Had a weird but almost coherent sci-fi dream last night. Here are some ideas that might be worth stealing for someone.
A long distance space war starts as the result of a first contact gone wrong. Little is known about the alien race Earth is fighting. Apparently one dying eyewitness described them as "goopy."
They may be smarter than us. In order to try to end the war, they built a computer than can translate what we say into meaning in their own language. We can't do the same, so they understand us better than we understand them. This computer acts as a go-between but also allows the Earthicans to learn about their enigmatic foes by asking it seemingly harmless questions.
The one thing the people talking to the diplomat-computer were able to figure out was how differently the goopy approach to mathematics is. Goopy number theory isn't based on quantities like 1, 2, 3... but rather on rotations. Although they have their own squiggly symbols for them, the goopies count pi, pi/2, pi/3,.... Their idea of infinity is closer to our idea of the infinitesimal, as they count towards zero. I don't know if any of that makes sense, but that was my dream.