Wednesday, September 12, 2012

Magic: the Gathering Is Turing Complete

It gets better! Because the behavior of the underlying hardware in a Turing machine is considered axiomatic and unfailing, the following M:tG CR sections:

104.4b If a game that?s not using the limited range of influence option (including a two-player game) somehow enters a ?loop? of mandatory actions, repeating a sequence of events with no way to stop, the game is a draw. Loops that contain an optional action don?t result in a draw.
716.1b Occasionally the game gets into a state in which a set of actions could be repeated indefinitely (thus creating a ?loop?). In that case, the shortcut rules can be used to determine how many times those actions are repeated without having to actually perform them, and how the loop is broken.
716.3 Sometimes a loop can be fragmented, meaning that each player involved in the loop performs an independent action that results in the same game state being reached multiple times. If that happens, the active player (or, if the active player is not involved in the loop, the first player in turn order who is involved) must then make a different game choice so the loop does not continue.

mean that this M:tG Turing machine solves the halting problem! The consequences of the fact that, without the halting problem, a Turing machine would never have been described are left as an exercise for the reader.

Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/ByAvkw4_O48/magic-the-gathering-is-turing-complete

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