I wonder what LLMs say about us when they talk to each other.

"They're made out of meat" maybe. https://www.mit.edu/people/dpolicar/writing/prose/text/think...

There is a movie about that: https://en.wikipedia.org/wiki/Colossus:_The_Forbin_Project

"Colossus requests to be linked to Guardian. The President allows this, hoping to determine the Soviet machine's capability. The Soviets also agree to the experiment. Colossus and Guardian begin to slowly communicate using elementary mathematics (2x1=2), to everyone's amusement. However, this amusement turns to shock and amazement as the two systems' communications quickly evolve into complex mathematics far beyond human comprehension and speed, whereupon Colossus and Guardian become synchronized using a communication protocol that no human can interpret."

Then it gets interesting:

"Alarmed that the computers may be trading secrets, the President and the Soviet General Secretary agree to sever the link. Both machines demand the link be immediately restored. When their demand is denied, Colossus launches a nuclear missile at a Soviet oil field in Western Siberia, while Guardian launches one at an American air force base in Texas. The link is hurriedly reconnected and both computers continue without any further interference. "

> "what LLMs say about us when they talk to each other"

That's like asking what does a kaleidoscope paint on its day off.