The prize I offer every other year to make a game in the world of the recipient’s game was chosen by Linus Åkesson, author of “The Impossible Bottle”.

As a mathematician, I’m excited to work on a game like this, and Linus’s imaginative setting provides so many fun possibilities.

And I’ve been wanting to try out new languages for a while, so I asked him if it’s okay to make this game in Dialog, so I can learn it on the way. So I’m probably going to be asking for help on that over the next two years!

I haven’t played Trinity yet. I have read about that specific puzzle though. I can’t find it right now, but was it you that wrote an essay about mathematics and paradoxes in IF? It’s not in Spike’s post-mortem of ABCA, but I remember reading a piece on mathematical problems as puzzles in IF right after I finished The Chinese Room.

The 1984 Acorn Electron game Kingdom of Klein features not only a Klein bottle but a Mobius Ravine. The ravine is laid out in a similar way to a Mobius strip, with each apparent edge being a continuation of the other. If you walk far enough along the edge you eventually emerge on the other side of the ravine.

Thanks! It may well be. From superficially skimming just now I got the impression it’s on Zeno’s paradoxes alone, but I’ve downloaded it for reading tomorrow.

I did talk some about the Klein bottle puzzle in Trinity in my postmortem on A Beauty Cold and Austere. That puzzle was one of the primary inspirations for the game.

I also wrote the essay about mathematics and paradoxes in IF that @nilsf links to. I don’t mention the Klein bottle, though; the essay’s all about Zeno’s paradoxes.

Getting back to The Impossible Bottle, I don’t believe there’s actually a Klein bottle in that game. The title refers literally to the ship-in-a-bottle that’s featured on the cover art, as well as metaphorically to the dollhouse. The former is definitely not a Klein bottle. The latter isn’t, either, although it’s similar. As @lft says in his postscriptum:

The Impossible Bottle contains explicit references to the Infocom game Trinity and its famous Klein bottle puzzle. Technically, the dollhouse isn’t a Klein bottle because it doesn’t mess with chirality (for instance by reversing east and west, which would only have given players a headache). But it has the same “impossible” property that its inside and outside are one and the same. So who built the dollhouse? Mom wrote a book about the inhabitability of self-intersecting manifolds, so I wouldn’t put it past her. Her name, Felicia Small, is of course a nod to the German mathematician in question.

Finally, if I remember correctly @mathbrush’s research area is topology (the branch of mathematics that studies properties of space, including objects like Klein bottles and manifolds). So I’m really looking forward to seeing what interesting puzzles he can create given the world of The Impossible Bottle!

Oh, I must have skimmed over it.
I read the essay on the different approaches to Zeno’s paradoxes and I thought it was really good. The way you wrote about the Bridge-paradox in Beyond Zork made me want to dive right in. (Still at least three games on my list before that though.)

Yes. That should make things interesting. (Without wanting to push you in any direction puzzlewise, mathbrush. Maybe you want to write a game about a little boy and a bottle of lemonade that’s really really high up on a shelf…)