Douglas Hofstadter claims that the process of finding an isomorphism that ends successfully brings to its discoverer great excitement and an example of such excitement is captured in "The Decipherment of Linear B" by John Chadwick. Tablets with some writing (later named Linear B) were found in the palace archives in Crete, Greece. Scholars first believed that the script on the tablets was actually two scripts and that one was representative of hieroglyphic inscriptions. Later Michael Ventris and John Chadwick have determined that the language was Mycenaean Greek. They declared: "Two generations of scholars had been cheated of the opportunity to work constructively on the problem." They have found an isomorphism ( a mapping from strings in the alphabet of one to strings inthe alphabet of the other) between Mycenean Greek and Linear B. Their experience and work are described in the book "The Decipherment of Linear B". Source:
Linear B. (n.d.). Retrieved October 6, 2014, from http://en.wikipedia.org/wiki/Linear_B
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Discovery of an isomorphism occurs mostly by chance. It requires knowledge of the parts of the two things that are later found isomorphic to each other. This discovery brings with it knowledge, awareness and meaning. Upon discovering an isomorphism, a human mind seems to understand the two structures in a different way often a deeper way and seems to be more aware of their aspects. This is because this isomorphism allows one to view, treat and think of each structure as the other. It allows the properties of one to be applicable to the other.
A decision procedure is analogous to a mathematical proof. Both must terminate by the nature of their purpose. Both let us know that a statement is true (a certain string is a theorem). Both are often a process of reasoning through steps to reach something. In a mathematical proof, the steps are mathematical operations or mathematical laws. In a decision procedure, the steps are the rules of inference. A decision procedure is merely a proof that a certain string is a theorem of a particular formal system. Vice versa, a proof is merely a decision procedure where the laws of logic substitute for the rules of inference.
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