July 24, 2026
Infinite beans, finite patience
The road to epsilon-zero: Nim always ends, even with infinite ordinals
Readers thought this was about a coding language, then got dragged into infinity-brain chaos
TLDR: The article says a strange version of Nim can feel endless but still always finishes, even when players can make piles huge again. Commenters were split between joking that "Nim" meant the programming language and marveling at how fast a simple game turns into brain-bending infinity talk.
A math post about the bean-taking game Nim somehow turned into a full-on "wait, what did I just read?" moment in the comments. The big claim is wild but simple at heart: even when the game includes weird "infinite" tokens that let players reset a pile and keep the action going, the game still must end eventually. You may not know when it ends, or even when you'll know when it ends, but there is still a finish line. That alone was enough to send readers spiraling into equal parts fascination and confusion.
The funniest reaction came instantly: one commenter admitted they saw "Nim" and assumed this was about the Nim programming language, which is exactly the kind of bait-and-switch the internet lives for. Others leaned into the deeper rabbit hole, warning that once you start using these strange number ideas to talk about ordinary counting, things get absurdly deep, absurdly fast. A commenter even dropped a YouTube rabbit hole about gigantic numbers, basically saying: if your brain isn't melted yet, just wait.
And then there was the painfully relatable side plot: the programmer who couldn't estimate a fix, but could estimate when he'd be able to estimate it. Readers didn't need a PhD for that one — they just needed a job. The community mood was a mix of nerdy awe, comedy, and "this is the most accurate description of software work I've ever seen."
Key Points
- •The article analyzes a Nim variant in which green tokens allow a player to remove tokens and then add any finite number of beans to a pile.
- •In standard finite Nim, the game length is bounded by the total number of beans because each move removes at least one bean.
- •With a pile of size ω, no fixed total move bound can be stated in advance, but after one move the token is gone and the remaining game becomes finitely bounded.
- •With ω², the author says the total length still cannot be predetermined, but within two moves all green tokens can be reduced to a finite-bean position from which a bound is possible.
- •A programming-estimation anecdote is used to illustrate nested knowledge about when an estimate of completion can itself be estimated.