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The epic of Glagalbagal the shepherd - Part 2
Growing his empire
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Glagalbagal hit upon a way to use just pebbles. Rather than having different types of objects, he decided to use different baskets. A pebble in the first basket would have the same meaning as a pebble in the earlier system - it would represent a single animal. A pebble in the second basket would represent the same amount of animals as a small rock had done. The third would be the same as a boulder, and the fourth the obelisk.
Outside each basket, he kept the maximum number of pebbles that the basket could take - outside the first basket were eight pebbles, outside the second were five, and outside the third were four. There were no pebbles outside the last basket since that basket didn’t have a limit - he could add in as many pebbles as required.
As each animal exited, he took a pebble from in front of the first basket and put it in the basket. When the pebbles in front of the first basket finished, he took them out and put a pebble in the second basket. He iterated on this till the pebbles in front of the second basket finished. He then took those out and put a pebble in the third basket. This continued to the fourth basket. He planned to do the opposite to count the herd back in.
Now, he could fire his team of triceratopses and replace them with a small number of highly trained velociraptors. This is the second recorded example of technological innovation resulting in a loss of jobs. The only previous example we know of was when people started cooking meat rather than eating it raw. As a result, many pharmacies, whose primary source of income came from selling diarrhea medicine, had to shut shop.
Try to relate Glagalbagal’s system to the number representation system you have learned. What are the similarities, and what are the differences?
On the first day of using the new system, Glagalbagal realized he had messed up. After counting the animals out, he had forgotten to have a way to differentiate between the different baskets. As a result, he was unable to tell which was which. If he knew what numbers were and remembered how many pebbles can go in a particular basket, he would have quickly figured it out. He would have known that eight pebbles corresponded to the first basket, five to the second, and so on. However, he couldn’t do that, and so he tried to find another solution.
How would you deal with this issue if you were Glagalbagal? What could you do to recreate the actual order of the baskets?
The only solution he could think of was very cumbersome, but he decided to go with it. He made various copies of the four baskets so that he had all possible combinations. He then counted in the sheep and cows using all of these different copies. Luckily for him, no sheep or cow had gotten lost that day, and precisely one of the copies gave the exact count. So, he had avoided a potential disaster. After that day, he had assigned spots to each of the baskets. He also put the different types of rocks he was using earlier behind their corresponding basket. That way, he would never forget which basket was which.
How many copies of the entire setup did Glagalbagal have to make, given that there were four baskets?
Things were going very well for Glagalbagal. His business was booming, and he now had the largest herd in the land. So, he decided to open a second location. He would take an overseeing role and appoint managers at each of the sites. However, he was worried that their incentives would not align with his - why would they care about growing the business since they didn’t own it? So, Glagalbagal decided to create a program to reward the managers for successfully increasing the size of the herd. But, how would he do that? How would he know whether the managers were doing a good job?
I will end this part on this cliffhanger like all other thrillers tend to do. Before reading Part 3, think about how Glagalbagal could achieve this goal. To help you out, here is a related question:
Glagalbagal’s town decided to have an election. However, they didn’t have numbers. So, they couldn’t count the number of votes each candidate received. They approached Glagalbagal to design an election system for them. They asked him to find a way in which they could tell who had more votes. Can you think of a system he could set up?