Magia Record Fan Makes Calculator for Friendship Ending Staircase

posted on by Kim Morrissy

In episode 2 of Magia Record: Puella Magi Madoka Magica Side Story, there's a rumor going around about the Friendship Ending Staircase. When two people break off their friendship with each other, they write their names on the sixth and seventh steps of the Friendship Ending Staircase. After that point, if one person tries to make amends with the other person, they'll get abducted by the Chain Monster.

After seeing the episode, one Japanese fan by the name of Sessions has written an article about how to use the Friendship Ending Staircase as a calculator through applying a logic gate. Specifically, Sessions makes use of a NAND gate, the inverse of the AND logic gate. The NAND gate has functional completeness, which means that combinations of it can be used to produce any basic operations.

With a NAND gate, the output is always at 1 (high) and only goes to 0 (low) when all the inputs are at 1. If we consider the friends on the Friendship Ending Staircase as individual inputs, then when they've broken their friendship but still exist in the world, their respective inputs are 1. When a friend attempts to apologize to the other friend and is dragged away by the monster, their status becomes 0. From this setup, we can infer that for the Friendship Ending conditions to be met, the person being apologized to has to exist in the world.

Sessions drew out a NAND gate truth table, with "a1" and "a2" representing each friend, and "a3" representing the outcome. As you can see, both a1 and a2 have to be 1 for a3 to become 0.

The setup can also be expanded to multiple people, all ending their friendships with each other and getting abducted by monsters. If there are three people involved, and person C wants to both apologize to person A and person B, then person C will get abducted. If person C breaks their friendship with person A or person B, then person C will remain if person A or B tries to make amends with the other two.

Sessions says that you can use a NAND gates to expand the number of inputs infinitely. If we're still continuing with the Friendship Ending Staircase analogy, this would probably result in monsters materializing all the way down the street, but it can't be helped for the sake of the exercise. They also end their article with a cheeky quip: "Instead of reading this crappy article, you could watch Magia Record."

Magia Record: Puella Magi Madoka Magica Side Story debuted in Japan on January 4.

Source: Qiita

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