Math Games with Bad Drawings

8 annotations • Feb 2023 – Aug 2024 • data

"All good thinking is play," writes Mason Hartman. She means that our best thoughts explore ideas the way a baby chimp explores the forest, with a kind of freedom and abandon. It's not a game of Parcheesi, with every move geared toward victory; rather, it's a game of make-believe, a game of "yes, and…," a game passed from generation to generation, a torch that never goes dark. "A finite game is played for the purpose of winning," wrote James Carse, "an infinite game for the purpose of continuing to play."

Humans are not, by nature, abstract thinkers. Quite the opposite. We are creatures of the concrete: animals who experience appetites, daydreams, and dizzy spells—sometimes all at once, if the Food Network is on. We think in particulars. That's why isomorphisms matter: They transport us from one set of particulars to another. An isomorphism is an abstract bridge between islands of experience.
James Ernest created this matchmaking game at the request of "a middle school teacher who was looking for a good interactive classroom game on the subject of love and marriage." It requires at least 15 players, and is suitable for a nerdy party or partying classroom.
All at once, you want to marry fast, marry close, and marry up. These impulses pull against each other, raising tricky questions.

There is a spooky connection between combinatorial complexity and our instinctive sense of fun. With eerie, unconscious consistency, we seek a special middle ground: puzzles whose solutions are hard to find, yet easy to appreciate once found.
Game What You're Combining The , the Better Poker Cards More Aces Scrabble Letters More Plausibly a Word Jenga Blocks More Stable Twister Limbs Fewer Displaced Internal Organs Dominos Dominos More Dominos Cards Against Humanity Offensive Tropes Less You Play This Game

This paper, in the journal Mathematics Magazine, spells out a guaranteed winning strategy (for player 2, it turns out). Yet quick and contained as the game may be, the strategy is too intricate to memorize. That's okay. Ramsey theory isn't about how to win. It's about how to design a game where ties are impossible. It's about guaranteeing that somebody wins. In Sim, specifically, we want someone to draw a triangle all in one color. How many dots does that require? Six dots suffice (for reasons we'll see later), but five do not. Sim on a pentagon might end in a tie.
In the 1950s, the Hungarian sociologist Sándor Szalai was watching groups of children. He noticed a strange pattern: Among a class of 20 or so, he could always find a group of four, all of whom were friends, or else a group of four, none of whom were friends. What explained these clusters? Why these mysterious quartets of friendship and alienation? Did it depend on the children's ages? On the specific culture of the school? On the presence of four-square courts? Then it struck Szalai. Maybe this isn't a sociological fact at all. Maybe it's a mathematical one.