> human language is only possible in beings capable of producing an infinite set of meaningful outputs in response to a finite input. > And so far, that list includes only two definite members: Homo sapiens sapiens, and computer programs built upon large language models.

In LLMs that's a bounded infinity though, the models themselves have only so many bits and the activations are also limited. Once you reach the same state twice the model is looping and it won't break out of that loop. I've seen such loops across tens of thousands of tokens so I'm not sure to what degree the infinite output rule holds true. It would be an interesting experiment to try to figure out to what extent the 'busy beaver' can be kept busy before it degenerates to looping or nonsense.