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> A human can sit down to play a game with unknown rules and write a spec as he goes.

Some humans can. Many, if not most humans cannot. A significant enough fraction of humans have trouble putting together Ikea furniture that there are memes about its difficulty. You're vastly overestimating the capabilities of the average human. Working in tech puts you in probably the top ~1-5% of capability to intuit and understand rules, but it distorts your intuition of what a "reasonable" baseline for that is.

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Yes, I am aware. However an idealized human can do so. Analogously, there are plenty of humans that can't run an 8 minute mile but if your bipedal robot is physically incapable of ever doing that then it isn't reasonable to claim having achieved human level athletic performance. When it can compete in every Olympic event you can claim human level performance at athletics in general.

If the model can't generalize to arbitrary tasks on its own without any assistance then it doesn't qualify as a general intelligence. AGI to my mind means meeting or exceeding idealized human performance on the vast majority of arbitrary tasks that are cherrypicked to be particularly challenging.

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