Magic is just as Turing complete as a Turing machine is. Magic is an abstract system, not pieces of cardboard. Just like a Turing machine is an abstract idea rather than a physical box. You can run the logic of a magic game using circuits, or gears, or humans, but it's fundamentally based on taking a set of rules and implementing them. The reason pen and paper is different is that a pen is not a rule-based system, it's merely an object. Same for an abacus.
I believe you have misunderstood what I have said. My issue with Magic was not with the logic specifically. It is with the fact that it requires the player to initiate state transition by specifically selecting actions. It would be permissible if the player simply functioned as a clock, but some of the state transition logic is actually shifted over to the player. It certainly is better than the pen and paper scenario, but the rule system is incomplete. It still requires a couple of rules for the player to follow (just as pen/paper or an abacus does).
The author mentions this problem explicitly on the "Difficulties" section of the site. It is very important to note this. The hope is for the effects of some cards to allow for the necessary computational depth to capture all of computation without additional human action (besides, lets say, initialization). People often look at Turing Machines and their components. They forget to think about state transitions and the recursion involved (recursion really is the "meat" of computation).
I really thought that all human-initiated action had been removed from the Magic machine. Oops. It's been a while since I read the complete writeup. But it looks like it should be possible to fix this.
I think it would be possible given new cards, but I imagine it would be incredibly difficult (not to mention game breaking). It would basically require cards that would handle arbitrary branching (algorithmically determined). A set of cards would have to contain effects that form a general template for doing this based on cards in a implementation of memory. I personally think it is unlikely and would be tricky to pull off. I admittedly don't have a very concrete reason for this.
What I find really cool is that, while they might not add a set of cards allowing for arbitrary branching, they could introduce cards that allow for some bounded branching. This could add limitations of resource bounds that are still scalable: polynomial time, space, exponential time, primitive recursion. There seems to be a lot more flexibility here than with some other mentioned "Turing-Complete" systems.
Someone else, here, commented that you would also need to implement infinite loops. Assuming you don't have to fuel the machine with cards, this method could be used to stall a real game indefinitely! Apparently this is possible. O_O
I'm a unsure what you're trying to say here. Are you talking about having a situation where the Turing machine resolves without any physical signs of execution? I don't see what's wrong with the current method of using tokens as a tape and infinite triggers based on those tokens until a halt state is reached. It just needs a bit of refinement on the triggers.
Just like a theoretical Turing machine doesn't require a human to feed it with a strip of tape, a theoretical Magic-Turing machine doesn't require a human to feed it with tokens and damage markers.
And game-breaking infinite loops in Magic are dime a dozen. Did you know that there's a combo that allows you to rip every card in your opponent's deck into confetti? (Unless they forfeit.)
Sorry if I entirely missed the point of what you were saying.
I didn't know there were that many infinite loops in Magic (I don't happen to play it). Could you link something describing the hilarious confetti combo?
I must have not been clear and concise. I apologize for this.
I was discussing the scenario where we introduce a set of cards that allow for an arbitrary number of triggers without human involvement. We clearly need to implement a way of handling nested loops, branching, and recursive calls. So the set of cards facilitating this need to either need to do this completely by themselves or construct the behavior given the state of the playing field. I did not assume we can do what is described in the paper (the site) because I have no reason to think the new cards must function in a way that is compatible with their setup. This is why I am interested in the possibility of implicit and bounded recursion.
The fuel comment was just relevant to implementing an infinite loop in a real game. If our supposed 100% autonomous system (with the new cards as mentioned above) relied on an additional resource (such as burning through cards each "tick"), then this wouldn't work in real life but would work if we generalized the size of the deck or available cards. This is not supposed to be a characteristic of Turing Machines in general (or at all). It was just a precaution for attempting to translate an instance of the generalized case to real life.
My question is what you mean by 'human involvement'. For example: if there is a card that says to add a specific token to a specific place, with no choices, does everything that happens after the card is triggered count as human involvement? Or if the card says to shuffle the library, does the shuffling count as human involvement?
If your answer is no, then I think the current cards are already sufficient, it just needs some clever finagling to take the current design and remove all 'may' choices.
If your answer is yes then I think your standards are flawed.
>Could you link something describing the hilarious confetti combo?
The answer is no. My standard mainly focuses on preventing the player from making choices after the "machine" executes. Choices here include instructions for the player from the spec about how to handle certain situations. As the author describes it, we would want the entire execution of the machine to act autonomously without choices. I guess it may be permissible to let the player choose not to act, but the idea is to not sneak any of the machines logic to the player.
As for whether or not the current cards suffice, I can't say much (I don't care about Magic tbh). It just speculation as far as I can tell. I was not presuming that new cards are necessary. I just considered it for the sake of the hypothetical.
