Lunch Break

Aoi returned from studying abroad, as always, with his avatar going around in the capsule.

"Aoi! welcome back!" I ruffled Aoi’s head as usual.

"Cut it out!"

Ah, is this considered dating violence? Well, whatever.

It seems like Aoi has been completely immersed in English during his language study. When I talk with my grandmother, I speak English, so during lunch breaks, I accompany Aoi in conversation practice.

Well, the conversations mostly revolve around trams and autonomous vehicles (self-driving cars on the ground without human drivers), though.

Fourth period

This time is for mathematics. Today, we're discussing the "Collatz Conjecture" [a real thing].

The Collatz Conjecture states that for any positive integer "n":

- If "n" is even, divide it by 2.

- If "n" is odd, multiply it by 3 and add 1.

When performing these operations, no matter what initial value we start with, after a finite number of steps, we will always reach 1, and then the loop 1 → 4 → 2 → 1 will occur.

Recently, they have been using quantum computers to calculate further, but it is still unproven whether there exist integers that never reach 1 even after an extremely large number of steps. It still remains unproven.

I was once fascinated by it too, but it's futile. Once you lose interest, it just becomes tiring.

If the Collatz Conjecture is proven, it will cause a tremendous upheaval in the world.