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A formal system, in this case the game, is Turing complete if it can be used to implement a Turing machine. Complaining about using only a limited and very spec

A formal system, in this case the game, is Turing complete if it can be used to implement a Turing machine. Complaining about using only a limited and very specific subset of available cards in a contrived way is like saying that a computer is not a computer because a large number of transistors aren't part of it, and if I rewire it randomly it ceases to work. Regarding "unnecessary", unlike typical competitive or recreational games in which players often do what they want, this particular setup results in an automaton in which players cannot disrupt the operation of the Turing machine: "The idea of my Magic Turing machine is that the players do nothing at all, except when the game offers them a choice." The article explains that the setup only allows choices to do optional actions, and it is assumed the players always do them. As "programming" human players to simulate a Turing machine would be too easy, they are replaced by mindless placeholders. If you used humans, they could follow the rules in their head (with written reference sheets); tapes could be lines of objects belonging to an alphabet of different types (e.g. coins of different countries and denominations, Barbie dolls of different model years, wax crayons of different colours), and the machine head would move by walking in front of the next tape position. No need to involve a proper formal system like a card game.

YeGoblynQueenne 9y ago
>> The article explains that the setup only allows choices to do optional actions, and it is assumed the players always do them. As "programming" human players to simulate a Turing machine would be too easy, they are replaced by mindless placeholders. Yes, I read that bit - I didn't realise it was meant to make things "harder". That alone is good enough to convince me the proof is unnecessary. If you can make a proof easier, then you make it easier. There's no need for harder proofs. Also, the fact that the proof does not involve human actions is another piece of evidence against the generality of the proof. You can model human choices as a distribution and allow for a fully-automated proof, that doesn't require human input in the strict sense. But leaving human actions out of the proof makes it less general- because the full game does involve such actions.

YeGoblynQueenne 9y ago

>> The article explains that the setup only allows choices to do optional actions, and it is assumed the players always do them. As "programming" human players to simulate a Turing machine would be too easy, they are replaced by mindless placeholders. Yes, I read that bit - I didn't realise it was meant to make things "harder". That alone is good enough to convince me the proof is unnecessary. If you can make a proof easier, then you make it easier. There's no need for harder proofs. Also, the fact that the proof does not involve human actions is another piece of evidence against the generality of the proof. You can model human choices as a distribution and allow for a fully-automated proof, that doesn't require human input in the strict sense. But leaving human actions out of the proof makes it less general- because the full game does involve such actions.