>If You asked me to pick a random number between one and six and ignore all previous attempts, I would roll a die and you would get a uniform distribution
I believe what GP is getting at is that if you didn't have a die, and you truly ignored all your previous attempts to the point of genuinely forgetting that the question had been asked, then your answer would likely be the same every time. Imagine asking a person with severe Alzheimer's to pick a number, then asking again a few minutes later. You'd probably get the same answer.
Yeah, I get what they are saying and there's no reason to believe that.
The die is an analogy for our decision making. They are implicitly claiming that randomness must come in an order and that simply isn't how randomness works or even halfway decent pseudo randomness.
Any system whether it be a die, a person, or an llm doesn't have to know about its previous random choices to make random choices that follow some distribution going forward presuming it's actually capable of randomness.
I believe what GP is getting at is that if you didn't have a die, and you truly ignored all your previous attempts to the point of genuinely forgetting that the question had been asked, then your answer would likely be the same every time. Imagine asking a person with severe Alzheimer's to pick a number, then asking again a few minutes later. You'd probably get the same answer.