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Juan Antonio

@nokyotsu.me

140 followers 430 following 39 posts

Geek de las matemáticas convertido en científico de cómputo—un entusiasta por la divulgación de la ciencia, la filosofía, el humanismo, y cosas … sobre todo cosas.

https://nokyotsu.com/me/es/

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Juan Antonio

@nokyotsu.me

I was thinking about magic squares of squares (infamously hard to find) and wondered whether, as a stepping stone, modular arithmetic could help. I threw in some "terrible python code" and soon I was finding plenty of them! Here is a fun one where the modulo and the total sum are also squares!

A magic square of squares with the numbers [[27^2, 20^2, 3^2], [57^2, 58^2, 60^2], [8^2, 6^2, 42^2]] where (modulo 11^2) all the rows, columns, and diagonals sum each to 7^2.

February 16, 2025 at 2:40 PM

Juan Antonio

@nokyotsu.me

By working together, the earliest humans were increasingly able to overcome the challenges that nature threw at them: food scarcity, water shortages, dangerous predators. But as a consequence, other humans became our primary threat. We were no longer battling against nature, but against each other.

Cooperation is, at heart, a means by which entities improve their own position in the world. In other words, cooperation is favoured if and when it offers a better way to compete. A corollary of this is that cooperation frequently has victims.

January 20, 2025 at 7:41 PM

Juan Antonio

@nokyotsu.me

Sometimes a male orb-weaving spider manages to force a copulation with a juvenile female, inserting both of his palps into the female's separate sperm- storage organs. If the male succeeds, something strange happens to him: his heart spontaneously stops beating and he dies in flagrante.

Ancestral Homo may have looked much like you or I, but to the sabre-toothed cats and gigantic lions that prowled the savannah, I suspect that our human relatives probably looked a lot like lunch.

A dominant male chimp rules by force. Dominance is taken and imposed upon others, against their will. But ancestral humans did things differently. In a world where anyone could hurl a stone or strike a spear from afar, brawn was no longer a viable means to wield authority. The mutiny had begun.

January 20, 2025 at 7:41 PM

Juan Antonio

@nokyotsu.me

📚 I've recently finished “The Social Instinct” by @nicholaraihani.bsky.social. It was a wonderful and thought provoking book, on how cooperation evolved in nature, and how crucial it is for our survival.

💡 Anyway, here a few of my favourite quotes from the book. What do you think of them?

The largest collective on Earth is a single international super-colony, spanning countries and continents, of a species called the Argentine ant. Although relations between members of the same super-colony are friendly, competition between ants from different families is ferocious.

When the spiderlings of a black-lace spider mother hatch, she provides a meal of unfertilised eggs for them to eat and, a few days later, actively encourages them to devour her alive.

It has become modish to assert that female-biased care is culturally entrenched, rather than biologically influenced, but a cursory look at our neighbours on the tree of life shows that we cannot lay all the blame for a mother's work never being done at the feet of the patriarchy.

January 20, 2025 at 7:41 PM

Juan Antonio

@nokyotsu.me

... and rearranged as a sum of cubes!

A sum of cubes 1^3 + 2^3 + ... + 9^3 = (1 + 2 + ... + 9)^2 = 45^2 = 2025.

January 6, 2025 at 10:45 AM

Juan Antonio

@nokyotsu.me

Most interestingly, the square of a triangle number can always be broken up groups, ...

A square where each side is made of (1 + 2 + ... + 9) units. Therefore, the square has 45^2 = 2025 units total.

January 6, 2025 at 10:45 AM

Juan Antonio

@nokyotsu.me

Calculating the sum of numbers from 1 to 9 is easy. If you duplicate the triangle, you obtain a 9 x 10 rectangle. So the sum must be (9 x 10) / 2 = 45.