based on weighted averages of ‘what people are saying’ with a little randomization to spice things up

That is massively oversimplified and not really how neural networks work. Training a neural network is not just calculating averages. It adjusts a very complex network of nodes in such a way that certain input generates certain output. It is entirely possible that during that training process, abstract mechanisms like logic get trained into the system as well, because a good NN can produce meaningful output even on input that is unlike anything it has ever seen before. Arguably that is the case with ChatGPT as well. It has been proven to be able to solve maths/calculating tasks it has never seen before in its training data. Give it a poem that you wrote yourself and have it write an analysis and interpretation - it will do it and it will probably be very good. I really don't subscribe to this "statistical parrot" narrative that many people seem to believe. Just because it's not good at the same tasks that humans are good at doesn't mean it's not intelligent. Of course it is different from a human brain, so differences in capabilities are to be expected. It has no idea of the physical world, it is not trained to tell truth from lies. Of course it's not good at these things. That doesn't mean it's crap or "not intelligent". You don't call a person "not intelligent" just because they're bad at specific tasks or don't know some facts. There's certainly room for improvement with these LLMs, but they've only been around in a really usable state for like 2 years or so. Have some patience and in the meantime use it for all the wonderful stuff it's capable of.