to use individual pebbles for each animal? Once again, remember that you cannot use numbers to count. Spend a little bit of time trying to think of a solution or just read on.
Once again, Glagalbagal thought of something. He picked up a few pebbles from the box and put them to the side. While he did not have a name for this, I can tell you that he had picked up eight pebbles.
When an animal exited the enclosure, he would take a pebble from the eight and put it in the basket. Then, when all eight were finished, he would take a small rock and put it in a bowl. Then, he would take the eight pebbles out of the basket and start again. Finally, when all the sheep and cows had left, some of the eight pebbles would be in the basket, and the rest would be by his side.
When the animals returned, Glagalbagal would start the entry check with the pebbles remaining in the basket at the end of the exit check. He would take out a pebble from the basket for each animal. When all eight pebbles were out of the basket, he would take a rock out of the bowl. Then he would put all eight of the pebbles back in the basket. He would repeat this till the rocks ran out. If all the animals returned, there would be no rock in the bowl, and all the pebbles would be outside the basket. This way, rather than having large numbers of pebbles, he could make do with just eight pebbles and a few rocks.
This accounting system for his herd was so highly efficient that Glagalbagal’s shepherding business grew and grew. Soon, he added boulders which were the same as five small rocks (not that he knew what five was), and eventually, he added obelisks, each of which was the same as four boulders.
This resulted in him having to hire staff since there was no way he could lift obelisks. He hired ten triceratopses. However, while they were hard-working and strong, they were not very intelligent. They kept messing up the accounting, and a lot of the herd was lost. So, Glagalbagal decided that he needed to do away with them and also with the impossibly heavy rocks.
He first thought about going back to using only pebbles but making them different colors to play the roles of the rocks, boulders, and obelisks. Then he remembered that, just like in old movies, the only colors which existed at the time were black and white. It would be years before yellow was invented. So, he sat and thought about other ways he could go back to using just pebbles.
Think of other ways Glagalbagal could make do with using just pebbles. The epic of Glagalbagal is far from complete, and I will pick it up from here in Part 2.
(Steven Strogatz’ book The Joy of X discusses something similar to the ideas in this series, and I highly recommend it)