Home Origin of the Theory of Measure (Family Friendly Edition)

Origin of the Theory of Measure (Family Friendly Edition)

Once upon a time there was an Amazonian tribe with an interesting tradition. Every person plant cucumbers and each year they would measure the length of their longest cucumber. The person with the longest cucumber will be named the Cucum Superior. They use a hand-me-down measuring stick that has endured over many generations. They would describe the length of cucumbers in terms of the length of the rod. For example, Alice has a cucumber of length 3 times that rod, while Bob has a cucumber of length one tenth of that rod. The tribe simply calls it ‘the Rod’.

One year, there came a young boy travelling from another tribe who also wanted to participale in this tradition. When he brought out his cucumber, everyone was shocked. The tribe scribe left such a wonderful and detailed description for us:

The fruit of his labour can only be described as a process. Suppose you take the Rod and remove the middle third. You are left with two segments with length one third separated by the space with length a third of the Rod. Repeat this process, and you will obtain 4 segments of length one nineth with separations one ninth, one third and one ninth. Repeat this process until the earth shatters and sun dims. Only then can you see the true magnificence of his cucumber.

They did not know how to measure the length of his cucumber. Some said it’s one Rod, since the distance between the base point and the tip of the cucumber stays the same and these two points are invariant under the process. Some said it obvious can’t be one since we can’t see his cucumber from the top or side but only the front, so it should be 0. Some said since his cucumber is so finely divided, the length must be huge. This started a blood feud between the three factions since the cucumber measuring festival is a sacred event and those who insist on a different opinion is committing blasphemy.

Families were separated, friendships were broken, etc etc. They lived in segregated parts of the village and encounters between them often ended in death. The young boy ran away from the bloodbath back to his own village.

It was a middle-aged mother who went to the shore to catch some fish who first saw the giant ship. It was of a glorious build, so glorious that the people who built it must all be Cucum Superior. It bore a large yellow flag with a weird snake-like thing with feet and scales that is looking at a red sun. Soon after she reported this sighting, a man visited the tribe.

He was a strange man who had a foreign appearance. He quickly learned the tongue of the tribe and was delighted to hear about their interesting predicament. The tribe started calling him Shaman Grody due to his knowledge of natural philosophy. From his sack he pulled out a very large book in yellow and white and started flipping the pages. He and the scribe worked together to translate the contents.

The completed transcription was distributed to every man and woman, who learned the contents within. Some moons after, the foreigner gathered the whole tribe no matter their stance on the cucumber. He started lecturing and two thirds of the tribe was soon balling on the ground for they have sinned. The length of the cucumber was indeed 0. Families were united, friendships were remade, etc etc. Everyone lived happily ever after.

This post is licensed under CC BY 4.0 by the author.
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