@StephanKolassa I thought Diaconis proved something sort of that a decade ago, although again I haven't seen it. But it is hell of a group of scientists. Seems interesting.

Indeed they have used the hierarchical model to capture the human-coin dependency.

This is the umpteenth number of post on likelihood interpretation based on some questionable cringy video by some guy. At some point, I wish I could mark every new such post as duplicate of already well answered posts of the past. Coincidentally, it is muchOP's second post on likelihood and it seems the previous one couldn't help them much:

@whuber One can't. ChatGPT doesn't mean anything it says - because meaning something requires links between the words you use & things out there in the world. Such links were forged for the authors of the corpus on which ChatGPT was trained as they learnt their first language ('Apple!', says Mummy, pointing at an apple both her & Baby can see), but not for ChatGPT itself.

Of course we're happy to accept the ability to engage in a coherent conversation as sufficient evidence of 'semantic understanding' in a human; & reasonably enough, given what we know about humans. But in other cases we oughtn't to be deprived of the chance to test communication in & about a common environment: this is where the Turing Test falls short.

@Scortchi-ReinstateMonica You raise the question about what "things out there in the world" refer to. Ultimately, for humans, information about all such things is provided by our senses, language, or how our brains are wired. We have no more right to appeal to some such "reality" than ChatGPT does.

In fact, I believe that far sooner than anyone expects, people will be attaching myriad sensory devices to GPT-like models to provide them the kind of sensory stimulation we have used to learn how to be in the world--only their inputs will be far more varied and richer than ours ever could be.