Turing Machines for Dummies; why representations do matter Peter van Emde Boas Abstract: Various methods exists in the literature for denoting the configuration of a Turing Machine. A key difference is whether the head position is indicated by some integer (mathematical representation) or is specified by writing the machine state next to the scanned tape symbol (intrinsic representation). From a mathematical perspective this will make no difference. However, since Turing Machines are primarily used for proving undecidability and/or hardness results these representations do matter. Based on a number of applications we show that the intrinsic representation should be preferred. Keywords: Turing Machine Configurations; Master reductions